curve #126

y² + xy + y = x³ − 14505x + 667472

a-invariants: [1, 0, 1, -14505, 667472]
c-invariants: [696217, -577740349]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 1066284226102
discriminant (Δ): 2132568452204
Faltings height: 1.2030
naive height: 40.3603
primes of bad reduction: 2, 302213, 1764127
regulator: 933.7798366942692057650934863707616263994964142286268
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:32 UTC
last updated: 2026-07-01 22:57:20 UTC

Witness: 7 independent points log in to add more points →

(65, -14)
(75, 16)
(61, 72)
(59, 104)
(64, 16)
(89, 244)
(62, 55)

Commentary

From the tables of Elkies-Watkins 2004, 'Elliptic curves of large rank and small conductor' (ANTS-VI, arXiv:math/0403374): a low-conductor / low-discriminant curve of this rank that was absent from the leaderboard. Witness: a maximal independent set of rational points (Neron-Tate height pairing).

last edited by David Renshaw at 2026-06-24 00:08:32 UTC · history