curve #2263

y² + xy + y = x³ − 6793929799133x + 6801790768837123556

a-invariants: [1, 0, 1, -6793929799133, 6801790768837123556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8527256430
discriminant (Δ): 83598527036239482902010611155290562500
Faltings height: 6.1556
naive height: 100.2548
primes of bad reduction: 2, 3, 5, 7, 11, 19, 37, 59, 89
regulator: 7.617539737095261213100414843755492532245
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:35 UTC
last updated: 2026-09-26 19:50:35 UTC

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

(2037162, 1188829138)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=37; A=(3q-p)(p+q)^3=448875, B=-(p+3q)(p-q)^3=18278731. 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 19:50:36 UTC · history