Moes, Levi (2022) On Elliptic Curves over the Rationals Containing Points of Order 3. Bachelor's Thesis, Mathematics.
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Abstract
In this paper we will discuss the group structure of elliptic curves over Q which contain a rational point of order 3, namely we will use 3-descent to prove that the group of rational points for such a curve is finitely generated abelian. This shows the methods used to prove the subcase of Mordell’s theorem for Elliptic Curves with a rational point of order 2 can be adapted to the case at hand. We shall finish by showing that the methods used in this thesis can provide bounds on the rank of curves of the form y 2 = x 3 + A2 (ax − b) 2 where all coefficients are rational
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Top, J. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 28 Jul 2022 11:53 |
| Last Modified: | 23 Aug 2022 10:41 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27949 |
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