Elkies (2006)
y2 + xy + y = x3 + x2 + 690560257169377937125059126423812540x - 33492188518937203020097127431557287129957999127407035 Torsion points: O, [48336483394805853, -24168241697402927], [883542747769245853, 1125336842235356652764997073], [883542747769245853, -1125336843118899400534242927], [4005178026762805853, 8184203792297326700054597073], [224631009320286053, 364641927591846714613884873], [4005178026762805853, -8184203796302504726817402927], [224631009320286053, -364641927816477723934170927] Independent points of infinite order: P1 = [286126088836986533, 433035480275757031966872273] P2 = [121390141610245853, 228306310388654208874997073] P3 = [377567526557995573, 530156507956449179371813753] P4 = [210538669890805853, 348180841544471134046597073] P5 = [20853081120020405853, 95301363213306571952478597073] P6 = [326728698269569003, 476458277653995656563456173]
Dujella - MacLeod - Peral (2013)
y2 + xy = x3 - 756828185715435657801375588494450478688880x + 253401847133358152315350001760510755926602193561212158650118400 Torsion points: O, [488270373699396020980, -522119461339460945407102274900], [-118081345724039567840, -18469507450545438959675271900080], [505910156890389864160, -252955078445194932080], [610824764162880776560, -4360662646017169114212121556480], [610824764162880776560, 4360662645406344350049240779920], [488270373699396020980, 522119460851190571707706253920], [-118081345724039567840, 18469507450663520305399311467920] Independent points of infinite order: P1 = [620360330455938117460, 4758091883195699130662218969420] P2 = [497190314206408214800, 136962231152035964282861848720] P3 = [4355219292628560802420, 282075815982149392450508425131820] P4 = [490711380442247094160, 424022366175406313485509707920] P5 = [-448543293347798650040, -22419392091058428164924864493080] P6 = [1562969108844553330473522536893440/2684692081009, 13987784198174075611499325865842096055521336633840/4398876028809489527]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 181610456457528727484901576033932410117420x + 28237703990352298099343957170848183918831345880437119331127757 Torsion points: O, [558290842392505431697, 10042866943307090210030910696601], [558290842392505431697, -10042866943865381052423416128299], [163779264270651744587, -1699068652294971678500307620529], [-274760643153223942843, -7575915234515549780971232322639], [-274760643153223942843, 7575915234790310424124456265481], [163779264270651744587, 1699068652131192414229655875941], [290566547041438749261, -145283273520719374631] Independent points of infinite order: P1 = [-262111421981438149703, -7604748244761082296499240767399] P2 = [1603280928397240856483/4, 35632863910443103768825980795453/8] P3 = [-457186661814710830273, -3963153939885314844704500853109] P4 = [-224502275521833029363287/529, -65380881667793259648646887167612433/12167] P5 = [353962605247773224817, 2881353967164064571433334624921] P6 = [10252458713508502560373/9, 973361599099440081832010470975427/27]
Voznyy (2021)
y2 + xy = x3 - 3165956472564282588349183356296344123080x + 68556991377202412800271408293265595826883848965311566892352 Torsion points: O, [40376400750367430544, 80937273933181949663338534728], [40376400750367430544, -80937273973558350413705965272], [105916883306527993044, -959919396621052129824033527772], [33569294397155260044, -10354772716925034748293169272], [33569294397155260044, 10354772683355740351137909228], [105916883306527993044, 959919396515135246517505534728], [131121445710117831551/4, -131121445710117831551/8] Independent points of infinite order: P1 = [17750661826608305544, 133985647071377314729416784728] P2 = [2437183282546211502906/49, 63372232375562012650626863255454/343] P3 = [21880359321696908904, 98792463770917906389388668888] P4 = [55948597958146717750244594/358801, 394329936946232557094066849818195586572/214921799] P5 = [5608341220821391208742/169, 13821487535430180656025188614452/2197] P6 = [-67529938508386821965888904/2879809, -1761385790564288050226275457245576077456/4887035873]
High rank curves with prescribed torsion | Andrej Dujella home page |