  Let $C$ be a smooth non rational projective curve over the complex field
$\mathbb{C}$. If $A$ is an abelian subvariety of the Jacobian $J(C)$, we
consider the Abel-Prym map $\varphi_A : C \rightarrow A$ defined as the
composition of the Abel map of $C$ with the norm map of $A$. The goal of this
work is to investigate the degree of the map $\varphi_A$ in the case where $A$
is one of the components of an isotypical decomposition of $J(C)$. In this case
we obtained a lower bound for $\mathrm{deg}(\varphi_A)$ and, under some
hypotheses, also an upper bound. We then apply the results obtained to compute
degrees of Abel-Prym maps in four cases. In particular, these examples show
that both bounds are sharp.
