curve #109

y² = x³ − 532x + 4420

a-invariants: [0, 0, 0, -532, 4420]
c-invariants: [25536, -3818880]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 37396136
discriminant (Δ): 1196676352
Faltings height: 0.4887
naive height: 30.4435
primes of bad reduction: 2, 4674517
regulator: 10.3187357247916407891471609820307434164395313639
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:10 UTC
last updated: 2026-07-01 23:03:09 UTC

Witness: 5 independent points log in to add more points →

(10, 10)
(18, 26)
(16, 2)
(6, 38)
(8, 26)

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 00:08:10 UTC · history