Descent via (5, 5)-isogeny on Jacobians of Genus 2 Curves
نویسنده
چکیده
We describe a family of curves C of genus 2 with a maximal isotropic (Z/5) in J [5], where J is the Jacobian variety of C, and develop the theory required to perform descent via (5, 5)isogeny. We apply this to several examples, where it can shown that non-reducible Jacobians have nontrivial 5-part of the Tate-Shafarevich group.
منابع مشابه
Descent via (3, 3)-isogeny on Jacobians of Genus 2 Curves
We give parametrisation of curves C of genus 2 with a maximal isotropic (Z/3) 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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