in general suppose is an ideal of a commutative domain then, as an module, is free if and only if it's cyclic. the reason is that if has a basis with more than one elements, then

we can choose two elements of the basis, say but which is impossible because belong to a basis of conversely if then would be a basis for because is

a domain. so, in your question, is not a free module because it cannot be generated by one element. (prove it!)