curve #136

y² + xy = x³ − x² − 38099014x + 115877816224

a-invariants: [1, -1, 0, -38099014, 115877816224]
rank (lower bound): ≥ 11
conductor (N): 66484354768372183177742
naive height: 64.4746
Faltings height: 3.3833
discriminant (Δ): -2260468062124654228043228
primes of bad reduction: 2, 17, 277, 25301, 279012130635919
regulator: 5402298.84447187773578025736585607570884012602919864656010005
submitted by: David Renshaw
last updated: 2026-07-01 22:48:34

Witness: 11 independent points

(3370, 158778)
(3710, 158098)
(2826, 174010)
(2622, 183088)
(2010, 216748)
(1398, 254930)
(5478, 264722)
(208, 328472)
(-778, 381240)
(-1424, 409664)
(3795, 159152)

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 00:08:44 · history