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Given a fixed genus g, we would like to know the largest possible integer t such that t copies of one elliptic curve E appear in the decomposition of the Jacobian variety JX for some curve X of genus g. In this paper we find nontrivial lower bounds for t for genus up to 10. For genus 3 through 6 we demonstrate curves X such that JX Eg.

Decomposing Jacobians of curves with extra automorphisms