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curve #654

y² + y = x³ − 13x + 18

a-invariants: [0, 0, 1, -13, 18]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 655
discriminant (Δ): -3275
Faltings height: -0.5181
naive height: 19.3315
primes of bad reduction: 5, 131
regulator: 0.0989535198921937605455687057557254270470861
submitted by: David Renshaw
submitted at: 2026-09-08 19:03:47 UTC
last updated: 2026-09-08 19:03:47 UTC

Witness: 2 independent points log in to add more points →

(1, 2)
(3, 2)

Commentary

Cremona 655a1 = LMFDB 655.a1. Curve data, generators (1, 2) and (3, 2) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/655/a/1

last edited by David Renshaw at 2026-09-08 19:03:47 UTC · history

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