Elkies (2006)
y2 + xy = x3 - 1086750289534747727483801311783198679020964x + 435973165715323898311705750809969552813996511661336976727731984 Torsion points: O, [608652855284830069192, -304326427642415034596], [765575145621101788360, 7258912294053670714797672847132], [765575145621101788360, -7258912294819245860418774635492] Independent points of infinite order: P1 = [667212090873280716424, 2811468741600154868659805081692] P2 = [588300445738899279592, 496738531576486238655704034844] P3 = [640878480652690741030, 1650227478438617514410537429218] P4 = [594914072761535795656, 61252759091705020914823536412] P5 = [638462258521963853092, 1543723151978346502319214760144] P6 = [611110705367872899304, 267524019061985430016982751484] P7 = [594950966257051623880, 53222697163458916334270893852] P8 = [716616869926847885656, 5020041299716878281470542342412] P9 = [627762722675286133960, 1069751374718071593281800264732] P10 = [510340803979604535780, 3778525680405340851280110580752] P11 = [617601639147843518920, 606053623188294616739131272988] P12 = [610092172393399908808, 198061390862962920112854267676]
Dujella - Peral (2014)
y2 + xy + y = x3 + x2 - 204436185783252342785934887233210383183371840x + 1165977772244037776901948451219544033496456897571880326934385121505 Torsion points: O, [8321256469951156635413, 202492403819802069202802590388693], [8321256469951156635413, -202492403828123325672753747024107], [-16576367231130988793387, 8288183615565494396693] Independent points of infinite order: P1 = [978748421021154077677013, 968189872097011478431309250996630293] P2 = [40938350455374318726499411487/734449, 8034798036372727657292256069809358560313049/629422793] P3 = [-1833858234229021806425707334957/129823236, -1643957467127684520633723817507798298370057463/1479205950984] P4 = [466652543424944830571020577/104329, 19679459405477726600184522257021115789031/33698267] P5 = [1855357476468407776750099333857/9048064, 2521230557158903421620671041761650894499866191/27216576512] P6 = [-3057825789598843317991399927/474721, -486854952876376400114202289959672893443583/327082769] P7 = [1316165334856113211967439783713/19351201, 1479078000627128774872361508989894420231052407/85125933199] P8 = [1813152158641149066379817305273/226532601, 702396508269043497895380089462203516064428283/3409542177651] P9 = [14504830996189006898486130877/4313929, 6440066697804847094677254799511744033478569/8960030533] P10 = [5609636083108794972298867953144693/459099749761, 218252275733512453971818858150694480104231578525237/311071758345811009] P11 = [-4174731052256571796429970002572787/492999175321, -523817741681937590070885889786485498002950586908993/346153947960711619] P12 = [6380415804693738957573514663666885797/274098255263569, 13629281585957393563736821264699724609670040970930713421/4537946867595440433497]
Elkies (2005)
y2 + xy + y = x3 + x2 - 10920091632464590365831264648975539x + 437651494057993449247068775775947593191303103178481 Torsion points: O, [63258054081367075, -31629027040683538], [96192118300939107, -16651818918278859993549458], [96192118300939107, 16651818822086741692610350] Independent points of infinite order: P1 = [12312962916337123, 17465954517603234702423470] P2 = [67285511500842939, 2740790813470355147146630] P3 = [45984212347729443, 5721494183071967029585390] P4 = [63658075732213475, 681407101617676553902702] P5 = [57081828073673891, 551746937417282363027054] P6 = [46468625331642675, 5527304026709760117608782] P7 = [113108473177593891, 25486327153555762916111854] P8 = [-8906302459944157, 23112824697957639230384366] P9 = [63489682889990683, 511303164918466268499686] P10 = [-3704626064653973325/49, 9888282977010465021877712866/343] P11 = [1685476156824117371/25, 350691194569447786722914054/125]
Eroshkin (2010)
y2 + xy = x3 - 615411322294732283803288785027250860840x + 5538719221187391635372324416383813743465156669756429313600 Torsion points: O, [33031894622115968880, -145780032072398118828250407240], [17040500771125811280, -8520250385562905640], [33031894622115968880, 145780032039366224206134438360] Independent points of infinite order: P1 = [18053404313496660780, 17678035935154218667942954860] P2 = [18328783455961838160, 20406585717086330830203665880] P3 = [29608841568563327280, 115215822286141843190344794360] P4 = [17294778830561783280, 8267224166145000557315682360] P5 = [17083804568307863280, 3342124281341824097293734360] P6 = [86478894245983532880, 773989414331611579789717868760] P7 = [22441632017274878280, 55046282104980150351733662360] P8 = [20595174804919271760, 39998625478512888593836472280] P9 = [17624343157730840832, 12920054428777609733507610072] P10 = [19406810773483363440, 30076980385559785010892114360] P11 = [21533376366441332972880, 3159860490394902449468489594828760]
Dujella - Peral (2014)
y2 = x3 -x2 - 28988736544619415368095370719165120x + 2092184664137813418988486724511221531954993872509532 Torsion points: O, [-198780831808763131, 0], [100472774249930694, -13923227690347515187963700], [100472774249930694, 13923227690347515187963700] Independent points of infinite order: P1 = [-89000242786181962, 62985827654559137516454420] P2 = [321430220667349174, 161194476035051426899197420] P3 = [378022639686402069, 212493865987873070406505700] P4 = [-566101963637165587/4, 463734408645541734832665303/8] P5 = [6573279977227087494, 16847251581507446314932887500] P6 = [548360548631527693/4, 210833999252583711856628007/8] P7 = [-168526343253234959/9, 1384243803975672042355038790/27] P8 = [-445046372896160167427/24964, 201249458022639301328770506615903/3944312] P9 = [118837756467477323337/961, 594649308054850367972835623386/29791] P10 = [934144748087810038, 888916130445674287868810220] P11 = [61137597239000642222229/3818116, 301403386312262003154014958582327325/7460598664]
Khoshnam - Moody (2016)
