curve #107

y² + y = x³ − 247x + 1476

a-invariants: [0, 0, 1, -247, 1476]
c-invariants: [11856, -1275480]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 22966597
discriminant (Δ): 22966597
Faltings height: 0.2182
naive height: 28.1418
primes of bad reduction: 47, 488651
regulator: 13.8258999407123215574851393149106059573573060505
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:07 UTC
last updated: 2026-07-01 23:02:11 UTC

Witness: 5 independent points log in to add more points →

(8, 3)
(10, 2)
(7, 9)
(11, 9)
(6, 14)

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 00:08:07 UTC · history