curve #673

y² + xy + y = x³ − 20x + 30

a-invariants: [1, 0, 1, -20, 30]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 18562
discriminant (Δ): 37124
Faltings height: -0.3609
naive height: 20.5280
primes of bad reduction: 2, 9281
regulator: 0.56674857488512761121462489661605399739221440
submitted by: David Renshaw
submitted at: 2026-09-08 19:26:47 UTC
last updated: 2026-09-08 19:26:47 UTC

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

(3, -3)
(2, -2)
(-1, 7)

Commentary

Cremona 18562c1 = LMFDB 18562.a1. Curve data, generators (3, -3), (2, -2), (-1, 7) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/18562/a/1

last edited by David Renshaw at 2026-09-08 19:26:47 UTC · history