curve #942

y² + xy + y = x³ + x² − 3x + 1

a-invariants: [1, 1, 1, -3, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 50
discriminant (Δ): -800
Faltings height: -0.7261
naive height: 15.3041
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:03:38 UTC
last updated: 2026-09-23 15:03:38 UTC

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Commentary

Cremona 50b1 = LMFDB 50.b3: https://www.lmfdb.org/EllipticCurve/Q/50/b/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 50, minimal discriminant -800, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:03:38 UTC · history