curve #1061

y² + xy = x³ − 6800x + 240000

a-invariants: [1, 0, 0, -6800, 240000]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 6690
discriminant (Δ): -4877010000000
Faltings height: 1.1659
naive height: 38.3047
primes of bad reduction: 2, 3, 5, 223
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:55 UTC
last updated: 2026-09-23 15:22:55 UTC

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Commentary

Cremona 6690j1 = LMFDB 6690.j2: https://www.lmfdb.org/EllipticCurve/Q/6690/j/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 6690, minimal discriminant -4877010000000, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:22:55 UTC · history