curve #917

y² + xy = x³ + x² − 11x

a-invariants: [1, 1, 0, -11, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 33
discriminant (Δ): 88209
Faltings height: -0.3592
naive height: 18.9461
primes of bad reduction: 3, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:00:23 UTC
last updated: 2026-09-23 15:00:23 UTC

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Commentary

Cremona 33a1 = LMFDB 33.a2: https://www.lmfdb.org/EllipticCurve/Q/33/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 33, minimal discriminant 88209, torsion ℤ/2ℤ × ℤ/2ℤ.

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