curve #138

y² + xy = x³ − x² − 34125664x + 69523358164

a-invariants: [1, -1, 0, -34125664, 69523358164]
c-invariants: [1638031881, -60060810310245]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 227946110025657660240686
discriminant (Δ): 455892220051315320481372
Faltings height: 3.2749
naive height: 63.6503
primes of bad reduction: 2, 151, 2581599337, 292372419289
regulator: 98660495.1036795550880639813729964725582620483236327750338506
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:47 UTC
last updated: 2026-07-01 22:48:34 UTC

Witness: 11 independent points log in to add more points →

(2482, 9188)
(2438, 27270)
(2408, 34950)
(2370, 43012)
(2360, 44938)
(2234, 65458)
(2086, 85044)
(4200, 14342)
(4218, 22642)
(2008, 94350)
(1950, 100958)

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 00:08:47 UTC · history