Picard group of $\mathbb Z[\sqrt{-5}]$

Question

I search for a simple proof for the fact that $\operatorname{Pic}(\mathbb Z[\sqrt{-5}])=\mathbb Z/2\mathbb Z$, where $\operatorname{Pic}(R)$ is the Picard group of the ring $R$ - the set of isomorphism classes of f.g. projective $R$-modules of of rank $1$.

I appreciate anybody cooperating!

Answer 1

For Dedekind domains we have $\operatorname{Pic}(R)\simeq\operatorname{Cl}(R)$, where $\operatorname{Cl}(R)$ is the ideal class group of $R$. Your case is treated here in detail.