curve #1029

y² + xy = x³ − x² − 24309x + 1426113

a-invariants: [1, -1, 0, -24309, 1426113]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 630
discriminant (Δ): 48243443062500
Faltings height: 1.4018
naive height: 41.9094
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:17:35 UTC
last updated: 2026-09-23 15:17:35 UTC

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Commentary

Cremona 630f6 = LMFDB 630.f3: https://www.lmfdb.org/EllipticCurve/Q/630/f/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 630, minimal discriminant 48243443062500, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:17:35 UTC · history