curve #1027

y² + xy = x³ − 87945x − 8655975

a-invariants: [1, 0, 0, -87945, -8655975]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/10ℤ
conductor (N): 570
discriminant (Δ): 11219310000000000
Faltings height: 1.8041
naive height: 45.7670
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 570l2 = LMFDB 570.l3: https://www.lmfdb.org/EllipticCurve/Q/570/l/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 570, minimal discriminant 11219310000000000, torsion ℤ/10ℤ.

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