curve #949

y² + xy = x³ − x² + x

a-invariants: [1, -1, 0, 1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 55
discriminant (Δ): -55
Faltings height: -0.9788
naive height: 10.9907
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 55a4 = LMFDB 55.a4: https://www.lmfdb.org/EllipticCurve/Q/55/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 55, minimal discriminant -55, torsion ℤ/2ℤ.

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