y2 + xy = x3 - 83598958924587909464854346830766301770x + 294558475635028689022196236625520239031964650641823108900 Torsion points: O, [5280266705656745140, -594924624464385582083718170], [5280266705656745140, 594924619184118876426973030], [-10559122671197498060, 5279561335598749030, 2] Independent points of infinite order: P1 = [-376658071791198860, -18055283474071165325696694170] P2 = [5126975891755967860, 845996987662141966273374310] P3 = [3061243374503166190, 8205441734919964615103472280] P4 = [1941917047927221472, 11812674654292737888137594566] P5 = [620417310829718740, 15586245343508460341818496230] P6 = [5301357312000892480, 601609041349147923620788090] P7 = [2881859166491031610, 8807508921706068412899766810] P8 = [4170532698807427752, 4294856170447441908261060786] P9 = [-3328999758526185560, -23150952839357719761727450970] P10 = [5122395271209196780, 858924728430079776471759430] P11 = [860309498550198580, 14942363941257491522837379430]
Khoshnam - Moody (2016)
y2 + xy + y = x3 - x2 - 6733405851080577415475454221932585499304047x + 4800325455798548390824144090920449266363788590480449836501600119 Torsion points: O, [-466406396651267428173, 88540213093604830382637677042086], [-466406396651267428173, -88540213093138423985986409613914], [2111993798863171867827, -1055996899431585933914] Independent points of infinite order: P1 = [612431631770882567827, 30104501132478688536678946066086] P2 = [711816938318439197427, 19184340278585521798388646194086] P3 = [4268560138861462087827, 232021827986848369563432827666086] P4 = [556272770601756280827, 35026387726633526512811324981086] P5 = [784176974198665091227, 1536340416191398554476259698086] P6 = [2116726688248123095327, 5622008589229975369763987328586] P7 = [-405612554541403539147, -86398769666485987658728130570312] P8 = [342432162195579242827, 50346243685237300680925648066086] P9 = [-1130345153944969017873, -104724297772201699033993373444714] P10 = [272850750430950673227, 54620725748904290293131623468686] P11 = [2121357868214022354099, 7925283056603117101549058856358]
Voznyy (2022)
y2 + xy = x3 - 16807300719676114741159074415663219985838088x + 26485415853243610398964585891912523713720572243019985442333257792 Torsion points: O, [2437698274691638852112, -1218849137345819426056], [1427837930075778859472, -73472973105340461896652285110536], [1427837930075778859472, 73472973103912623966576506251064] Independent points of infinite order: P1 = [-4648750166642176469488, -64457619026540953139403339016456] P2 = [-12115098394194783933440752/2809, -20384006038466890959973684924992509672/148877] P3 = [-1194118111020657194453668/361, -1469300806972833957609372980866396204/6859] P4 = [999593655487329402954896/361, 235280644078336487820336635919191720/6859] P5 = [1409600760387461937270032/361, 979468891631966955668511059152061096/6859] P6 = [478582565391696627582033408992/1394761, 331058278112161405758201104956985444966926024/1647212741] P7 = [9510453474341142722298752/3721, 3399671379801898296092421848764945064/226981] P8 = [828049328228405852971088/361, 9036721387786914249620879466468200/6859] P9 = [134886982654478699683088/49, 11265432007040524997481242473003592/343] P10 = [-2150008162113382697670774208/896809, -195518725900403925824370295148530122681944/849278123] P11 = [5637427309363026547802095877648/1043483809, 10299726730852441124845858900570149562430126728/33707657482127]
Voznyy (2022)
y2 + xy + y = x3 - x2 - 65307967645295697830427336722134356346912165902774467x + 6776556666061653734253097820671526771886795499021732626074384890594739542801859 Torsion points: O, [-296874251695587001057277733, 148437125847793500528638866], [149326371695000079245646267, 595053608798268266824311379377910514866], [149326371695000079245646267, -595053608798417593196006379457156161134] Independent points of infinite order: P1 = [-15858125931733047129277733, -2794321140690579614070730086127367361134] P2 = [-137721076403273141509223220953/841, -88205278284985986104851460440149576681607126/24389] P3 = [132493098645274713591385167, 670478429717454516206588749899851768866] P4 = [151781528101766785431202267, 600583524471246770486322606417900158866] P5 = [132150505971881036148502267, 673735793559147712567660276621042858866] P6 = [-20147734915775975389991823, -2843270245932917435036374570949344156034] P7 = [-258531502760718766083286726413/961, -65781715872798720159313938318819640124167994/29791] P8 = [-174039969799769690972196877413/961, -106016438030311386542660255514033087028486994/29791] P9 = [-4572719815037198399046212324661/96721, -93966312621561315228779896785261471579368287042/30080231] P10 = [188979135046311233404995893294931/316969, 2392668038443781649937777079532998595697142560454/178453547] P11 = [111517697825424830105842722979795587/1051640041, 34839344810465509114833153533834318500751625590630474/34103634889589]
Voznyy (2022)
y2 + xy + y = x3 - 25608438138583363750453644220110015973x + 48850271826555999667034974046685502042020878022915152756 Torsion points: O, [13031852518377921639/4, -13031852518377921643/8], [761058421198939795, -5459081142391210440927616048], [761058421198939795, 5459081141630152019728676252] Independent points of infinite order: P1 = [3714957595181452035, 2232891675453869424154155112] P2 = [52942253926750485753565/9409, 8310030562840609480525630480819646/912673] P3 = [-1345845383538959330, -8993194126322818500991676173] P4 = [136594593573114679885/169, 11765792953857756289686076177004/2197] P5 = [33525830666154009430/9, 61255029266872647391477837154/27] P6 = [-3412633787657997006074/961, -290378335563937316532841984514086/29791] P7 = [5734295604847363066128340/2313441, 2734109536714773679614687066086811472/3518743761] P8 = [26073998596261383583015/15876, 6701149472546673454267582436523907/2000376] P9 = [4835510255543659655290/841, 233536810144194765033662425506703/24389] P10 = [488738899328903792325838/205209, 108772538266988726031103049829145046/92959677] P11 = [4361448006818835011738153245/2690185689, 475106929099042848174688263019971056373626/139531861131363]
