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curve #652

y² + y = x³ + x² − 4x + 2

a-invariants: [0, 1, 1, -4, 2]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 571
discriminant (Δ): -571
Faltings height: -0.7175
naive height: 16.1167
primes of bad reduction: 571
regulator: 0.177253140262004931744091099725954374009089
submitted by: David Renshaw
submitted at: 2026-09-08 19:03:41 UTC
last updated: 2026-09-08 19:03:41 UTC

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

(1, 0)
(0, 1)

Commentary

Cremona 571b1 = LMFDB 571.a1. Curve data, generators (1, 0) and (0, 1) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/571/a/1

last edited by David Renshaw at 2026-09-08 19:03:41 UTC · history

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