Given diophantine equation:
$$s^2 = (ad)^2 + (bc-ad+4ac)^2$$
$s,a,b,c,d$ are all variables. They are all odd.
a and b are coprime. c and d are coprime.
How do you parametrize all the solutions? Are there any methods to do so? Appreciate any tips to analyzing the solutions to this. Thanks.
EDIT: Interesting property (at least at first glance to me). If I run for solutions on a computer... and I set $a,b,c,d$ all $\ge n$ for some n, the frequency of solutions drops fast as I increase n. If I set n to 199, I get no solutions checking all variables up to 1000. What's the reason for this?