Voznyy (2022)
y2 + xy + y = x3 - x2 - 253117693608320317481471859070333603713560604347x + 48928612825281236145946031275063726668034883245591529738101538876498219 Torsion points: O, [300388533188292313369803, -150194266594146156684902], [432986116140324513506427, -143202981047792723394031543079137814], [432986116140324513506427, 143202981047359737277891218565631386] Independent points of infinite order: P1 = [3031870403766188323366827, 5210679739323119541483463355308626586] P2 = [131556884977737904418296803/484, 154357129144781894581999707280826301583/10648] P3 = [-43170655160157055133709634797/162409, -20429594220499370407107247991244769891025378/65450827] P4 = [248971093945011165587659, 36640097734088184644611355826883482] P5 = [252818540261333556288210819/841, 49120367480159889483654947157194016098/24389] P6 = [-125257372932976394323491449517/597529, -140688518878789347105971176363589838925010638/461889917] P7 = [11310260885931220076984443479/1681, 1199572406544815374922321074008132976892222/68921] P8 = [16807048486007808650180560723/54289, 195423008109251813741470347172469954803722/12649337] P9 = [439692609609097525705606803/289, 8768764205126377836536761605997492908218/4913] P10 = [9923244519102466154616912929643/23493409, 15008985669597946494882137354352235897946094278/113872553423] P11 = [594998768680892479540491397442853/923430544, 10988504905368161316238961268743000812759299857767/28061207371072]
Voznyy (2022)
y2 + xy = x3 - 101634854745305789909593544356506871024975808975x + 12471286206505690638915431397948987770853556352343302542131897789660000 Torsion points: O, [184273670355417640439200, -92136835177708820219600], [199619745210754049497375, -11722564747058369862644546561381525], [199619745210754049497375, 11722564746858750117433792511884150] Independent points of infinite order: P1 = [147695786024769367617907, 26116833670524048667487732980486591] P2 = [119250285500346189861280, 45245055192994025620439342759582800] P3 = [183326482834983218947825, 521590709742404468274673661013025] P4 = [184273813157271150694825, 5800120368805796787557314729150] P5 = [117268676881033036606075, 46533572569932582885674160975109150] P6 = [234776341502159072262475, 39378705841793305538511652158448375] P7 = [381766883601170535357025, 171205849425833915557661294730171025] P8 = [184475449406819022674281, 264642357067669586606439520528702] P9 = [3418829721882733115742974425/23104, 91036076309745277299409530126868757048825/3511808] P10 = [1681800404520858334418999425/69169, 1820460692458296876133777439970523846153175/18191447] P11 = [40194609793224326407893008725/529, 8058383074893091975351883739864379760250650/12167]
Voznyy (2022)
y2 + xy = x3 - 1234140270416378250678088578402933925437564x + 527447606280303914796391760482999986982123024359861103558856208 Torsion points: O, [653020238752531025784, -326510119376265512892], [440497237068337744248, -8323782120287706078552815728572], [440497237068337744248, 8323782119847208841484477984324] Independent points of infinite order: P1 = [3835407722965517628792, 228504301248000433460701865863236] P2 = [800421217404316984151994/841, 357592581751334850718936215428924382/24389] P3 = [1042482966150433380168888/1849, 261916528689335052190062060227055372/79507] P4 = [-8638346270099840316816216/80089, -581973137012577697848855182784328429620/22665187] P5 = [-2657308988904526189437066/2209, -1710062594654663285568572758865404458/103823] P6 = [18779390259223821452763634104/128881, 2573413917211842125088416607016428228809052/46268279] P7 = [124109078951801959056412663128/1138489, 43720272984384566451063222665058730163805708/1214767763] P8 = [377497067519865683415814392/573049, 246700213804495007075372771521967091252/433798093] P9 = [64804783401535186901758778242/104468841, 814885466607887455628930566582482991070806/1067776023861] P10 = [-6576059757207854095972240224/8994001, -869404526623524049939971860682467344052004/26973008999] P11 = [993910598494520311209918693678414/1275569206921, 8984443087288728057329356738484938248373090017408/1440641893557853531]
Voznyy (2022)
y2 = x3 + x2 - 98157972552649846551441608681894049x + 17173523831080699917850997782683206552726896135031487 Torsion points: O, [-378805909904245639, 0], [197669397097277667, -74123347163736915087632784], [197669397097277667, 74123347163736915087632784] Independent points of infinite order: P1 = [128855060092964637, 81638432561593390605208164] P2 = [-7938783333687338421/25, 15969799545743675692435201008/125] P3 = [24817026840736474269, 123620432467089668380394853924] P4 = [12309421217494150611/49, 31377430254863109626702062128/343] P5 = [4557714551401009933251/16129, 224391997963421310525101749971792/2048383] P6 = [1551372858474736219998651/64009, 1932138513456898568279766310524953808/16194277] P7 = [1677453647094357397905987/261121, 2170065217864825235714208165103733424/133432831] P8 = [107899012783006936461819/51529, 35077189914780926191611962760851760/11697083] P9 = [-1414306374225384339701/29241, 738407823739449169949563410382256/5000211] P10 = [-1034333775630154712091/3844, 37001289006451624962607023421785/238328] P11 = [25439111806571211796699713/161086864, 153143561548162495891268778410148849033/2044514477888]
Voznyy (2022)
