curve #124

y² + y = x³ − 5707x + 151416

a-invariants: [0, 0, 1, -5707, 151416]
c-invariants: [273936, -130823640]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 1991659717477
discriminant (Δ): 1991659717477
Faltings height: 1.0973
naive height: 37.5619
primes of bad reduction: 154681, 12875917
regulator: 1172.532507747258989672291236129267860617335012322613
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:30 UTC
last updated: 2026-07-01 22:56:22 UTC

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

(32, 39)
(31, 65)
(29, 101)
(28, 116)
(54, 26)
(55, 62)
(69, 293)

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 00:08:30 UTC · history