curve #2195

y² + xy = x³ − 598522898339300x + 5635916179156412490000

a-invariants: [1, 0, 0, -598522898339300, 5635916179156412490000]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 7553448210
discriminant (Δ): 299521717204814490890200926338657856000000
Faltings height: 7.1049
naive height: 113.6901
primes of bad reduction: 2, 3, 5, 7, 11, 109, 131, 229
regulator: 9.262894535608928395903548802490513094298
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:21 UTC
last updated: 2026-09-26 19:46:21 UTC

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

(14163400, 37135900)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=60; A=(3q-p)(p+q)^3=304799, B=-(p+3q)(p-q)^3=169648799. 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 19:46:21 UTC · history