curve #2465

y² + xy + y = x³ − 4079587249x − 23725042222384

a-invariants: [1, 0, 1, -4079587249, -23725042222384]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 44021670
discriminant (Δ): 4102232736038225146765291476900
Faltings height: 4.5649
naive height: 78.0014
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 59
regulator: 5.246230827077484881461788730617088889441
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:15 UTC
last updated: 2026-09-26 20:03:15 UTC

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

(-183413/4, 65632219/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-2, q=19; A=(3q-p)(p+q)^3=289867, B=-(p+3q)(p-q)^3=509355. 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 20:03:15 UTC · history