Vol. 1, No. 1, 2013

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Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups

Jennifer Paulhus

Vol. 1 (2013), No. 1, 487–505

We decompose the Jacobian varieties 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 E12 × E22 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 for questions of ranks of elliptic curves and ranks of their twists.

Jacobian varieties, hyperelliptic curves, automorphism groups of Riemann surfaces
Mathematical Subject Classification 2010
Primary: 14H40
Secondary: 11G30, 14H37
Published: 14 November 2013
Jennifer Paulhus
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States