Trying to find prime factorization of ideals in number fields
Let L=Q(√−5,i) and K=Q(√−5). Let OK and OL be the rings of algebraic integers of K and L. It can be checked that
2OK=⟨2,√−5+1⟩2
I want to find the factorization of the ideal ⟨2,√−5+1⟩OL in OL ?
The problem I am having is this. I don't know the syntax for the ideal generated by ⟨2,√−5+1⟩OL.
What to do ?