Groen, Steven (2019) Descent by 3-isogeny on elliptic curves. Master's Thesis / Essay, Mathematics.
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Abstract
Descent by a rational isogeny has shown to be a useful tool in computing the rank of elliptic curves. After outlining the general theory, we recall the well-known theory of descent by 2-isogeny. A relatively new approach is descent by a 3-isogeny. In this thesis, we formulate an algorithm that computes the Selmer group of any rational 3-isogeny. We apply these techniques to a family of elliptic curves that allow both types of descent. We force elements into the Selmer group of the 3-isogeny, while we show by 2-descent that the elliptic curves have rank zero. This yields a construction of elements of order 3 in a Tate-Shafarevich group.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Jul 2019 |
| Last Modified: | 16 Jul 2019 12:36 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/20240 |
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