curve #1007

y² + xy + y = x³ − 578x + 2756

a-invariants: [1, 0, 1, -578, 2756]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 210
discriminant (Δ): 8930250000
Faltings height: 0.6064
naive height: 30.6898
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:14:21 UTC
last updated: 2026-09-23 15:14:21 UTC

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Commentary

Cremona 210b2 = LMFDB 210.b6: https://www.lmfdb.org/EllipticCurve/Q/210/b/6 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 210, minimal discriminant 8930250000, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:14:21 UTC · history