y2 + xy + y = x3 + x2 - 9616802040765253686519863489400032714x + 11458141648950677597857694544338957425465840088897243351 Torsion points: O, [1851990373201879945, -925995186600939973], [2672236059890973113, -2200409385461146359569970229], [2672236059890973113, 2200409382788910299678997115] Independent points of infinite order: P1 = [1084146104289492873, 1518683309539256514245998651] P2 = [1375161852338459147203/529, 24411918982693235834049597225355/12167] P3 = [15422310165617800073, 59424785067732305697277231675] P4 = [14591018719842282655/9, 9671991429426159057884111189/27] P5 = [13841374557228493796289/841, 1601390214571428264506169246227495/24389] P6 = [10405602055730261253, 32219128799494318875079868191] P7 = [2749938751531443734567847/1437601, 428407644928952276034519608229665825/1723683599] P8 = [57281960365991295632024633/3073009, 427884710327425088879593927830812916179/5386984777] P9 = [-70551359216673824299171/303601, -618733463976659279322191600671118035/167284151] P10 = [161949936045576405934466353/247464361, 9083669727279833423555403950536285817641/3892861862891] P11 = [-955960764580198934391664725617255/493884441167121, -52432633421565222424864633837673543172412771585123/10975846311006366381831]
Voznyy (2022)
y2 + xy = x3 - 204612883217644162374401645935933337240x + 1126458801999575619505157608163376285898744251881550465600 Torsion points: O, [8316639696921356080, -4158319848460678040], [6617638717645512880, -7887449354112646449715846040], [6617638717645512880, 7887449347495007732070333160] Independent points of infinite order: P1 = [8516689742361939760, 1258557746444139996430355560] P2 = [87151157544487517830, 803265529207451947250387612710] P3 = [1726456402245267089830, 71732928956835871254964242920710] P4 = [89877195839939054896, 841876686600359771888361686632] P5 = [4014405800817444147760/529, 39864065312678465090276882922200/12167] P6 = [7353521281977893280, 4412476003028123558085446760] P7 = [46219346744713441546960, 9936551405074724996120320013857480] P8 = [990903204473409123760/361, 165968122228853630339350672422520/6859] P9 = [1147807797564561615472/121, 8321895429390224494641744582776/1331] P10 = [226000159585908090165664/10609, 87656215263243991410412542676632664/1092727] P11 = [416445801148637774289040/49729, 5540488986506714228645753000442520/11089567]
Voznyy (2022)
y2 + xy + y = x3 + x2 - 21867223320112239016783671995123950489x + 39354506601874758642325518766562884477556802289319976926 Torsion points: O, [2722011719392931145, -1361005859696465573], [2121328706960296288, -1585242091020863279049363579], [2121328706960296288, 1585242088899534572089067290] Independent points of infinite order: P1 = [24732512710203778780/9, 3301823666656208241591779234/27] P2 = [1761921743490658633, 2509148111321239324296323131] P3 = [163508330617070294453, 2089941357655756156848881887041] P4 = [2298089380222767728, 1112823686752402012572175530] P5 = [7602910627595664572, 17679946510704434260598732925] P6 = [13018573601018243020, 44284362094015236647610890077] P7 = [41516282021171101989/16, 18575917855584889611077597215/64] P8 = [-18467972809008322938016/57121, -92984173365396273958232105339982330/13651919] P9 = [345349833367586271490068/139129, 31532953016429304254615419069916134/51895117] P10 = [8723565315738477727921996/3583449, 5021194902199967569996659253707031070/6783468957] P11 = [277664718631328317393427830/104101209, 71735717309677383678351186541196567239/1062144635427]
Voznyy (2022)
y2 + xy + y = x3 - x2 - 595526764519545473538759784349237221738404650282x + 207404712817763552978197730613335214330524536966377034126822264871403881 Torsion points: O, [-907749466601149462784559, 453874733300574731392279], [462104729225716126671441, 175747498503850620440840806083040279], [462104729225716126671441, -175747498504312725170066522209711721] Independent points of infinite order: P1 = [263385382871596577215041, 262341765293768874617852167469619079] P2 = [13884044773743433733841, 446250007211976531142848021383046679] P3 = [62696561667055960948425441, 496401252915531579828061889970166252279] P4 = [319445922309616026821601, 223078905661425343002424117884506359] P5 = [8546413940666077862815441, 24886905021942923687704829027612992279] P6 = [27196947075306390843721041, 141777585068685928302001021901624761879] P7 = [1484995076990113432880565441, 57225218845606403407155098116249028692279] P8 = [5479172528132737704827241/25, 36956995456165990672720785116198003771/125] P9 = [3585555444950117964152719/9, 4933137826348422574707936102681101533/27] P10 = [6639774897237945165589163049/289, 540740160779152581570315001710356763359927/4913] P11 = [20521987420448115281323587321/169, 2939817567270529944385336846917363859414627/2197]
Voznyy (2022)
y2 + xy + y = x3 + x2 - 2435109968648812284250327501767338349106208713x + 46251325990521754026689983318486396751949337631251172036297849383406 Torsion points: O, [28537664503990119507945, -14268832251995059753973], [25694265591055000445680, 803863600647378612983197533500922], [25694265591055000445680, -803863600673072878574252533946603] Independent points of infinite order: P1 = [28249476777825481619230, 68966919135415511094965346852397] P2 = [28684194095819223838170, 55009232057118016842353045253877] P3 = [10096064279813987704021105/256, 13923404495257906311519264999806510287/4096] P4 = [118122318351864384735080759020/109561, 40555577639978171877388947749543888328603282/36264691] P5 = [16478998180802258531106430/961, 92000029541776379694245439517639283052/29791] P6 = [302780580291955926869056645/10609, 4778808892731683510945250686753697519/1092727] P7 = [758236476045213915905173770/26569, 10526662133379160210090443466088291959/4330747] P8 = [-4498680646908684216518885348720/89510521, -5467757907824274947514756713939309406370537518/846859039181] P9 = [2361629687316200258046809835834864/83030998801, 41859814819749868610714230562366067684859859347/23925465335506951] P10 = [11960942584465581707124843631570/413593569, 1051547435015886751967540917226114385504903541/8411252412753] P11 = [8330238964895550899659071373820970/270157734289, 97530833579632740061531859774175726099385705207136/140419075078190663]
