curve #2543

y² + xy = x³ − x² − 9156294x + 4087006308

a-invariants: [1, -1, 0, -9156294, 4087006308]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 10710
discriminant (Δ): 41921259685871942250000
Faltings height: 3.0339
naive height: 59.7035
primes of bad reduction: 2, 3, 5, 7, 17
regulator: 3.123974337434075463478246872713198794198
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:09 UTC
last updated: 2026-09-26 20:08:09 UTC

Witness: 1 independent point log in to add more points →

(-3143, 44114)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=5; A=(3q-p)(p+q)^3=-9261, B=-(p+3q)(p-q)^3=14739. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:08:09 UTC · history