curve #943

y² + xy + y = x³ + x² + 22x − 9

a-invariants: [1, 1, 1, 22, -9]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 50
discriminant (Δ): -819200
Faltings height: -0.1768
naive height: 20.8839
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:04:39 UTC
last updated: 2026-09-23 15:04:39 UTC

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Commentary

Cremona 50b2 = LMFDB 50.b4: https://www.lmfdb.org/EllipticCurve/Q/50/b/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 50, minimal discriminant -819200, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:04:39 UTC · history