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abstract: 'For given $r \geq 1$ elliptic curves $E_1, \ldots, E_r$, there exists a closed Riemann surface of the minimal genus $e(E_{1},\ldots,E_{r})$ whose jacobian variety is isogenous to a product $E_1 \times \cdots \times E_r \times A$, where $A$ is also a product of jacobian varietes. Let $e(r)$ be the maximum of the values $e(E_1,\ldots,E_r)$, where $E_{1}, \ldots, E_{r}$ runs over the space of elliptic curves. If $r \leq 3$, then it is known that $e(E_1,\ldots,E_r)=r=e(r)$; we provide explicit equations of such a minimal genus Riemann surface. If $r \geq 4$, then we obtain that $e(r) \leq \widehat{e}(r)$, where (i) $\widehat{e}(r)=1+2^{(r-2)/2}r$ (for $r$ even) and (ii) $\widehat{e}(r)=1+2^{(r-3)/2}(r-1)$ (for $r$ odd). Our constructions also permits to obtain a $2$-dimensional family of Riemann surfaces of genus $g \in \{5,9\}$ and also of a $1$-dimensional family of genus $g=13$ whose jacobian varieties are isogenous to the product of elliptic curves.'
address: 'Departamento de Matemática y Estadística, Universidad de La Frontera. Casilla 54-D, Temuco, Chile'
author:
- 'Ruben A. Hidalgo'
title: Elliptic factors in the jacobian variety of Riemann Surfaces
---

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Introduction
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An abelian variety is called simple if it is not isogenous to a product of two abelian varieties of 