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Title: Applications of S-unit equations to the arithmetic of elliptic curves
Author: Koutsianas, Angelos
ISNI:       0000 0004 6061 9390
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2016
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Let K be a number field and S a finite set of prime ideals of K. By a classical result of Shafarevich ([Sil86]) we know that there are finitely many isomorphism classes ƸK;S of elliptic curves de ned over K with good reduction outside S. Many people have developed methods of computing ƸK;S explicitly. At the end, all the methods ask for solutions of specific Diophantine equations in order to determine ƸK;S. In this thesis we develop a new algorithmic method of computing EK;S by solving S{unit equations. The method is implemented in the mathematical software Sage ([Dev16]) and examples are included in this thesis.
Supervisor: Not available Sponsor: Akadēmia Athēnōn ; Bekiari-Vekri Foundation
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics