curve #892

y² = x³ + x² − 41x − 116

a-invariants: [0, 1, 0, -41, -116]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 20
discriminant (Δ): 2000
Faltings height: -0.3806
naive height: 22.7786
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:56:06 UTC
last updated: 2026-09-23 14:56:06 UTC

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Commentary

Cremona 20a4 = LMFDB 20.a1: https://www.lmfdb.org/EllipticCurve/Q/20/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 20, minimal discriminant 2000, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:56:06 UTC · history