curve #1010

y² + xy = x³ + 210x + 900

a-invariants: [1, 0, 0, 210, 900]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 210
discriminant (Δ): -928972800
Faltings height: 0.4081
naive height: 27.6546
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:14:23 UTC
last updated: 2026-09-23 15:14:23 UTC

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Commentary

Cremona 210e1 = LMFDB 210.e7: https://www.lmfdb.org/EllipticCurve/Q/210/e/7 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 210, minimal discriminant -928972800, torsion ℤ/8ℤ.

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