curve #984

y² = x³ − x² − 2x

a-invariants: [0, -1, 0, -2, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 96
discriminant (Δ): 576
Faltings height: -0.7728
naive height: 14.1555
primes of bad reduction: 2, 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:10:05 UTC
last updated: 2026-09-23 15:10:05 UTC

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Commentary

Cremona 96b1 = LMFDB 96.a3: https://www.lmfdb.org/EllipticCurve/Q/96/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 96, minimal discriminant 576, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:10:05 UTC · history