curve #108

y² + xy = x³ − x² − 415x + 3481

a-invariants: [1, -1, 0, -415, 3481]
rank (lower bound): ≥ 5
conductor (N): 34672310
naive height: 29.7728
Faltings height: 0.4039
discriminant (Δ): -346723100
primes of bad reduction: 2, 5, 79, 43889
regulator: 7.98812089828060622749800735401369801305082865558
submitted by: David Renshaw
last updated: 2026-07-01 23:03:08

Witness: 5 independent points

(8, 21)
(13, 6)
(18, 31)
(3, 46)
(12, 5)

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 00:08:09 · history