curve #918

y² + xy = x³ + x² − 146x + 621

a-invariants: [1, 1, 0, -146, 621]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 33
discriminant (Δ): 395307
Faltings height: -0.0126
naive height: 26.5751
primes of bad reduction: 3, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:00:24 UTC
last updated: 2026-09-23 15:00:24 UTC

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Commentary

Cremona 33a3 = LMFDB 33.a1: https://www.lmfdb.org/EllipticCurve/Q/33/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 33, minimal discriminant 395307, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:00:24 UTC · history