I'm reading this text on Algebraic Number theory: (https://www.jmilne.org/math/CourseNotes/ANT.pdf, pg.68). They state the following:
Let $\alpha$ be a nonzero ideal in the ring of integers $\mathscr{O}_{K}$ of a number field $K$. Then $\alpha$ is of finite index in $\mathscr{O}_{K}$ and we let $\mathbb{N}\alpha$, the numerical norm of $\alpha$ be this index: $$ \mathbb{N}\alpha = (\mathscr{O}_{K} : \alpha )$$
Just exactly what index are they referring to? Does this mean that $\alpha$ has a finite set of ramification indices and we pick the largest? Does it refer somehow to the class number, although how?!
Frantic google searching just returns the definition of a Norm for an ideal, which is explicitly said not to be the same thing.
Would really appreciate anybody who could illuminate this for me.