curve #2269

y² + xy + y = x³ − 39659408900423x + 96131351357982158006

a-invariants: [1, 0, 1, -39659408900423, 96131351357982158006]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 12353367390
discriminant (Δ): 44248342403321467621188119899092562500
Faltings height: 6.4081
naive height: 105.5477
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 71, 163
regulator: 4.050728159588305093568475764046947027430
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:59 UTC
last updated: 2026-09-26 19:50:59 UTC

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

(3681720, 148023277)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=39; A=(3q-p)(p+q)^3=-55909, B=-(p+3q)(p-q)^3=43602875. 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 19:50:59 UTC · history