curve #1026

y² + xy = x³ + 9335x − 737383

a-invariants: [1, 0, 0, 9335, -737383]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/10ℤ
conductor (N): 570
discriminant (Δ): -287450726400000
Faltings height: 1.4575
naive height: 40.5470
primes of bad reduction: 2, 3, 5, 19
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:17:34 UTC
last updated: 2026-09-23 15:17:34 UTC

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Commentary

Cremona 570l1 = LMFDB 570.l4: https://www.lmfdb.org/EllipticCurve/Q/570/l/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 570, minimal discriminant -287450726400000, torsion ℤ/10ℤ.

last edited by David Renshaw at 2026-09-23 15:17:34 UTC · history