curve #992

y² = x³ + x² − 20x

a-invariants: [0, 1, 0, -20, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 120
discriminant (Δ): 518400
Faltings height: -0.2131
naive height: 20.6504
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:12:11 UTC
last updated: 2026-09-23 15:12:11 UTC

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Commentary

Cremona 120a2 = LMFDB 120.b4: https://www.lmfdb.org/EllipticCurve/Q/120/b/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 120, minimal discriminant 518400, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:12:11 UTC · history