curve #2436

y² + xy = x³ − 22436333731x + 1291511784458945

a-invariants: [1, 0, 0, -22436333731, 1291511784458945]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 37447410
discriminant (Δ): 2249884650778460442362438222400
Faltings height: 4.7162
naive height: 83.1154
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 43
regulator: 3.925067892111339029630620285490472202011
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:29 UTC
last updated: 2026-09-26 20:01:29 UTC

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

(314867/4, 28698523/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=18; A=(3q-p)(p+q)^3=22295, B=-(p+3q)(p-q)^3=1048727. 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 20:01:29 UTC · history