Voznyy (2022)
y2 = x3 - 944350340701979900709096424316569452x + 351982210527405532452913727852239888857539342858675696 Torsion points: O, [587981882605635556, 0], [283321839089223190, -327367893264950076421954104], [283321839089223190, 327367893264950076421954104] Independent points of infinite order: P1 = [38254916231980109305/64, 16777169165426102075826590733/512] P2 = [-18750900605870873341295/21316, 2205015052135300753750914135675609/3112136] P3 = [82535380295061133467062/22801, 22932283690078837935213080092568200/3442951] P4 = [-113875989962068818524408/145161, 43196683471633451523632373497805020/55306341] P5 = [688878499471005282902/121, 17832799164339424213464306070600/1331] P6 = [301838641211894138055389/75625, 161311889604268215124849389013203787/20796875] P7 = [482724803077483366159732/1018081, 106831406043053549774123781730277880/1027243729] P8 = [1670497998040055352029060/3481, 2159076594773081080192801590570282896/205379] P9 = [34077331595867471432087461/286225, 198922518214977527829310211025423289209/153130375] P10 = [-255049975187481208364790218/821338281, 18463838919342848703883023541179689343880/23538733795179] P11 = [-105635307959015288236949372/103286569, 522772318161554324725216926818096493600/1049701400747]
Voznyy (2022)
y2 = x3 - 71016450598376685828738822609116652x + 7262019996454072966062130364617906017922660966355696 Torsion points: O, [160750617222142756, 0], [80091877996173622, 45694038820021232280733800], [80091877996173622, -45694038820021232280733800] Independent points of infinite order: P1 = [590570941802758957, 413881117676024094193872915] P2 = [486460870147091782, 296367050257566784853447160] P3 = [93068439245587659286/25, 895609680842394633167167157784/125] P4 = [13633090461214947622/81, 6403866092638841715230090440/729] P5 = [22832849567776951798/169, 25380126005861616020352158040/2197] P6 = [-3945302181194111383/16, 6329408988650232042162538315/64] P7 = [32669525469732318327541/185761, 1165818454502900530104418402049265/80062991] P8 = [-65114466074481061191242/413449, 32056601099762566609947153300588840/265847707] P9 = [3726052363107527062, 7174480684765838367651735960] P10 = [-1662524697198869271565802/16104169, 7506976486515505378148934374734803240/64626030197] P11 = [2504026697401386137958790/18412681, 863047192812114567750670212901106184/79008814171]
Elkies (2005)
y2 + xy + y = x3 + x2 - 178794778214407978859461188x + 919419935068616719030140166742670899781 Torsion points: O, [7902333519965, -3951166759983], [10825661583645, 15892163331274543377], [10825661583645, -15892174156936127023] Independent points of infinite order: P1 = [7991223717565, 973476603398652017] P2 = [7157502138095, 2524594321090659027] P3 = [6490090505595, 5691791551237981527] P4 = [8260503930845, 2479531125255223377] P5 = [7068765426045, 2961370070561940177] P6 = [7986191049565, 940173095443704017] P7 = [7906176561445, 182183392974586577] P8 = [7447027420345, 963938571466557377] P9 = [7536040864245, 36725312300251577] P10 = [5577275134045, 9783604580829236177]
Eroshkin (2008)
y2 = x3 + x2 - 110907705551334904313030730340x + 14209200477703631816262785853057594833158688 Torsion points: O, [195804468832796, 0], [131691564567386, -1373853819454733446830], [131691564567386, 1373853819454733446830] Independent points of infinite order: P1 = [7487174762891, 3657763636175745336240] P2 = [66153929096078, 2676141294657606477702] P3 = [-13347561044449, 3960703205400133720710] P4 = [181718532279926, 236339226851902975710] P5 = [129109836878846, 1429021260168509457450] P6 = [145247830530626, 1079064641655703813110] P7 = [88799390252396, 2249639192885701617000] P8 = [-199927079309134, 5328358228788194289690] P9 = [187628598971846, 71501205004095977550] P10 = [68197418265338, 2638704196747226745522]
Eroshkin (2008)
y2 + xy = x3 - 1281493142199716912383484016491195x + 20908478821228455374087389955630487236070347099025 Torsion points: O, [21486290540011990, 1814750762615772718487905], [21486290540011990, -1814750784102063258499895], [-42159575397842210, 21079787698921105] Independent points of infinite order: P1 = [-1884428609245490, -4828733727563649610956095] P2 = [9999761497788040, 3015589736530490299309855] P3 = [12200758408015870, 2662607223124380557977105] P4 = [4933348790184430, 3834904647907043298422065] P5 = [3519275753727790, 4054890671211978028291105] P6 = [14461367628578290, 2323931548228764087838105] P7 = [-2033604490069460, -4848310938042222755152895] P8 = [8994062137272190, 3179655310614273671989105] P9 = [16053683488503262, 2114984845243170564101137] P10 = [26966762358435790, 2441547962033335259143105]
Eroshkin (2008)
y2 + xy = x3 - 760145319394626167366827836801635935x + 326380843415620023885693187007160075335038240252804697 Torsion points: O, [-1036794707078723866, 518397353539361933], [533136652721679734, -269546737807367996487415267], [533136652721679734, 269546737274231343765735533] Independent points of infinite order: P1 = [9351912801440222, 565042342279830932298098525] P2 = [213713389039346534, 416759679868093440475592333] P3 = [393973467736036454, 296739590176255292862135053] P4 = [406816171100407334, 290635968208203911412939533] P5 = [234359676554991974, 401379509123341236684375053] P6 = [400579344813463634, 293531629923125075348299433] P7 = [-64825358359178866, -612686803147736648313213067] P8 = [1554210922215654122, 1702722065578612070128963925] P9 = [237074990359828634, 399367114886444437383304433] P10 = [510752320135368038, 267158678585778218818603661]
Eroshkin (2008)
