Klijn, Vivianne (2022) Points of order 3 on elliptic curves in characteristic 3. Bachelor's Thesis, Mathematics.
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Abstract
In this paper we will study points of order 3 on elliptic curves defined over perfect fields of characteristic 3. First, there is a short introduction on elliptic curves and related concepts. After this, we distinguish the two forms elliptic curves over characteristic 3 can have. We then do specific computations for points of order 3 in these forms. Finally, we classify elliptic curves that contain points of order 3 in characteristic 3 by showing that any elliptic curve with a point of order 3 is isomorphic to some curve in a certain family of elliptic curves. These points of order 3 can be K-rational, for which the work has already been done, but they can also be K( √ d)-rational for some quadratic extension K( √ d) of K.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Top, J. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 28 Jul 2022 11:34 |
| Last Modified: | 04 Apr 2025 08:49 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27853 |
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