curve #2466

y² + xy = x³ − 16890587001x + 844862508613305

a-invariants: [1, 0, 0, -16890587001, 844862508613305]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 10976790
discriminant (Δ): 40425784243314805352393640000
Faltings height: 4.5379
naive height: 82.2637
primes of bad reduction: 2, 3, 5, 11, 29, 31, 37
regulator: 7.017835795256774092896119508052496475210
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:19 UTC
last updated: 2026-09-26 20:03:19 UTC

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

(-171073/4, 308873173/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=2; A=(3q-p)(p+q)^3=-902393, B=-(p+3q)(p-q)^3=-898425. 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 20:03:19 UTC · history