curve #120

y² + xy + y = x³ − 14733x + 694232

a-invariants: [1, 0, 1, -14733, 694232]
c-invariants: [707161, -600877405]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 536670340706
discriminant (Δ): -4293362725648
Faltings height: 1.2354
naive height: 40.4278
primes of bad reduction: 2, 93463, 2871031
regulator: 747.6205461568833835575943461684343776186191875739400
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:25 UTC
last updated: 2026-07-01 22:57:20 UTC

Witness: 7 independent points log in to add more points →

(71, 50)
(79, 118)
(55, 198)
(83, 170)
(51, 250)
(87, 226)
(68, 55)

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 00:08:25 UTC · history