Saturation of Mordell-Weil Groups of Elliptic Curves over Number Fields
Publication Date
2004
Creator
Abstract
Given a subgroup B of a finitely-generated abelian group A, the saturation B of B is defined to be the largest subgroup of A containing B with finite index.
In this thesis we consider a crucial step in the determination of the Mordell-Weil group of an elliptic curve, E(K). Methods such as Descent may produce subgroups H of E(K) with [H:H]>1. We have determined an algorithm for calculating H given H, and hence for completing the process of finding the Mordell-Weil group. Our method has been implemented in MAGMA with two versions of the programs; one for general number fields K and the other for Q. It builds upon previous work by S. Siksek.
Our problem splits into two. First we can use geometry of numbers arguments to establish an upper bound N for the index [H:H]. Second for each remaining prime p
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
10052
UoN Repository URI
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