y2 + xy + y = x3 - x2 - 1438890788668364715460404815472111782x + 664238447429240521151735809720974728393274982519227189 Torsion points: O, [699504630281583497, -349752315140791749], [869884777856821097, -266102711989934394825413349], [869884777856821097, 266102711120049616968592251] Independent points of infinite order: P1 = [520887678470565777, 236785302619335675555907371] P2 = [710270859444232457, 23601426293735409770127291] P3 = [647688470016257117, 63174492741286520948721951] P4 = [709562420082172937, 22478274457271147570215611] P5 = [702959263351471497, 11196955863283826439240251] P6 = [711442588904296697, 25442532030235744453497051] P7 = [699713582108187017, 2481405925156054230971451] P8 = [517284388093930737, 241535268737908928011771811] P9 = [702701713122958997, 10690728311934648509815251] P10 = [-196617500442541171, -969303167941575286336924593]
Eroshkin (2008)
y2 = x3 - 2901413377029475814340493444042767x + 60112620677766830193510638729425884294374453937874 Torsion points: O, [31760259820397783, 0], [42928470713286833, -3830178611508582492309150], [42928470713286833, 3830178611508582492309150] Independent points of infinite order: P1 = [9646618920345158, 5746431883465628287663500] P2 = [22516670868944423, 2489661273896584110839880] P3 = [-11731608543750967, 9619575762996283592576250] P4 = [31932595197275909, 155981139952020471555390] P5 = [32234760310611533, 284153673834028171923750] P6 = [33132846938761673, 594386933433533810843130] P7 = [14198652836651958, 4666790390939468272881400] P8 = [32130881903267393, 243651479979758871850830] P9 = [32807820520613813, 486179240037017139923310] P10 = [11055368642843465, 5421035543526884598589062]
Eroshkin (2008)
y2 + xy = x3 - 469917050010248316855222453915732505x + 121700328613583346435162710697715924409177216507045177 Torsion points: O, [767486105638297994, 461650993946261693920122803], [767486105638297994, -461650994713747799558420797], [438895821028911194, -219447910514455597] Independent points of infinite order: P1 = [-146286683898037306, -432796061234100100258416097] P2 = [108038449934232194, 268686205122140342089930403] P3 = [452441406303420482, 41311174649746778876836763] P4 = [452695314206676944, 41752991757258929222247653] P5 = [-253366593281982232, -473810970451121523534799459] P6 = [442081176832193294, 18902908600673667767825003] P7 = [227860822860174452, 162650862827172354406068323] P8 = [85157260367825594, 286881543391818429188711603] P9 = [449352484018106474, 35695023271699947299504243] P10 = [-67833587645935306, -391489921725469422537090097]
Eroshkin (2008)
y2 + xy = x3 - 87362539812439413437833065426284x + 1241608478171540522727605890546080801398358040464 Torsion points: O, [-13413637921750568, 6706818960875284], [7856399856190384, 1019889278393031984370684], [7856399856190384, -1019889286249431840561068] Independent points of infinite order: P1 = [12671735539611790, -1472857965505361554356272] P2 = [-5742943676520860, -1246561784318309584428668] P3 = [2138788584575050, 1031766535181282505457558] P4 = [-6702171337531556, -1235342734384161373398716] P5 = [-759249792205406, -1143460008124367165861378] P6 = [-12995920712039624, -426652860429217686365708] P7 = [28054933432416298, -4568601038777740126291424] P8 = [1152874383209740, 1068841779862998610161328] P9 = [-3563935899462440, -1227882379605974010717548] P10 = [-12170113713276020, -708720448433330741811152]
Eroshkin (2008)
y2 = x3 + x2 - 18930547595582330633859100826042865x + 743333575262731208284792941763359206829310485395775 Torsion points: O, [243395856800774595, 102736862257161790173215700], [243395856800774595, -102736862257161790173215700], [110458120688643645, 0] Independent points of infinite order: P1 = [20559514928248395, 19047862763645511972676500] P2 = [39565101831733395, 7501975394540494976608500] P3 = [28287947149303395, 15181023867991162550596500] P4 = [-32685445410724035, 36430314859269554797617120] P5 = [-11186576971152435, 30882061465346532434966280] P6 = [118419368795569395, 12735866015645411612200500] P7 = [124314225677221770, 17639517362720208634940625] P8 = [182624320292371875, 58111756167727774877945580] P9 = [110642430084334065, 1807888292870044459854780] P10 = [23321632188969315, 17734906498764828289125780]
Eroshkin (2010)
y2 = x3 + x2 - 50491061391988204405194159029361x + 135663699587915859546796760459040265253947368735 Torsion points: O, [4539034041928485, 0], [7903172670072207, -479851415254420547970060], [7903172670072207, 479851415254420547970060] Independent points of infinite order: P1 = [594879530959527, 325327708047053156882580] P2 = [2884705001402037, 118393501187363110445880] P3 = [-1520096210813991, 457058525564559582882036] P4 = [2775663697578585, 130007938722486060873780] P5 = [-1133633732800665, 437544521662602852957420] P6 = [4540694038684071, 4338712096157000607084] P7 = [-2587491423319143, 498984311740534566303060] P8 = [16514120392102887, 1950773163564108331686420] P9 = [3618616115188602, 18424847821955205003945] P10 = [1321489924618677, 266923276622854745030280]
Eroshkin (2010)
y2 + xy + y = x3 - x2 - 28562016892450236469278130528841147x + 1855604032124054096684337837801147788788173909411371 Torsion points: O, [141241169865718611, 25280448179887316452374994], [141241169865718611, -25280448321128486318093606], [100384705906350411, -50192352953175206] Independent points of infinite order: P1 = [-35654245600770339, -53184928493164853355793706] P2 = [102663271430755911, 2319240609938111081641294] P3 = [52673995966314411, 22299665827759615565408794] P4 = [91736654652562531, 2727711406692375247325914] P5 = [100595198949492411, 603919072698101752016794] P6 = [-65816389876514589, -58739676675009736575030206] P7 = [104943321056725411, 3736640023782459047249794] P8 = [85100033778102759, 6424267594322106960581806] P9 = [109620193709308971, 6472309265284227861714874] P10 = [131809366710013161, 19516154123990917016704294]
Eroshkin (2010)
