curve #122

y² + xy = x³ − x² − 92656x + 10865908

a-invariants: [1, -1, 0, -92656, 10865908]
rank (lower bound): ≥ 7
conductor (N): 858426129202
naive height: 45.9236
Faltings height: 1.6070
discriminant (Δ): 121896510346684
primes of bad reduction: 2, 71, 607, 9959233
regulator: 507.9996880326439166864305051339475554028263290755461
submitted by: David Renshaw
last updated: 2026-07-01 22:57:21

Witness: 7 independent points

(168, 58)
(239, 1407)
(26, 2898)
(97, 1620)
(-258, 4318)
(594, 12554)
(-187, 4744)

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 00:08:27 · history