curve #923

y² + y = x³ + x² − x

a-invariants: [0, 1, 1, -1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 35
discriminant (Δ): -35
Faltings height: -0.9712
naive height: 12.6842
primes of bad reduction: 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:01:27 UTC
last updated: 2026-09-23 15:01:27 UTC

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Commentary

Cremona 35a3 = LMFDB 35.a2: https://www.lmfdb.org/EllipticCurve/Q/35/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 35, minimal discriminant -35, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 15:01:27 UTC · history