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Descent via (3,3)-isogeny on Jacobians of genus 2 curves
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Bruin, Nils, Flynn, E. Victor and Testa, Damiano (2014) Descent via (3,3)-isogeny on Jacobians of genus 2 curves. Acta Arithmetica, Volume 165 (Number 3). pp. 201-223. doi:10.4064/aa165-3-1 ISSN 0065-1036.
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Official URL: http://dx.doi.org/10.4064/aa165-3-1
Abstract
We give a parametrization of curves\nonbreakingspace C of genus 2 with a maximal isotropic (Z/3)2 in J[3], where J is the Jacobian variety of\nonbreakingspace C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate–Shafarevich group.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Acta Arithmetica | ||||
| Publisher: | Polska Akademia Nauk: Instytut Matematyczny | ||||
| ISSN: | 0065-1036 | ||||
| Official Date: | 2014 | ||||
| Dates: |
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| Volume: | Volume 165 | ||||
| Number: | Number 3 | ||||
| Page Range: | pp. 201-223 | ||||
| DOI: | 10.4064/aa165-3-1 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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