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]
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