curve #663

y² + xy + y = x³ + x² − 10x + 6

a-invariants: [1, 1, 1, -10, 6]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 18097
discriminant (Δ): 18097
Faltings height: -0.4611
naive height: 18.5276
primes of bad reduction: 18097
regulator: 1.1075578754610291734579984750859975728205268
submitted by: David Renshaw
submitted at: 2026-09-08 19:17:39 UTC
last updated: 2026-09-08 19:17:39 UTC

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

(2, -1)
(0, 2)
(3, 2)

Commentary

Cremona 18097b1 = LMFDB 18097.a1. Curve data, generators (2, -1), (0, 2), (3, 2) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/18097/a/1

last edited by David Renshaw at 2026-09-08 19:17:39 UTC · history