curve #888

y² = x³ + x² + 4x + 4

a-invariants: [0, 1, 0, 4, 4]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 20
discriminant (Δ): -6400
Faltings height: -0.5834
naive height: 15.5396
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:56:04 UTC
last updated: 2026-09-23 14:56:04 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 20a1 = LMFDB 20.a4: https://www.lmfdb.org/EllipticCurve/Q/20/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 20, minimal discriminant -6400, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 14:56:04 UTC · history