publication . Thesis

Applications of S-unit equations to the arithmetic of elliptic curves

Koutsianas, Angelos;
Open Access English
  • Country: United Kingdom
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.\ud \ud The method is implemented in the mathematical software Sage ([Dev16]) and examples are included in this thesis.\ud
free text keywords: QA
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; tn) . For each Q 2 S we de ne K. Wildanger. Uber das Losen von Einheiten- und Indexformgleichungen in algebraischen Zahlkorpern. J. Number Theory, 82(2):188{224, 2000.

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