curve #2005

y² + xy = x³ − 995958483293563903385875x + 377520782530656905075289364307760161

a-invariants: [1, 0, 0, -995958483293563903385875, 377520782530656905075289364307760161]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 40191415156983276757320394144365170036138946
discriminant (Δ): 1657682051283192925132351603435434371701542292113378754520367268729454592
Faltings height: 12.6597
naive height: 177.3876
primes of bad reduction: 2, 3, 7, 11, 19, 41, 53, 71, 101, 199, 239, 347, 353, 431, 2341, 3923, 5813, 31957
regulator: 1520065370067395733.90223741907783143441233333720732843204413131732
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:58:11 UTC
last updated: 2026-09-26 04:58:11 UTC

(16956727648286, 69707004163023969353)
(6743032243342/9, 6150592261023130163/27)
(693280423100558/841, 8331410455640310484141/24389)
(19857316535551694/4225, 2739604749215239169732473/274625)
(172006701933883406/25921, 70572742372677932758204441/4173281)
(40675106784492094/56169, 2527187498079050949954509/13312053)
(72369532634563826/2401, 19458010285258503026124029/117649)
(383828693485203086/312481, 175325400770988316912448087/174676879)
(3478584180539569/5184, -39769129190276697963637/373248)
(157170240789120158, 62309673736142217435983513)
(40796482044375934/21609, 7261963759672184105503283/3176523)
(2929601687977733534/4305625, -1089195651444365449977791477/8934171875)
(1252845343026969554/134689, 1394553173918276875353019139/49430863)
(297339060610604013314/453391849, 773320224139066569679098709777/9654072640757)

2-isogenous partner of curve#1199 (Dujella (2009)).

last edited by Steps Unbounded at 2026-09-26 21:37:27 UTC · history