curve #119

y² + y = x³ + x² − 390x + 5460

a-invariants: [0, 1, 1, -390, 5460]
rank (lower bound): ≥ 6
conductor (N): 9694585723
naive height: 30.7807
Faltings height: 0.6081
discriminant (Δ): -9694585723
primes of bad reduction: 9694585723
regulator: 198.72083733594502037312969609344942463062529685365
submitted by: David Renshaw
last updated: 2026-07-01 22:58:19

Witness: 6 independent points

(12, 51)
(13, 52)
(5, 60)
(2, 68)
(17, 63)
(-4, 83)

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 00:08:23 · history