curve #1008

y² + xy + y = x³ + 1922x + 20756

a-invariants: [1, 0, 1, 1922, 20756]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/12ℤ
conductor (N): 210
discriminant (Δ): -637994920500
Faltings height: 0.9530
naive height: 34.2977
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:14:22 UTC
last updated: 2026-09-23 15:14:22 UTC

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Commentary

Cremona 210b5 = LMFDB 210.b8: https://www.lmfdb.org/EllipticCurve/Q/210/b/8 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 210, minimal discriminant -637994920500, torsion ℤ/12ℤ.

last edited by David Renshaw at 2026-09-23 15:14:22 UTC · history