I am trying to an exercise that goes like this:
Show that there are an infinite number of Unramified Holomorphic maps $F:\mathbb{C}/L \rightarrow\mathbb{C}/L $ that are not automorphisms.
Well we know that for the map not to be an automorphism its degree cannot be $1$, but locally at any point it has to look like $z$, so we need maps that are not injective but somehow behave nicely in local coordinates, and i cant come up with any , any tips or advice is appreciated. Also i read that if we consider the lattice $L=\mathbb{Z}+\gamma\mathbb{Z}, Im(\gamma)>0 $ , then its degree $d$ will be a square and i cant seem to see this too.Thanks in advance.