Dwarshuis, Arjan (2020) Finding a pointless rational genus one curve with specified automorphism group. Master's Thesis / Essay, Mathematics.
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Abstract
The aim of this thesis is to find an example of genus one curve over the rationals that has no rational points and contains the dihedral group of order 18 in its automorphism group. Three methods to obtain such a curve are investigated. The arises from Poncelet sequences with which some new constructions are explored. A much more direct method involves the use of invariant theory, in which one starts with polynomials invariant under the D_9-action and tries to build a genus one curve from those. Finally, a method using twists of elliptic curves is presented. The first and last method were successful, in both an explicit equation of a curve with the desired properties was found.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 07 Jul 2020 12:12 |
| Last Modified: | 08 Jul 2020 08:51 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22500 |
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