Let $S_g$ be the compact Riemann surface of genus $g$. For $g>1,\, $we can construct a holomorphic map from $S_g$ to $S_1$ as below: $S_g \rightarrow \mathbb{C}^g/\mathbb{Z}^{2g} \rightarrow S_1=\mathbb{C}/\mathbb{Z}^2.$
The first map $\varphi:S_g \rightarrow \mathbb{C}^g/\mathbb{Z}^{2g}$ is Albanese map.(See Huybrechts Complex Geometry : An Introduction Definition 3.3.7)
The second map $\psi:\mathbb{C}^g/\mathbb{Z}^{2g} \rightarrow \mathbb{C}/\mathbb{Z}^2\,$is the projection, i.e. $\psi([(z_1,...,z_g)])=[z_1].$(The bracket [] means the eqivalent class defined by the quotient.)
This is a nonconstant holomorphic map between two compact Riemann surfaces thus a branched covering. My question is how can I compute the degree of it?