curve #2288

y² + xy = x³ − 15460304421681x + 23397543626639327145

a-invariants: [1, 0, 0, -15460304421681, 23397543626639327145]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6847602090
discriminant (Δ): 5321081871017800627308552763553793600
Faltings height: 6.1917
naive height: 102.7215
primes of bad reduction: 2, 3, 5, 7, 19, 23, 29, 31, 83
regulator: 5.304960212779292506264564141908337446690
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:15 UTC
last updated: 2026-09-26 19:52:15 UTC

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

(2641884, 994861161)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=38; A=(3q-p)(p+q)^3=49735, B=-(p+3q)(p-q)^3=27266247. 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 19:52:15 UTC · history