More fun in 2015, Part 23

How many orthogonal 2 x 2 matrices $A$ are there such that all the entries of $2015A$ are integers?

For those who don't know matrices yet, we state the problem (less elegantly) in terms of vectors: How many ordered pairs of perpendicular unit vectors $v,w$ with two real components are there such that all the components of $2015v$ and of $2015w$ are integers?

Hint: Find the Pythagorean triples with 2015 as the hypotenuse.