Stuck calculating the class group of a cubic
I'm trying to calculate the class group of f=x^3-5x-5. I know that the ring of integers (O_K) is generated by {1,alpha,alpha^2} where alpha is a root of f, and I've found the factorization of 2*O_K, and 3*O_K (the minkowski bound is 3).
2*O_K=<2>...