curve #1000

y² + xy = x³ − x + 137

a-invariants: [1, 0, 0, -1, 137]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 174
discriminant (Δ): -8118144
Faltings height: 0.0047
naive height: 23.3643
primes of bad reduction: 2, 3, 29
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:13:16 UTC
last updated: 2026-09-23 15:13:16 UTC

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Commentary

Cremona 174b1 = LMFDB 174.e2: https://www.lmfdb.org/EllipticCurve/Q/174/e/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 174, minimal discriminant -8118144, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:13:17 UTC · history