curve #1036

y² + xy = x³ − 5774401x + 5346023177

a-invariants: [1, 0, 0, -5774401, 5346023177]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 858
discriminant (Δ): -26211168887701209984
Faltings height: 2.6358
naive height: 58.3226
primes of bad reduction: 2, 3, 11, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:18:39 UTC
last updated: 2026-09-23 15:18:39 UTC

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Commentary

Cremona 858k1 = LMFDB 858.k1: https://www.lmfdb.org/EllipticCurve/Q/858/k/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 858, minimal discriminant -26211168887701209984, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:18:39 UTC · history