curve #909

y² + xy + y = x³ + x + 2

a-invariants: [1, 0, 1, 1, 2]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 30
discriminant (Δ): -2160
Faltings height: -0.6783
naive height: 15.0318
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:59:18 UTC
last updated: 2026-09-23 14:59:18 UTC

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Commentary

Cremona 30a1 = LMFDB 30.a8: https://www.lmfdb.org/EllipticCurve/Q/30/a/8 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 30, minimal discriminant -2160, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 14:59:18 UTC · history