curve #1050

y² + xy = x³ − 25725x + 1577457

a-invariants: [1, 0, 0, -25725, 1577457]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/12ℤ
conductor (N): 2730
discriminant (Δ): 11650189824000
Faltings height: 1.3453
naive height: 42.0793
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:20:48 UTC
last updated: 2026-09-23 15:20:48 UTC

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Commentary

Cremona 2730bd1 = LMFDB 2730.bd7: https://www.lmfdb.org/EllipticCurve/Q/2730/bd/7 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 2730, minimal discriminant 11650189824000, torsion ℤ/12ℤ.

last edited by David Renshaw at 2026-09-23 15:20:48 UTC · history