curve #932

y² + xy = x³ + x² − 4x − 5

a-invariants: [1, 1, 0, -4, -5]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 39
discriminant (Δ): 1521
Faltings height: -0.6649
naive height: 16.1397
primes of bad reduction: 3, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:02:32 UTC
last updated: 2026-09-23 15:02:32 UTC

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Commentary

Cremona 39a1 = LMFDB 39.a3: https://www.lmfdb.org/EllipticCurve/Q/39/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 39, minimal discriminant 1521, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:02:32 UTC · history