curve #131

y² + xy = x³ − x² − 124294x + 14418784

a-invariants: [1, -1, 0, -124294, 14418784]
rank (lower bound): ≥ 8
conductor (N): 315734078239402
naive height: 46.8048
Faltings height: 1.8936
discriminant (Δ): 33467812293376612
primes of bad reduction: 2, 53, 1471, 2024896927
regulator: 4378.89783766902967798504852401281835368190735016307202
submitted by: David Renshaw
last updated: 2026-07-01 22:55:24

Witness: 8 independent points

(78, 2240)
(290, 1498)
(131, 544)
(-134, 5420)
(25, 3353)
(-240, 5632)
(343, 3300)
(502, 8600)

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 00:08:38 · history