Generalized Pythagorean Equation

Consider the Diophantine equation $x^2+13xy+y^2=z^2$

How many solutions are there with $0<x<y<{10}^7(x,y,z$ coprime)

Answer format: $count,\sum x,\sum y,\sum z$

You are given : 28989,580750261,1448965526,3481052101 for a threshold of ${10}^5$

[My timing: 20 sec]