curve #2249

y² + xy = x³ − x² − 11899200148164x + 11877425697057838848

a-invariants: [1, -1, 0, -11899200148164, 11877425697057838848]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1277049690
discriminant (Δ): 46884820528126570794285981569477420250000
Faltings height: 6.5139
naive height: 101.9361
primes of bad reduction: 2, 3, 5, 7, 17, 43, 47, 59
regulator: 9.490852178051083343315789375993353101659
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:43 UTC
last updated: 2026-09-26 19:49:43 UTC

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

(2880612, 1224750744)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=47; A=(3q-p)(p+q)^3=6559875, B=-(p+3q)(p-q)^3=26493891. 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 19:49:43 UTC · history