curve #5043

y² = x³ − 6226984745272516x

a-invariants: [0, 0, 0, -6226984745272516, 0]
c-invariants: [298895267773080768, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 99631755924360256
discriminant (Δ): 15453020451645655148412198264249274280114834182144
Faltings height: 8.1280
naive height: 120.7166
primes of bad reduction: 2, 17, 71, 97, 337
regulator: 108198.804938005892175850186160612830224705207086
submitted by: David Renshaw
submitted at: 2026-10-21 01:49:32 UTC
last updated: 2026-10-21 01:49:32 UTC

Witness: 5 independent points log in to add more points →

(571326208, 13525199639328)
(932665088, 28381054384992)
(-510348311406/14161, 710183089846835520/1685159)
(-240831503/4, 3166430707671/8)
(726826432/9, 4167077641264/27)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x with n = 78911246. Found by a Mestre-Nagao sieve over n <= 3*10^9 (n = 5,6,7 mod 8), top candidates checked with ellrank.

last edited by David Renshaw at 2026-10-21 01:49:32 UTC · history