curve #5601

y² + xy = x³ − 234654435766406739042175x + 43750563812724215469979012405427225

a-invariants: [1, 0, 0, -234654435766406739042175, 43750563812724215469979012405427225]
c-invariants: [11263412916787523474024401, -37800487134210617285437048003500159001]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 7463552732895129427410
discriminant (Δ): 28986406871769215019010844249857250251694823189712718836964456198400
Faltings height: 12.0648
naive height: 173.0508
primes of bad reduction: 2, 3, 5, 7, 17, 23, 41, 53, 79, 149, 293, 941, 12889
regulator: 2975844.052471699887326847642169263644893865496069335
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 21:57:45 UTC
last updated: 2026-10-23 21:57:45 UTC

(-529010976850, 140855621487404885)
(-268948535290, 295646192435070845)
(379461576710, 96681282098699645)
(386934912062, 104335484977650077)
(1135961991950, 1114920216986994485)
(614760970959818/2209, 94053658553152591771/103823)
(12453491789919893/35344, 461056725827104124985697/6644672)

(u,v) = (87453,1833008) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.

last edited by Daniel Błażewicz at 2026-10-23 21:57:45 UTC · history