curve #115

y² + xy + y = x³ − x² − 63147x + 6081915

a-invariants: [1, -1, 1, -63147, 6081915]
rank (lower bound): ≥ 6
conductor (N): 6663562874
naive height: 44.7733
Faltings height: 1.5798
discriminant (Δ): 218351628255232
primes of bad reduction: 2, 523, 6370519
regulator: 54.245797479930550808197728346032949250551289682168
submitted by: David Renshaw
last updated: 2026-07-01 22:59:18

Witness: 6 independent points

(171, 426)
(107, 682)
(155, -70)
(43, 1834)
(203, 1162)
(131, 146)

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 00:08:18 · history