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Rational Points on Elliptic Curves

  • Textbook
  • © 1992

Overview

Authors:
  1. Joseph H. Silverman

    1. Department of Mathematics, Brown University, Providence, USA

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    You can also search for this author in PubMed   Google Scholar

  2. John Tate

    1. Department of Mathematics, University of Texas at Austin, Austin, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • Joseph H. Silverman, John Tate
    Pages 1-8

  3. Geometry and Arithmetic

    • Joseph H. Silverman, John Tate
    Pages 9-37

  4. Points of Finite Order

    • Joseph H. Silverman, John Tate
    Pages 38-62

  5. The Group of Rational Points

    • Joseph H. Silverman, John Tate
    Pages 63-106

  6. Cubic Curves over Finite Fields

    • Joseph H. Silverman, John Tate
    Pages 107-144

  7. Integer Points on Cubic Curves

    • Joseph H. Silverman, John Tate
    Pages 145-179

  8. Complex Multiplication

    • Joseph H. Silverman, John Tate
    Pages 180-219

  9. Back Matter

    Pages 220-284
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Keywords

About this book

In 1961 the second author deliv1lred a series of lectures at Haverford Col­ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran­ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por­ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter­ est in the theory of elliptic curves for subjects ranging from cryptogra­ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig­ inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove.

Reviews

From the reviews:

"The authors' goal has been to write a textbook in a technically difficult field which is accessible to the average undergraduate mathematics major, and it seems that they have succeeded admirably..."--MATHEMATICAL REVIEWS

"This is a very leisurely introduction to the theory of elliptic curves, concentrating on an algebraic and number-theoretic viewpoint. It is pitched at an undergraduate level and simplifies the work by proving the main theorems with additional hypotheses or by only proving special cases. … The examples really pull together the material and make it clear. … a great book for a first introduction to the subject of elliptic curves. … very clearly written and you will understand a lot when you are done." (Allen Stenger, The Mathematical Association of America, August, 2008)

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    Joseph H. Silverman

  • Department of Mathematics, University of Texas at Austin, Austin, USA

    John Tate

Bibliographic Information

  • Book Title: Rational Points on Elliptic Curves

  • Authors: Joseph H. Silverman, John Tate

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-4252-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1992

  • Hardcover ISBN: 978-0-387-97825-3Published: 24 June 1992

  • Softcover ISBN: 978-1-4419-3101-6Published: 01 December 2010

  • eBook ISBN: 978-1-4757-4252-7Published: 17 April 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: X, 281

  • Topics: Algebraic Geometry

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