curve #786

y² + xy + y = x³ − x² − 40458649392x + 3123308218829715

a-invariants: [1, -1, 1, -40458649392, 3123308218829715]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 31637890823944880544503354
discriminant (Δ): 24362694553197107373533718740992
Faltings height: 4.8873
naive height: 84.8842
primes of bad reduction: 2, 47, 336573306637711495154291
regulator: 34062994.294555534148032422287168082027650825171596303658522049
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:39:53 UTC
last updated: 2026-09-18 12:39:53 UTC

(84621, 17439057)
(123293, 2975729)
(-209411, -49012175)
(22205, 47273905)
(110941, -532239)
(103421, -6775343)
(92045, 13337425)
(-75555, -75783375)
(92893, -12952271)
(131997, 9027185)
(504989, 333620465)
(71325, 24468209)

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-18 12:39:53 UTC · history