curve #110

y² + y = x³ + x² − 100x + 110

a-invariants: [0, 1, 1, -100, 110]
rank (lower bound): ≥ 5
conductor (N): 55726757
naive height: 25.4391
Faltings height: 0.1792
discriminant (Δ): 55726757
primes of bad reduction: 647, 86131
regulator: 23.8551122555658031101980388427178666066140386433
submitted by: David Renshaw
last updated: 2026-07-01 23:01:14

Witness: 5 independent points

(1, 3)
(0, 10)
(-1, 14)
(-2, 17)
(-4, 21)

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 00:08:11 · history