curve #927

y² + y = x³ + x² − 3x + 1

a-invariants: [0, 1, 1, -3, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 37
discriminant (Δ): 37
Faltings height: -0.8765
naive height: 15.2255
primes of bad reduction: 37
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:01:29 UTC
last updated: 2026-09-23 15:01:29 UTC

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Commentary

Cremona 37b3 = LMFDB 37.b3: https://www.lmfdb.org/EllipticCurve/Q/37/b/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 37, minimal discriminant 37, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 15:01:29 UTC · history