curve #2366

y² + xy + y = x³ − 165995708798x + 23157096630244256

a-invariants: [1, 0, 1, -165995708798, 23157096630244256]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 147773010
discriminant (Δ): 61071478416306428949723178892250000
Faltings height: 5.4054
naive height: 89.1193
primes of bad reduction: 2, 3, 5, 7, 11, 17, 53, 71
regulator: 4.521770795654539598960207889865980496732
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:06 UTC
last updated: 2026-09-26 19:57:06 UTC

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

(-462930, 28404277)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=9; A=(3q-p)(p+q)^3=-3044125, B=-(p+3q)(p-q)^3=-2530909. 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 19:57:06 UTC · history