Torsion group Z/2Z × Z/4Z, rank = 8

Elkies (2005)

y2 + xy + y = x3 + x2  - 2245321045583713014514387556551626518613389075x 
      + 40951023798706743647147655022412395573869307978556305934134697952785 

	Torsion points:

O, [29763029845850765905683, -699062028100151372099326510447442], 
[29763029845850765905683, 699062028070388342253475744541758], 
[25020708005132605807283, -659819080891533619932483575588242], 
[25020708005132605807283, 659819080866512911927350969780958], 
[27391868925491685856483, -13695934462745842928242], 
[-54715261409445312524061, 27357630704722656262030], 
[109293569935814506670307/4, -109293569935814506670311/8] 

	Independent points of infinite order:

P1 = [27217950144770714592483, 38762407781313186093387207311758]
P2 = [27320269699175805115083, 4282784155038060041953794941758]
P3 = [26418172070836772829603, 267416980432082210201830462862158]
P4 = [10414141517367257310883, 4324048052446654998517502008537358]
P5 = [14754827562060331594233, 3321731136830881492136790818111758]
P6 = [25585681690941092682203, 502030908890298294255957345396638] 
P7 = [986362241207870406575223, 978503144438732243193326482294398358]
P8 = [46128952570662176815171889384353/7777652481, 
     3619335153700852172354561908429346471339075334368/685918949951871]

Eroshkin (2008)

y2 = x3 - x2 - 3600510377430985267434688529347574077140x 
    + 83138379062405631329348360175446817662846629397471808788100

	Torsion points:

O, [34229494755989932566, 0], 
[35055806040511421530, 0], 
[-69285300796501354095, 0], 
[25770428610439666980, -86407241469249848980704067350], 
[25770428610439666980, 86407241469249848980704067350], 
[44341183470583176080, -103288366988754759023178655150], 
[44341183470583176080, 103288366988754759023178655150]

	Independent points of infinite order:

P1 = [27511666916754609030, 70040648032618306626353925000]
P2 = [34229379576265773880, 99263845939143951371702550]
P3 = [10971836682199381472, 212025871290888247368613734722]
P4 = [8338450132387552080, 231722836999797935854676725650]
P5 = [32659973917695474330, 19579215436552380987396572400]
P6 = [-45604229710736283684, 390501827997281792196178261950]
P7 = [-12333515316119324970, 354498531541702609016748618000]
P8 = [19128709204098397905, 145823871611640213929311101000]

Eroshkin (2008)

y2 = x3 + x2 - 23686061832482481624168232900x 
         + 1401294826072670363740983663536729053022048

	Torsion points:

O, [91442724267692, 0], 
[128849323043966, -698954455279281979050], 
[128849323043966, 698954455279281979050], 
[54036125491418, 528367347363098395698], 
[54036125491418, -528367347363098395698], 
[86243530797416, 0], 
[-177686255065109, 0]

	Independent points of infinite order:

P1 = [-19578753643834, 1362913540526632116750]
P2 = [7039133112536, 1111266965543810963160]
P3 = [76748038982126, 188419870198587400230]
P4 = [-32194246291774, 1459616860760570800470]
P5 = [85367453744006, 37417621531734692430]
P6 = [85225678008086, 40788683120841618690]
P7 = [71598493464386, 269159820951235640790]
P8 = [94712810727878, 86857168689634948878]

Dujella - Eroshkin (2008)

y2 = x3 - x2 - 866893152450363503763740085700x 
    + 61220734062068506723288644020689511073795652

	Torsion points:

O, [-964553620677266, 0], 
[-342699560964996, 17834151956634131617730], 
[-342699560964996, -17834151956634131617730], 
[2129738165284264, 88741191035298932908470], 
[2129738165284264, -88741191035298932908470], 
[71034318517633, 0], 
[893519302159634, 0]

	Independent points of infinite order:

P1 = [44067817038164, 4806685314955215492570]
P2 = [-10736855835311, 8398047577801604981580]
P3 = [-130593986210846, 13122671738229868426920]
P4 = [960440019693249, 10703970375598940056760]
P5 = [54120967930564, 3802914955516162348170]
P6 = [-820100918833816, 14852239103603527475850]
P7 = [-6811698256976, 8193011203460150583390]
P8 = [-1950786692688, 7931699078003287923106]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 79803310703487437168280400573137070x 
         + 8580075521385909204798110196185094214069266303840275

	Torsion points:

O, [-325790548478330174, 162895274239165087], 
[176991358629130790, -88495679314565395], 
[595196759396797535/4, -595196759396797535/8], 
[296048119817520815, 104409969138874520663894480], 
[296048119817520815, -104409969434922640481415295], 
[57934597440740765, 64429461731296463071772630], 
[57934597440740765, -64429461789231060512513395]

	Independent points of infinite order:

P1 = [77453929409112770, 53513084916901067806613855]
P2 = [-170797570009527145, -131254762955578219832362360]
P3 = [20353565720999740085/169, 58780040321920278978933581585/2197]
P4 = [-285337308928151965/4, -943518525241689473472819785/8]
P5 = [145355941987959590, 7163889827590147924320605]
P6 = [8299757602781346415/81, 28033456909165933393433537920/729]
P7 = [147942534837381665, 3433476697149808365624605]
P8 = [-427591904897299165/4, -1008423586826373027829927385/8]