curve #914

y² = x³ + 4x

a-invariants: [0, 0, 0, 4, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 32
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 14:59:21 UTC
last updated: 2026-09-23 14:59:21 UTC

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Commentary

Cremona 32a1 = LMFDB 32.a4: https://www.lmfdb.org/EllipticCurve/Q/32/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 32, minimal discriminant -4096, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 14:59:21 UTC · history