curve #921

y² + y = x³ + x² + 9x + 1

a-invariants: [0, 1, 1, 9, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 35
discriminant (Δ): -42875
Faltings height: -0.4218
naive height: 18.0921
primes of bad reduction: 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:00:25 UTC
last updated: 2026-09-23 15:00:25 UTC

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Commentary

Cremona 35a1 = LMFDB 35.a3: https://www.lmfdb.org/EllipticCurve/Q/35/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 35, minimal discriminant -42875, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 15:00:25 UTC · history