curve #891

y² = x³ + x² − 36x − 140

a-invariants: [0, 1, 0, -36, -140]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 20
discriminant (Δ): -4000000
Faltings height: -0.0341
naive height: 23.2260
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 20a3 = LMFDB 20.a2: https://www.lmfdb.org/EllipticCurve/Q/20/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 20, minimal discriminant -4000000, torsion ℤ/2ℤ.

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