curve #958

y² = x³ − 4x

a-invariants: [0, 0, 0, -4, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 64
discriminant (Δ): 4096
Faltings height: -0.6174
naive height: 15.7725
primes of bad reduction: 2
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:06:48 UTC
last updated: 2026-09-23 15:06:48 UTC

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Commentary

Cremona 64a1 = LMFDB 64.a3: https://www.lmfdb.org/EllipticCurve/Q/64/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 64, minimal discriminant 4096, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:06:48 UTC · history