curve #118

y² + y = x³ − 889x + 9150

a-invariants: [0, 0, 1, -889, 9150]
c-invariants: [42672, -7905816]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 8796007189
discriminant (Δ): 8796007189
Faltings height: 0.6407
naive height: 31.9839
primes of bad reduction: 8796007189
regulator: 141.73365659632160880961097078808226407232604818979
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:22 UTC
last updated: 2026-07-01 22:58:19 UTC

Witness: 6 independent points log in to add more points →

(12, 14)
(11, 26)
(10, 35)
(22, 15)
(23, 29)
(25, 50)

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 00:08:22 UTC · history