curve #1041

y² + xy + y = x³ + x² − 4890x + 129447

a-invariants: [1, 1, 1, -4890, 129447]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 1230
discriminant (Δ): 15114240000
Faltings height: 0.8653
naive height: 37.0985
primes of bad reduction: 2, 3, 5, 41
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:19:42 UTC
last updated: 2026-09-23 15:19:42 UTC

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Commentary

Cremona 1230f1 = LMFDB 1230.f7: https://www.lmfdb.org/EllipticCurve/Q/1230/f/7 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 1230, minimal discriminant 15114240000, torsion ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 15:19:42 UTC · history