curve #444

y² + y = x³ − 547x − 2934

a-invariants: [0, 0, 1, -547, -2934]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 6756532597
discriminant (Δ): 6756532597 ★ record for rank ≥ 6
Faltings height: 0.5860
naive height: 30.5269
primes of bad reduction: 6756532597
regulator: 173.76732813657803196853009268630119828606458634789
submitted by: Andrew Sutherland
submitted at: 2026-08-30 15:11:38 UTC
last updated: 2026-08-30 15:11:38 UTC

Witness: 6 independent points log in to add more points →

(105, 1047)
(64, -474)
(404, 8106)
(-14, 44)
(31, -100)
(523, 11948)

Commentary

Curve taken from Stein-Watkins database described in https://wstein.org/papers/stein-watkins/ants.pdf and available in the LMFDB at https://www.lmfdb.org/EllipticCurve/Q/stein-watkins.

last edited by Andrew Sutherland at 2026-08-30 15:14:05 UTC · history