curve #1062

y² + xy = x³ − 210177x + 37101321

a-invariants: [1, 0, 0, -210177, 37101321]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/9ℤ
conductor (N): 6942
discriminant (Δ): -1008907331567616
Faltings height: 1.7993
naive height: 48.3824
primes of bad reduction: 2, 3, 13, 89
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:56 UTC
last updated: 2026-09-23 15:22:56 UTC

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Commentary

Cremona 6942n1 = LMFDB 6942.l2: https://www.lmfdb.org/EllipticCurve/Q/6942/l/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 6942, minimal discriminant -1008907331567616, torsion ℤ/9ℤ.

last edited by David Renshaw at 2026-09-23 15:22:56 UTC · history