curve #2605

y² + xy = x³ − 13560575399351x + 19219442787951571305

a-invariants: [1, 0, 0, -13560575399351, 19219442787951571305]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2692356810
discriminant (Δ): 17985038618541174603172472435019278400
Faltings height: 6.2053
naive height: 102.3282
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 29, 67
regulator: 22.7382977447255204841107665925144305378158
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:16 UTC
last updated: 2026-09-26 20:12:16 UTC

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

(8225887/4, 1365331613/8)
(2146780, 39674335)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=38; A=(3q-p)(p+q)^3=104247, B=-(p+3q)(p-q)^3=25564855. 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 20:12:16 UTC · history