curve #117

y² + y = x³ − 379x + 5172

a-invariants: [0, 0, 1, -379, 5172]
rank (lower bound): ≥ 6
conductor (N): 8072781371
naive height: 30.6253
Faltings height: 0.5937
discriminant (Δ): -8072781371
primes of bad reduction: 8072781371
regulator: 150.95696885474745111489758710978373050933997082981
submitted by: David Renshaw
last updated: 2026-07-01 22:58:19

Witness: 6 independent points

(8, 51)
(12, 48)
(7, 53)
(15, 53)
(2, 66)
(-1, 74)

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 00:08:20 · history