curve #1048

y² + xy + y = x³ − 15753x + 759256

a-invariants: [1, 0, 1, -15753, 759256]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2310
discriminant (Δ): 270140062500
Faltings height: 1.1354
naive height: 40.6079
primes of bad reduction: 2, 3, 5, 7, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:20:47 UTC
last updated: 2026-09-23 15:20:47 UTC

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Commentary

Cremona 2310l2 = LMFDB 2310.l5: https://www.lmfdb.org/EllipticCurve/Q/2310/l/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 2310, minimal discriminant 270140062500, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:20:47 UTC · history