curve #129

y² = x³ − 481663x + 128212738

a-invariants: [0, 0, 0, -481663, 128212738]
c-invariants: [23119824, -110775805632]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 314214346667560
discriminant (Δ): 50274295466809600
Faltings height: 2.0606
naive height: 50.8686
primes of bad reduction: 2, 5, 7855358666689
regulator: 3808.43724670657225361488978860267064159808223292200143
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:35 UTC
last updated: 2026-07-01 22:55:24 UTC

Witness: 8 independent points log in to add more points →

(369, 850)
(429, 730)
(379, 320)
(449, 1570)
(479, 2720)
(249, 4870)
(229, 5470)
(381, 74)

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 00:08:36 UTC · history