curve #1052

y² + xy + y = x³ − 61744x + 5898926

a-invariants: [1, 0, 1, -61744, 5898926]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2730
discriminant (Δ): 5797789779600
Faltings height: 1.4420
naive height: 44.7058
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 2730n2 = LMFDB 2730.o6: https://www.lmfdb.org/EllipticCurve/Q/2730/o/6 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 2730, minimal discriminant 5797789779600, torsion ℤ/2ℤ × ℤ/6ℤ.

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