$(\lambda_{1},\ldots,\lambda_{r}) \in \Delta_{r}$, then $$X=\left\{(x,y_{1},\ldots,y_{r}) \in {\mathbb C}^{r+1}:  y_{j}=x(x-1)(x-\lambda_{j}); \; j=1,\ldots,r \right\}$$ defines a closed Riemann surface of genus $g=1+2^{r-2}(r-1)$ whose jacobian variety is isogenous to a product $E_{\lambda_{1}} \times \cdots \times E_{\lambda_{r}} \times A_{g-r}$, where $A_{g-r}$ is the product of certain explicit elliptic/hyperelliptic Riemann surfaces.

Preliminaries: The jacobian variety of a closed Riemann surface
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Abelian varieties
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A [*polarized abelian variety*]{} of dimension $g$ is a pair $A=(T,Q)$, where $T={\mathbb C}^{g}/L$ is a complex torus of dimension $g$ and $Q$ (called a [*principal polarization*]{} of $A$) is a positive-definite Hermitian product in ${\mathbb C}^{g}$ with ${\rm Im}(Q)$ having integral values over elements of the lattice $L$. There is basis of $L$ for which ${\rm Im}(Q)$ can be represented by the matrix $$\left( \begin{array}{cc}
0 & D\\
-D & 0
\end{array}
\right)$$ where $D$ is a diagonal matrix, whose diagonal entries are $d_{1},\ldots,d_{g}$, where $d_{j} \geq 1$ divides $d_{j+1}$. The tuple $(d_{1},\ldots,d_{g})$ is called the [*polarization type*]{}. When $d_{1}=\cdots=d_{g}=1$, we say that the polarization is [*principal*]{} and that the abelian variety is [*principally polarized*]{}.

A non-constant surjective morphism $h:A_{1} \to A_{2}$ between abelian varieties is called an [*isogeny*]{} if it has a finite kernel. In this case we say 