curve #125

y² + xy + y = x³ − 5983x + 164022

a-invariants: [1, 0, 1, -5983, 164022]
c-invariants: [287161, -142145965]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 1005276094726
discriminant (Δ): 2010552189452
Faltings height: 1.1022
naive height: 37.7034
primes of bad reduction: 2, 269, 2347, 796141
regulator: 893.2081712006927339910880239250292484334567123159772
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:31 UTC
last updated: 2026-07-01 22:56:23 UTC

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

(33, 36)
(29, 108)
(55, 18)
(57, 66)
(34, -3)
(7, 346)
(56, 45)

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 00:08:31 UTC · history