curve #112

y² + y = x³ − 7077x + 235516

a-invariants: [0, 0, 1, -7077, 235516]
rank (lower bound): ≥ 6
conductor (N): 5258110041
naive height: 38.2622
Faltings height: 1.0982
discriminant (Δ): -1277720739963
primes of bad reduction: 3, 584234449
regulator: 76.535132380495369224456093961543943630934899860102
submitted by: David Renshaw
last updated: 2026-07-01 22:59:17

Witness: 6 independent points

(46, 85)
(55, 112)
(64, 211)
(43, 103)
(19, 328)
(82, 454)

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 00:08:14 · history