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curve #651

y² + xy + y = x³ + x² − 15x + 16

a-invariants: [1, 1, 1, -15, 16]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 563
discriminant (Δ): -563
Faltings height: -0.5717
naive height: 19.7445
primes of bad reduction: 563
regulator: 0.219229003517995456286946191043342445936013
submitted by: David Renshaw
submitted at: 2026-09-08 19:03:37 UTC
last updated: 2026-09-08 19:03:37 UTC

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

(2, -2)
(4, 4)

Commentary

Cremona 563a1 = LMFDB 563.a1. Curve data, generators (2, -2) and (4, 4) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/563/a/1

last edited by David Renshaw at 2026-09-08 19:03:37 UTC · history

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