curve #133

y² + y = x³ − 3835819x + 2889890730

a-invariants: [0, 0, 1, -3835819, 2889890730]
rank (lower bound): ≥ 9
conductor (N): 62986816173592807
naive height: 57.0933
Faltings height: 2.5119
discriminant (Δ): 4220116683630718069
primes of bad reduction: 67, 940101733934221
regulator: 54040.743340650066495609885765423138876129719521622311100
submitted by: David Renshaw
last updated: 2026-07-01 22:54:24

Witness: 9 independent points

(1108, 234)
(1175, 2244)
(1041, 4991)
(773, 19664)
(572, 29714)
(1711, 36548)
(237, 44655)
(2180, 69914)
(2247, 74939)

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 00:08:41 · history