# module isomorphisms

so I am currently learning about modules, I'm pretty new to them, but i have some experience with rings and linear algebra and stuff. I got the following problem:

Let $$R$$ be the ring $$\mathbb{Z}[\sqrt{-5}]$$ and $$I$$ be the ideal $$\langle 2,1+ \sqrt{-5} \rangle$$ in $$R$$. Show that $$I^2$$ is $$R$$-module isomorphic to $$R^2$$. Is there some $$n \in \mathbb{N}_0$$ such that $$I$$ is $$R$$-module isomorphic to $$R^n$$?

I managed to show that $$I^2$$ is the same as $$\langle 2 \rangle$$ just by multiplying things out and basically showing $$I^2 \subseteq \langle 2 \rangle$$ and $$\langle 2 \rangle \subseteq I^2$$. Though I don't really know how to progress from here or whether that is even useful. I need to find an isomorphism, but I'm not sure how to. multiplying by $$2$$ for example won't work, as the only units in $$\mathbb{Z}[\sqrt{-5}]$$ are $$\pm 1$$. Any help would be really appreciated!