curve #1049

y² + xy = x³ − 6411x + 23985

a-invariants: [1, 0, 0, -6411, 23985]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2310
discriminant (Δ): 16604321025600
Faltings height: 1.2265
naive height: 37.9109
primes of bad reduction: 2, 3, 5, 7, 11
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 2310t2 = LMFDB 2310.u7: https://www.lmfdb.org/EllipticCurve/Q/2310/u/7 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 2310, minimal discriminant 16604321025600, torsion ℤ/2ℤ × ℤ/6ℤ.

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