Descent via (3,3)-isogeny on Jacobians of genus 2 curves

Published 3 Jan 2014 in math.NT | (1401.0580v1)

Abstract: We give parametrisation of curves C of genus 2 with a maximal isotropic (ZZ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it can shown that non-reducible Jacobians have nontrivial 3-part of the Tate-Shafarevich group.

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