let $X$ a smooth algebraic curve over a field , let $A$ be its jacobian and $n:A\rightarrow A$ the multiplication by $n$ map (can assume $n$ coprime with the char of the base field if this semplifies things ). Since the curve embedds in its Jacobian which is the corresponding map $X\rightarrow X$, or $X\rightarrow Y$ where this is a finite map and $Y$ is a smooth curve?
thanks