curve #1965

y² = x³ − 638805515169212436324680847x + 6358462695374588202686457566308630996530

a-invariants: [0, 0, 0, -638805515169212436324680847, 6358462695374588202686457566308630996530]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 529207053387428721332538924292729467321994953619156880941805248245912
discriminant (Δ): -782327564609844531243959409420015147518391572704552747682718769037822388241321728
Faltings height: 14.3035
naive height: 196.8244
primes of bad reduction: 2, 3, 7, 23, 29, 47, 113, 7933, 692591, 53948410584830384839732093627534979474186417934323
regulator: 15306492737842254151.5359741984494430375963820294775004364426041145085906068451
submitted by: Ritik Jain
submitted at: 2026-09-25 20:07:01 UTC
last updated: 2026-09-25 20:07:01 UTC

(50200507943065, 317490077807841478510)
(348878577080884102841907714573/18897663000250441, -76064749280499203524937524489144709352343794/2597838507416600816478011)
(4263223374383451/49, 267756703564912140568968/343)
(113231631803554209/7921, -8572710932906716257300954/704969)
(2681864505423286899/19321, 4323813132483461097625424616/2685619)
(14753154988614116187/97969, -55916283325278497740813528488/30664297)
(517279664813209/49, 9648340697617683533774/343)
(207543964789701/25, 5042637031170637086426/125)
(272565932691793/1369, 3998471373795017726700886/50653)
(266391099993955321/18225, -29530841210178905113710994/2460375)
(53911388907861, 358621906208692595238)
(8883516994333, 37211321372525035246)
(2259557461845621/121, -40837744636629510378582/1331)
(20043694661193, -40087257722327147454)
(20420095305117, -42764126352529417362)
(183239095345808642028627/422261401, 78308026557749113262864920818157512/8677049529149)
(2518289575251142745421/203889841, -54671677840074327155860862102238/2911343039639)
(113770604294872311903/6355441, 411489470564667711648907412544/16022066761)
(32644743513112869/9409, 59034331506262968130441014/912673)
(2253914657785398011409/137334961, 27642245449655981853326376299574/1609428407959)

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