curve #1020

y² + xy + y = x³ + x² − 65x + 47

a-invariants: [1, 1, 1, -65, 47]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 390
discriminant (Δ): 15210000
Faltings height: 0.0709
naive height: 24.1377
primes of bad reduction: 2, 3, 5, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:16:30 UTC
last updated: 2026-09-23 15:16:30 UTC

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Commentary

Cremona 390b2 = LMFDB 390.f5: https://www.lmfdb.org/EllipticCurve/Q/390/f/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 390, minimal discriminant 15210000, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:16:30 UTC · history