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Record Nr. |
UNINA9910782193903321 |
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Autore |
Schmitt Susanne |
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Titolo |
Elliptic curves [[electronic resource] ] : a computational approach / / Susanne Schmitt, Horst G. Zimmer ; with an appendix by Attila Pethòˆ |
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Pubbl/distr/stampa |
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Berlin ; ; New York, : Walter de Gruyter, c2003 |
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ISBN |
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1-282-19428-3 |
9786612194283 |
3-11-019801-0 |
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Descrizione fisica |
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1 online resource (377 p.) |
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Collana |
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De Gruyter studies in mathematics ; ; 31 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [351]-363) and index. |
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Nota di contenuto |
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Front matter -- Contents -- Chapter 1. Elliptic curves -- Chapter 2. Elliptic curves over the complex numbers -- Chapter 3. Elliptic curves over finite fields -- Chapter 4. Elliptic curves over local fields -- Chapter 5. The Mordell-Weil theorem and heights -- Chapter 6. Torsion group -- Chapter 7. The rank -- Chapter 8. Basis -- Chapter 9. S-integral points -- Appendix A. Algorithmic theory of diophantine equations -- Appendix B. Multiquadratic number fields -- Back matter |
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Sommario/riassunto |
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The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available. |
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