Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups
نویسنده
چکیده
We decompose the Jacobian variety of hyperelliptic curves up to genus 20, defined over an algebraically closed field of characteristic zero, with reduced automorphism group A4, S4, or A5. Among these curves is a genus 4 curve with Jacobian variety isogenous to E2 1 × E2 2 and a genus 5 curve with Jacobian variety isogenous to E5, for E and Ei elliptic curves. These types of results have some interesting consequences to questions of ranks of elliptic curves and ranks of their twists.
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