y2 + xy = x3 - 1034642810304700336989303292996335x + 27194354320720666208457979454230524027566043738297 Torsion points: O, [-41172155077932666, 20586077538966333], [22473710859921534, 3910605563287108844697933], [22473710859921534, -3910605585760819704619467] Independent points of infinite order: P1 = [1963070251109334, 5017055188546855513152333] P2 = [2685645541820454, 4943181282395407331179293] P3 = [7997842751105574, 4408064167520510706622653] P4 = [9767429295482214, 4245043305621547405927773] P5 = [-5651061635916666, -5732427126985005778937667] P6 = [16574454263852334, 3820853916529487973711333] P7 = [7436414620847334, 4462236776055147090486333] P8 = [19476238825878894, 3798842748743389505855013] P9 = [-6605865818580816, -5808683381863099996969317] P10 = [13748357584511334, 3945680279355505842090333]
Eroshkin (2010)
y2 = x3 + x2 - 1943429743722969114553996571920532980x + 14884792023408679915420022260951621825514385918921561728 Torsion points: O, [-2722332069468628924, 0], [1782093082051715126, 4132927520396891255805415650], [1782093082051715126, -4132927520396891255805415650] Independent points of infinite order: P1 = [-427172584770742117, 3954367586298572428628234592] P2 = [760257887621777546, 3721116398478610908210262290] P3 = [606915923615763026, 3732137348465002791209459850] P4 = [1068510370143712046, 3745417316748935152721248710] P5 = [-839006221187752474, 3990581262430580122452759150] P6 = [2022554584651863956, 4384953595030965159721878360] P7 = [6639950657837281478, 17167671130294892638491378318] P8 = [464669811929636006, 3752608357156476706290191790] P9 = [-200110161257290129, 3907131791504323450172525190] P10 = [4499207948473513826, 9859908154317940015940535750]
Eroshkin (2010)
y2 = x3 + x2 - 38396932203315800018086858812203832603560x + 2895935359083517194158307262550771514346143693455215925052708 Torsion points: O, [113414196619751906611, 0], [127249216727992963336, -265370194766021422762990755450], [127249216727992963336, 265370194766021422762990755450] Independent points of infinite order: P1 = [113916758950557205111, 13500221026921276791248250750] P2 = [113896389823119173431, 13096470814850457576925850610] P3 = [113590449221455398496, 6656667623985127552184010630] P4 = [30455989741818665911, 1324676853536502975722736519150] P5 = [114142831910452099927, 17902270485010503247645720170] P6 = [79428078175202623027, 589269244861500242748997345200] P7 = [138439983835588620736, 483274323444600799593635175750] P8 = [113987591930549406256, 14893171177371804903757972710] P9 = [84735300792849385411, 500764667481151987168163808900] P10 = [111510896511728917936, 29348679413717229219858354150]
Voznyy (2023)
y2 = x3 + x2 + 5365964600284239371851791x + 14610806763317668249280146321957009215 Torsion points: O, [-1740415499715, 0], [2061308179779, 5867724792430860372], [2061308179779, -5867724792430860372] Independent points of infinite order: P1 = [-481561549686, 3451824108575669073] P2 = [14226198513, 3832381364126005692] P3 = [-876724802157, 3038493239492760972] P4 = [1572849910698, 5190536505800612673] P5 = [-1530696957942, 1676504493512744337] P6 = [167896430085453, 2175725964008832334632] P7 = [2291392442418, 6239971645725964203] P8 = [2249038281533, 6168880912264161312] P9 = [-577134290262, 3364771968584939583] P10 = [2580925660593, 6756623848368234972]
Kulesz - Stahlke (2001)
y2 + xy = x3 - 791410724196656192877500062111x + 270985332491881387056053084997768958465063385 Torsion points: O, [448086509574998, -2516417112919062906259], [448086509574998, 2516416664832553331261], [515072096254310, -257536048127155] Independent points of infinite order: P1 = [-74068218887962, -18143796961075289154739] P2 = [511534686823160, 58470570596143399925] P3 = [357745618823558, 5800567653253786719341] P4 = [46172989499126, 15314763171500332546349] P5 = [355981327890944, 5862491533929390068891] P6 = [602281137752798, 3578629072947333881861] P7 = [380819855348144, 4982804555495324973515] P8 = [-703211300867866, -21903697871091460615219] P9 = [487486341852188, 1015429697665547098151]
Dujella (2005)
y2 + xy = x3 - 166949722612780501168288982743613641730x + 834840766609103026403820802333562999484076469013075040452 Torsion points: O, [-14928863831425505756, 7464431915712752878], [7468975423264965244, -2135092766480393408286474122], [7468975423264965244, 2135092759011417985021508878] Independent points of infinite order: P1 = [-8820362216509922756, 40263932840798434036966781878] P2 = [-782860091620997756, 31065402787828962844224056878] P3 = [-5636143289585842256, 39959416553160222669625340878] P4 = [9961806811829238544717456/573049, 24485557556804809925082322730120724154/433798093] P5 = [-537544178655329825148656/39601, 193027647463604874596475787842840322/7880599] P6 = [6904282448278329892, 3360620299363613882353063918] P7 = [1741500512137540439760724/168921, 1004730397874305643252222751219816218/69426531] P8 = [-11975077422549535854893084/840889, 13884475622003938729376902028644617014/771095213] P9 = [6752874832387240284195425865364/14123183281, 17541877711551772567165400626439982280674660638/1678413224297321]
Eroshkin (2008)
y2 = x3 + x2 - 205496172578185251395440662829934785x + 11849852981876652616557426694362320162271429199181183 Torsion points: O, [421139626921969361, 0], [-150331792760363809, -198355779911253887186223960], [-150331792760363809, 198355779911253887186223960] Independent points of infinite order: P1 = [-354190018494997279, 200502385826984101223443080] P2 = [-437037439569393439, 134849804811372529303534200] P3 = [-97475078008482769, 175938795101499865283688840] P4 = [-144765896268442582, 196379244958849401511041903] P5 = [-410120921945459473, 164760838222673865206745480] P6 = [-416990865640816369, 158217988422627336188933640] P7 = [-111756092132904814, 182810100770872307835777675] P8 = [582484911105669551, 299636387842864495851517320] P9 = [1904291285507941919/49, 21481588372636373466395144520/343]
