curve #3436

y² + xy = x³ − 303448314x + 970310480139

a-invariants: [1, 0, 0, -303448314, 970310480139]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4129873336563
discriminant (Δ): 1381524155860374508084890489 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
Faltings height: 3.9032 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
naive height: 70.2058 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 6
primes of bad reduction: 3, 13, 61, 97, 109, 113, 1453
regulator: 1837.0454326967836455902246679013938989500066489423
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:33:17 UTC
last updated: 2026-09-27 05:33:17 UTC

(495885, 348735777)
(20754, 1890147)
(43719/25, 83276193/125)
(195/4, 7819851/8)
(-2993913/2809, 169336442652/148877)
(19305, 1509222)

Torsion Z/2+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:33:17 UTC · history