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The rank of elliptic curves of the form E_AB: y^2=x^3+A(x-B)^2

Timmeren, L. van (2015) The rank of elliptic curves of the form E_AB: y^2=x^3+A(x-B)^2. Master's Thesis / Essay, Mathematics.

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Abstract

In this thesis we study the group of rational points on elliptic curves E, having the special property that the multiplication by 3-map factors as a product of two isogenies of degree three. We compute the rank of the group of rational points on E. A computer program implementing this will be explained. We present examples of families of such elliptic curves with a higher rank, and we specialize in order to find even higher rank examples over the rational numbers.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:05
Last Modified: 15 Feb 2018 08:05
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/13007

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