curve #123

y² + xy = x³ − x² − 18664x + 958204

a-invariants: [1, -1, 0, -18664, 958204]
rank (lower bound): ≥ 7
conductor (N): 896913586322
naive height: 41.1167
Faltings height: 1.3388
discriminant (Δ): 23319753244372
primes of bad reduction: 2, 13, 34496676397
regulator: 434.6225864840429444004928220928854851124416317346907
submitted by: David Renshaw
last updated: 2026-07-01 22:57:20

Witness: 7 independent points

(54, 298)
(106, 350)
(67, 38)
(28, 662)
(132, 818)
(158, 1312)
(15, 818)

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 00:08:29 · history