curve #962

y² + xy + y = x³ + x² − 352x − 2689

a-invariants: [1, 1, 1, -352, -2689]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 66
discriminant (Δ): 66
Faltings height: -0.0950
naive height: 29.2047
primes of bad reduction: 2, 3, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:06:50 UTC
last updated: 2026-09-23 15:06:50 UTC

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Commentary

Cremona 66b3 = LMFDB 66.b1: https://www.lmfdb.org/EllipticCurve/Q/66/b/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 66, minimal discriminant 66, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:06:50 UTC · history