Rational points on elliptic curves [electronic resource] / Joseph H. Silverman, John Tate.
Silverman, Joseph H., 1955- author.; Tate, John Torrence, 1925-2019 author.
2015
QA567.2.E44
Available Online

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Title Rational points on elliptic curves [electronic resource] / Joseph H. Silverman, John Tate.
Author Silverman, Joseph H., 1955- author.
Edition Second edition.
ISBN 9783319185880 electronic book
3319185888 electronic book
9783319185873
DOI https://doi.org/10.1007/978-3-319-18588-0
Published Cham : Springer, 2015.
Language English
Description 1 online resource (xxii, 332 pages) : illustrations.
Item Number 10.1007/978-3-319-18588-0 doi
Call Number QA567.2.E44
Dewey Decimal Classification 516.3/52
Summary The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and group structure of elliptic curves, the Nagell-Lutz theorem describing points of finite order, the Mordell-Weil theorem on the finite generation of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 9, 2015).
Added Author Tate, John Torrence, 1925-2019 author.
Series Undergraduate texts in mathematics.
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
Introduction
Geometry and Arithmetic
Points of Finite Order
The Group of Rational Points
Cubic Curves over Finite Fields
Integer Points on Cubic Curves
Complex Multiplication.

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