curve #2494

y² + xy = x³ − 643376861x + 2231977487985

a-invariants: [1, 0, 0, -643376861, 2231977487985]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 13946970
discriminant (Δ): 14891978896708922111587406400
Faltings height: 4.0984
naive height: 72.4603
primes of bad reduction: 2, 3, 5, 17, 23, 29, 41
regulator: 6.477577735427672568479084633935711285649
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:05 UTC
last updated: 2026-09-26 20:05:05 UTC

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

(-33809/4, 21299585/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=6; A=(3q-p)(p+q)^3=-201433, B=-(p+3q)(p-q)^3=-121945. 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 20:05:05 UTC · history