  Let $k$ be a field of characteristic zero containing a primitive $n$-th root
of unity. Let $C^0_n$ be a singular plane curve of degree $n$ over $k$
admitting an order $n$ automorphism, $n$ nodes as the singularities, and $C_n$
be its normalization.
  In this paper we study the factors of Prym variety
$\mbox{Prym}(\widetilde{C}_n/C_n)$ associated to the double cover
$\widetilde{C}_n$ of $C_n$ exactly ramified at the points obtained by the
blow-up of the singularities. We provide explicit models of some algebraic
curves related to the construction of $\mbox{Prym}(\widetilde{C}_n/C_n)$ as a
Prym variety and determine the interesting simple factors other than elliptic
curves or hyperelliptic curves with small genus which come up in $J_n$ so that
the endomorphism rings contains the totally real field
$\mathbb{Q}(\zeta_n+\zeta^{-1}_n)$.
