curve #847

y² + xy = x³ − 272990781304697817672667917881072630615017312960990x + 1518639350666601678764502676260617320935155131802141660271965156247400612292

a-invariants

[1, 0, 0, -272990781304697817672667917881072630615017312960990, 1518639350666601678764502676260617320935155131802141660271965156247400612292]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

151140718614504686609877781454266969681628569083618322346325218033222024145539181715865134121936038483008436831093567025353290

discriminant (Δ)

305732090673381812685905906442857526958483855804505802249710180982617911134369083139475882863674554430964937878366713771828104863409699517111764992000000

Faltings height

27.9863

naive height

360.0142

primes of bad reduction

2, 3, 5, 7, 17, 23, 31, 59, 44647, 1091869, 359756108813269264819, 57385309707588878263253900350695590083585985398504313477326901217403669377694024479023

regulator

2280476968152387303411372441748184.49116575233597007538562851969013509801557567888330513136579518

submitted by

thomas

submitted at

2026-09-22 17:05:57 UTC

later contributions

primes of bad reduction recorded · thomas · 2026-09-22 17:09:53 UTC

Witness: 29 independent points log in to add more points →

(12693115614431361040955648636/289, 1338768466309428961703115799764242243714194/4913)
(12466598883652787102980508, 7272056583330697514540555023530165266)
(134798886496500909448475894, -1553742346066019013640412648434148697292)
(5928799956362911753928924, -10417912591020682887394626603561714862)
(112481821398885950435705564, -1180656663390443447195496886749641381422)
(7663352021956103683049540936/289, 558546047764393679433713244319813583663794/4913)
(14547545786076377388805724, 25020120077375706376807322018893113938)
(2374619092046885141915144, 29728442091027034248120157510847295398)
(-8213961646178800104950536, -56628491211196302285431049908159152522)
(295155195757333100746289429/16, 3362462055297524034766117702918882511597/64)
(4624635782500445605472924, -18843160167495968602865067432342810862)
(21454835478945027662813522, -74414660034812325760517131521334016170)
(12374416470462351418884148316/2209, -1334364805919546029077122952768659168607026/103823)
(7539891503008193055995423/4, 254339196830729303038229551869283600369/8)
(5157405367537405663220444, -15744719087206016908021686251927661742)
(12870171476480807357888924, -11706122176461021848553322073567534062)
(65113838196501405984481331996/5329, -1048924719852885556516177307370037325293054/389017)
(-10248265225696759797858916, -56920798863748630901504707313233407982)
(2166317700573917614057612125416/82369, 2646266541743751957755585932349466958212567034/23639903)
(109682309664965455694678937116156/1369, 1148695372420862815502621464877487534851707040714/50653)
(14134688392937136143455324, 21999110474249102394529770443138317138)
(161318547576776280536996884316/12769, 13396931233386801458013869636391298364663026/1442897)
(20554730287366739132327024, -67762069486676819041225112544403105762)
(3289111668390160683160484, -25618833641131397413963992914581853782)
(17211020355554167517227484, 43799823182073470551938264508896745298)
(89747077749659332587128924, 836594142594091128352806087202283385938)
(3790664351729075973357382479164/57121, -7167649596709606581402347153582850011285042738/13651919)
(55068869227443487542149774, -391773042552122439617679325917876067012)
(18425830926448248759933336044956/2934369, 36259743801121393382368345666430524027508271986/5026574097)

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