curve #916

y² = x³ − 11x + 14

a-invariants: [0, 0, 0, -11, 14]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 32
discriminant (Δ): 512
Faltings height: -0.6174
naive height: 18.8073
primes of bad reduction: 2
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:00:23 UTC
last updated: 2026-09-23 15:00:23 UTC

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Commentary

Cremona 32a4 = LMFDB 32.a2: https://www.lmfdb.org/EllipticCurve/Q/32/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 32, minimal discriminant 512, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:00:23 UTC · history