curve #1037

y² + xy = x³ − 4480x − 25600

a-invariants: [1, 0, 0, -4480, -25600]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/10ℤ
conductor (N): 870
discriminant (Δ): 5479747200000
Faltings height: 1.1349
naive height: 36.8358
primes of bad reduction: 2, 3, 5, 29
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:19:40 UTC
last updated: 2026-09-23 15:19:40 UTC

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Commentary

Cremona 870i1 = LMFDB 870.h4: https://www.lmfdb.org/EllipticCurve/Q/870/h/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 870, minimal discriminant 5479747200000, torsion ℤ/10ℤ.

last edited by David Renshaw at 2026-09-23 15:19:40 UTC · history