curve #679

y² + y = x³ + x² − 146x + 636

a-invariants: [0, 1, 1, -146, 636]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 18745
discriminant (Δ): -2155675
Faltings height: 0.0536
naive height: 26.5820
primes of bad reduction: 5, 23, 163
regulator: 0.30988917736899827657289346902341147555311928
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:41 UTC
last updated: 2026-09-08 19:27:41 UTC

Witness: 3 independent points log in to add more points →

(9, 11)
(7, 2)
(58/9, 44/27)

Commentary

Cremona 18745a1 = LMFDB 18745.a1. Curve data, generators (9, 11), (7, 2), (58/9, 44/27) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/18745/a/1

last edited by David Renshaw at 2026-09-08 19:27:41 UTC · history