Descent via (3,3)-isogeny on Jacobians of genus 2 curves
Number Theory
2015-01-07 v1
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.
Keywords
Cite
@article{arxiv.1401.0580,
title = {Descent via (3,3)-isogeny on Jacobians of genus 2 curves},
author = {Nils Bruin and E. Victor Flynn and Damiano Testa},
journal= {arXiv preprint arXiv:1401.0580},
year = {2015}
}
Comments
17 pages