curve #139

y² + xy = x³ − x² − 56880994x + 168642718624

a-invariants: [1, -1, 0, -56880994, 168642718624]
rank (lower bound): ≥ 11
conductor (N): 252948166615918192888894
naive height: 65.2251
Faltings height: 3.3331
discriminant (Δ): -505896333231836385777788
primes of bad reduction: 2, 1601, 78996928986857649247
regulator: 91182620.3414038712920906292443019334784271018144625666456613
submitted by: David Renshaw
last updated: 2026-07-01 22:48:35

Witness: 11 independent points

(4432, 57680)
(4198, 59750)
(4568, 61852)
(4056, 66140)
(4606, 63654)
(4018, 68352)
(3986, 70350)
(4654, 66278)
(4688, 68352)
(3830, 81508)
(3738, 88910)

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 00:08:48 · history