curve #2607

y² + xy = x³ − 8313317029345x + 9190579581315910025

a-invariants: [1, 0, 0, -8313317029345, 9190579581315910025]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 10872959790
discriminant (Δ): 281150699887800040379071577560281000000
Faltings height: 6.2300
naive height: 100.8602
primes of bad reduction: 2, 3, 5, 7, 11, 17, 43, 47, 137
regulator: 16.4872573350650799828234160001457672043782
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:23 UTC
last updated: 2026-09-26 20:12:23 UTC

Witness: 2 independent points log in to add more points →

(1550810, 166320755)
(1919552, 551915261)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=30; A=(3q-p)(p+q)^3=-673081, B=-(p+3q)(p-q)^3=19630919. 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 20:12:23 UTC · history