curve #889

y² = x³ + x² − x

a-invariants: [0, 1, 0, -1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 20
discriminant (Δ): 80
Faltings height: -0.9300
naive height: 12.4766
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:56:05 UTC
last updated: 2026-09-23 14:56:05 UTC

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Commentary

Cremona 20a2 = LMFDB 20.a3: https://www.lmfdb.org/EllipticCurve/Q/20/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 20, minimal discriminant 80, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 14:56:05 UTC · history