curve #968

y² + xy = x³ − x² − x

a-invariants: [1, -1, 0, -1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 73
discriminant (Δ): 73
Faltings height: -0.9440
naive height: 12.1292
primes of bad reduction: 73
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:07:54 UTC
last updated: 2026-09-23 15:07:54 UTC

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Commentary

Cremona 73a2 = LMFDB 73.a1: https://www.lmfdb.org/EllipticCurve/Q/73/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 73, minimal discriminant 73, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:07:54 UTC · history