curve #961

y² + xy + y = x³ + x² − 2x − 1

a-invariants: [1, 1, 1, -2, -1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 66
discriminant (Δ): 528
Faltings height: -0.7881
naive height: 13.7241
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 66b1 = LMFDB 66.b4: https://www.lmfdb.org/EllipticCurve/Q/66/b/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 66, minimal discriminant 528, torsion ℤ/4ℤ.

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