curve #1045

y² + xy + y = x³ − x² + 63058x − 7866691

a-invariants: [1, -1, 1, 63058, -7866691]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/9ℤ
conductor (N): 1890
discriminant (Δ): -42674688000000000
Faltings height: 1.8763
naive height: 45.2754
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:20:46 UTC
last updated: 2026-09-23 15:20:46 UTC

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Commentary

Cremona 1890r3 = LMFDB 1890.x3: https://www.lmfdb.org/EllipticCurve/Q/1890/x/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 1890, minimal discriminant -42674688000000000, torsion ℤ/9ℤ.

last edited by David Renshaw at 2026-09-23 15:20:46 UTC · history