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curve #667

y² + y = x³ − 67x + 216

a-invariants: [0, 0, 1, -67, 216]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 953243
discriminant (Δ): -953243
Faltings height: -0.0731
naive height: 24.2760
primes of bad reduction: 953243
regulator: 3.366212426966199290870250443802940114147690352
submitted by: David Renshaw
submitted at: 2026-09-08 19:18:05 UTC
last updated: 2026-09-08 19:18:05 UTC

Witness: 4 independent points log in to add more points →

(4, 3)
(3, 6)
(5, 2)
(6, 5)

Commentary

LMFDB 953243.a1. Curve data, generators (4, 3), (3, 6), (5, 2), (6, 5) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/953243/a/1

last edited by David Renshaw at 2026-09-08 19:18:05 UTC · history

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