curve #919

y² + xy = x³ − 3x + 1

a-invariants: [1, 0, 0, -3, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 34
discriminant (Δ): 1088
Faltings height: -0.7164
naive height: 14.9302
primes of bad reduction: 2, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:00:24 UTC
last updated: 2026-09-23 15:00:24 UTC

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Commentary

Cremona 34a1 = LMFDB 34.a4: https://www.lmfdb.org/EllipticCurve/Q/34/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 34, minimal discriminant 1088, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:00:24 UTC · history