curve #130

y² + xy = x³ − x² − 71899x + 5522449

a-invariants: [1, -1, 0, -71899, 5522449]
rank (lower bound): ≥ 8
conductor (N): 314658846776578
naive height: 45.1627
Faltings height: 1.7848
discriminant (Δ): 10698400790403652
primes of bad reduction: 2, 17, 487, 19003433191
regulator: 4338.70733787285461646054617796147519133767881422521590
submitted by: David Renshaw
last updated: 2026-07-01 22:55:23

Witness: 8 independent points

(80, 487)
(216, 79)
(12, 2153)
(250, 1643)
(63, 1082)
(-260, 2697)
(-294, 1235)
(267, 2170)

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 00:08:37 · history