curve #113

y² + xy = x³ − x² − 2326x + 43456

a-invariants: [1, -1, 0, -2326, 43456]
rank (lower bound): ≥ 6
conductor (N): 5739520802
naive height: 34.8696
Faltings height: 0.7566
discriminant (Δ): 11479041604
primes of bad reduction: 2, 331, 383, 22637
regulator: 98.157903581098532023878844268831034352354437276555
submitted by: David Renshaw
last updated: 2026-07-01 22:59:16

Witness: 6 independent points

(26, -6)
(30, -14)
(24, 20)
(32, 16)
(34, 36)
(25, 9)

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 00:08:16 · history