curve #930

y² + xy + y = x³ + x² + 1

a-invariants: [1, 1, 1, 0, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 38
discriminant (Δ): -608
Faltings height: -0.7869
naive height: 13.8649
primes of bad reduction: 2, 19
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:02:31 UTC
last updated: 2026-09-23 15:02:31 UTC

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Commentary

Cremona 38b1 = LMFDB 38.b2: https://www.lmfdb.org/EllipticCurve/Q/38/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 38, minimal discriminant -608, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:02:31 UTC · history