curve #1042

y² + xy = x³ + 2305x − 15975

a-invariants: [1, 0, 0, 2305, -15975]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 1230
discriminant (Δ): -896670000000
Faltings height: 0.9823
naive height: 34.8421
primes of bad reduction: 2, 3, 5, 41
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:19:43 UTC
last updated: 2026-09-23 15:19:43 UTC

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Commentary

Cremona 1230k1 = LMFDB 1230.k2: https://www.lmfdb.org/EllipticCurve/Q/1230/k/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 1230, minimal discriminant -896670000000, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:19:43 UTC · history