Is there a way to generate all possible Pythagorean quadruplets?

[SeventhSigma]

Given http://en.wikipedia.org/wiki/Pythagorean_quadruple it shows how to get primitive solutions, but what if I want even solutions that don't have coprime a, b, c, d?

 

[Borek]

If (a,b,c,d) is a Pythagorean quadruple, what can you say about (2a,2b,2c,2d)?