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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:707403 |
| Date | January 2016 |
| Creators | Koutsianas, Angelos |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/86760/ |
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