curve #1051

y² + xy = x³ − 41405x − 576975

a-invariants: [1, 0, 0, -41405, -576975]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2730
discriminant (Δ): 4400862921000000
Faltings height: 1.6919
naive height: 43.5071
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:21:50 UTC
last updated: 2026-09-23 15:21:50 UTC

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Commentary

Cremona 2730bd2 = LMFDB 2730.bd6: https://www.lmfdb.org/EllipticCurve/Q/2730/bd/6 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 2730, minimal discriminant 4400862921000000, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:21:50 UTC · history