curve #948

y² + xy = x³ − x² − 4x + 3

a-invariants: [1, -1, 0, -4, 3]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 55
discriminant (Δ): 3025
Faltings height: -0.6322
naive height: 15.9099
primes of bad reduction: 5, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:04:41 UTC
last updated: 2026-09-23 15:04:41 UTC

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Commentary

Cremona 55a1 = LMFDB 55.a3: https://www.lmfdb.org/EllipticCurve/Q/55/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 55, minimal discriminant 3025, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:04:41 UTC · history