curve #959

y² = x³ + x

a-invariants: [0, 0, 0, 1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 64
discriminant (Δ): -64
Faltings height: -0.9640
naive height: 11.6136
primes of bad reduction: 2
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:06:49 UTC
last updated: 2026-09-23 15:06:49 UTC

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Commentary

Cremona 64a4 = LMFDB 64.a4: https://www.lmfdb.org/EllipticCurve/Q/64/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 64, minimal discriminant -64, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:06:49 UTC · history