curve #77

y² + xy = x³ − x² − 222751x + 40537273

a-invariants: [1, -1, 0, -222751, 40537273]
rank (lower bound): ≥ 8
conductor (N): 292246301470558
naive height: 48.5559
Faltings height: 1.7884
discriminant (Δ): -584492602941116
primes of bad reduction: 2, 5904737, 24746767
regulator: 30188.1405517264055310896306502872057316069977838122348
submitted by: David Renshaw
last updated: 2026-07-01 22:55:24

Witness: 8 independent points

(-21, -6713)
(26, 5883)
(-37, -6962)
(-47, -7111)
(109, 4134)
(116, 3973)
(137, 3478)
(194, 2047)

Commentary

Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [1,-1,0,-222751,40537273], |Delta|=584492602941116, I=101. The submitted integral points give the rank >= 8 witness checked by the site.

last edited by David Renshaw at 2026-06-02 18:44:30 · history