TITLE: Norm of an ideal
QUESTION [8 upvotes]: Would someone attempt to give me a simple explanation of how to compute the norm of an ideal. I like the definition |$O/a$| but find it difficult to apply. Perhaps the "determinant version" lends itself better to application. In any event, I need some hints for a problem which asks for all ideals of $\mathbb Z[\sqrt{(-5)}]$ which contain the element $6$. The previous post with a similar title really doesn't address this issue clearly.

REPLY [3 votes]: Hint $\ $ This is easy if you write the ideal as a module in "normal" form,  e.g. see section 2.3 in the nice exposition by Franz Lemmermeyer.
These normal forms generalize to higher degree number fields, e.g. see the discussion on Hermite and Smith normal forms in Henri Cohen's A Course in Computational Number Theory.