curve #913

y² + xy + y = x³ − 334x − 2368

a-invariants: [1, 0, 1, -334, -2368]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 30
discriminant (Δ): 9000000
Faltings height: 0.2176
naive height: 29.0427
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:59:20 UTC
last updated: 2026-09-23 14:59:20 UTC

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Commentary

Cremona 30a6 = LMFDB 30.a3: https://www.lmfdb.org/EllipticCurve/Q/30/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 30, minimal discriminant 9000000, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:59:20 UTC · history