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arXiv · 1401.0580

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

Nils Bruin·E. Victor Flynn·Damiano Testa
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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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Nils Bruin, E. Victor Flynn, Damiano Testa. 2014-01-03. Descent via (3,3)-isogeny on Jacobians of genus 2 curves. https://doi.org/10.4064/aa165-3-1

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