curve #662

y² + y = x³ − x + 6

a-invariants: [0, 0, 1, -1, 6]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 16811
discriminant (Δ): -16811
Faltings height: -0.5098
naive height: 17.1883
primes of bad reduction: 16811
regulator: 0.84700223921541012052410287828147546156759794
submitted by: David Renshaw
submitted at: 2026-09-08 19:17:33 UTC
last updated: 2026-09-08 19:17:33 UTC

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

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

Commentary

Cremona 16811a1 = LMFDB 16811.a1. Curve data, generators (0, 2), (1, 2), (-2, 0) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/16811/a/1

last edited by David Renshaw at 2026-09-08 19:17:34 UTC · history