Eroshkin (2008)
y2 = x3 + x2 - 246850542450447117600763943437460x + 2124703140418099231592606536930952455079436940608 Torsion points: O, [9864754457609206, -805950219044077741466910], [9864754457609206, 805950219044077741466910], [-18947023375137164, 0] Independent points of infinite order: P1 = [-1880660411281574, 1606951619114589607243230] P2 = [-1623386504886464, 1587815711394256785718200] P3 = [53194260738466, 1453124997658357390638810] P4 = [2524678293767631, 1231899847699778544207690] P5 = [3083221020040426, 1180219570536845236882770] P6 = [12040644818635588, 947671639507458641010312] P7 = [3981613914031006, 1097707203286600656164310] P8 = [7254218066499856, 846013666593435770097360] P9 = [145648955101134916, 55280308365256034344100040]
Eroshkin (2008)
y2 + xy + y = x3 - 1742907593966990756845614x + 884438686985072950763948120250518212 Torsion points: O, [3140269971671/4, -3140269971675/8], [1110774894341, -564764161159305741], [1110774894341, 564763050384411399] Independent points of infinite order: P1 = [-75449078194, -1007725103207297976] P2 = [820809034388, 82740042886701567] P3 = [411269065781, 487029241050481419] P4 = [935988672731, 270356715099523419] P5 = [263042753099, 666468018565637865] P6 = [916824173531, 239061498026206299] P7 = [2928006134039/4, 233685892742150397/8] P8 = [738992386706, 3766605528298749] P9 = [789721893716, 23342402566444524]
Eroshkin (2008)
y2 + xy + y = x3 - x2 - 176620653974058428143264127x + 903414674763811890417046406006315779751 Torsion points: O, [7718659159251, -3859329579626], [9172083968451, 7419985594402839574], [9172083968451, -7419994766486808026] Independent points of infinite order: P1 = [7768993064691, 406346675232305014] P2 = [4347401613651, 14755987046504074774] P3 = [8207792508501, 2586575356972455874] P4 = [249263407251, 29315611689872948374] P5 = [4777788280851, 12985466545844741974] P6 = [7865802003931, 902972932760584854] P7 = [7808702553939, 615370768676079766] P8 = [7721544259651, 79289152381169574] P9 = [9142567814251, 7269385757356565374]
Eroshkin (2008)
y2 = x3 - x2 - 63101137631999143241257265x + 191341468112384598938400129107933347137 Torsion points: O, [4922161372179, 0], [1826700164329, 9064767173835187100], [1826700164329, -9064767173835187100] Independent points of infinite order: P1 = [4046893030649, 1501755661273561980] P2 = [-207449533823, 14297651626859442556] P3 = [-325725187176, 14555429899070970195] P4 = [3981277360529, 1795508458242684900] P5 = [5946541104089, 5136700039591756740] P6 = [809049061709929, 23011314698170406393500] P7 = [37491752675879, 224778020445313965300] P8 = [2264866538708309/196, 86996381245561229373525/2744] P9 = [5807638191824, 4555957985766417945]
Eroshkin (2008)
y2 + xy = x3 - 3796945199097665047266867217657570x + 90053238757721148532503511375148048023191940383812 Torsion points: O, [37810942192819364, -737721397592643487120882], [37810942192819364, 737721359781701294301518], [35598869204894564, -17799434602447282] Independent points of infinite order: P1 = [28976854476915914, 2088147659103842244510818] P2 = [32835719065976564, 883614424636281921448718] P3 = [31994009520868964, 1150364535137936227811918] P4 = [19798347862574564, 4758197751976174562272718] P5 = [35647438683607592, 22129387556019059551178] P6 = [35610546243722564, 8467716416727238900718] P7 = [35972156521606874, 129460455676705830809348] P8 = [35607291607482724, 6984928715105109452878] P9 = [36765729402447614, 390779703902764130106368]
Dujella (2009)
y2 + xy = x3 - 483725969460602178479334521365188x + 190358540102254190991536781247531330227214704382992 Torsion points: O, [-60325983573810168, 30162991786905084], [41820709534592712, -15597179772769573766807556], [41820709534592712, 15597179730948864232214844] Independent points of infinite order: P1 = [-16645085583782268, -13921154095846610086268016] P2 = [30569176457931912, 14287671347748000840206844] P3 = [16638057761691912, 13671726629420585942126844] P4 = [-1795117496287224, -13828271777700233522135556] P5 = [38614274101441608, 15141205218230059828962300] P6 = [134075838854196312, 50355676623093919804459644] P7 = [20335183698911112, 13745213070611076417605244] P8 = [-56432036076432888, -6159882060292563595722756] P9 = [98489398436756232, 33137286223500682310303484]
Dujella (2009)
y2 = x3 - x2 - 16275673326928004830300499825x + 22374180470634970227928749712599947693981025 Torsion points: O, [-301008832994949, 0], [204504054373925, 5253426414016928203980], [204504054373925, -5253426414016928203980] Independent points of infinite order: P1 = [-77014662931824, 4813611129563743070025] P2 = [-106173766036725, 4785953101507739912520] P3 = [31413536475375, 4679092135601877391020] P4 = [96000948900701, 4657946180745108640620] P5 = [540550068665225925, 397423806070678002049531020] P6 = [230752447751901, 5559256565264735519340] P7 = [-79459122953443, 4813080716618069800212] P8 = [-65863763757800, 4812529297203127196605] P9 = [11734315925224435105/2704, 40184485126455200520458751625/140608]
Voznyy (2023)
y2 + xy + y = x3 - x2 - 12595569846799730587572505x + 17205797813043188222391188752442437497 Torsion points: O, [2049464139559, -1024732069780], [1976389306599, 179028516128616300], [1976389306599, -179030492517922900] Independent points of infinite order: P1 = [-1365084886601, -5644115121196512100] P2 = [2050179682599, 2638919079368300] P3 = [2048460936999, 909906266069100] P4 = [-943982574201, -5315506132459837300] P5 = [-1354803427545, -5637692797515722644] P6 = [1600442612775, 1070845269289591916] P7 = [63684624301863, 507447295857069989996] P8 = [115404196615, 3969099734681083148] P9 = [2043654754849, 13276177323863600]
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