curve #2427

y² + xy = x³ − x² − 36792233730x + 2713430669688900

a-invariants: [1, -1, 0, -36792233730, 2713430669688900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8534610
discriminant (Δ): 6819706902311369803777138736400
Faltings height: 4.8259
naive height: 84.5993
primes of bad reduction: 2, 3, 5, 7, 19, 23, 31
regulator: 9.050238410080564194513018707851204140743
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:55 UTC
last updated: 2026-09-26 20:00:55 UTC

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

(-638745/4, 538288395/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=19; A=(3q-p)(p+q)^3=23667, B=-(p+3q)(p-q)^3=1340595. 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 20:00:56 UTC · history