| 000 -LEADER |
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| fixed length control field |
02411nam a22002417a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20241125161458.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
190204b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387094939 |
| 040 ## - CATALOGING SOURCE |
|---|
| Transcribing agency |
Educational Supplies |
| Original cataloging agency |
ICTS-TIFR |
| 050 ## - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA567 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Joseph H. Silverman |
| 245 ## - TITLE STATEMENT |
|---|
| Title |
The arithmetic of elliptic curves |
| Remainder of title |
: second edition |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
New York: |
| Name of publisher, distributor, etc. |
Springer, |
| Date of publication, distribution, etc. |
[c2009] |
| 300 ## - Physical Description |
|---|
| Pages: |
400 p |
| 490 ## - SERIES STATEMENT |
|---|
| Series statement |
Graduate Texts in Mathematics |
| Volume/sequential designation |
Vol. 106 |
| 505 ## - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
1. Algebraic Varieties<br/>2. Algebraic Curves<br/>3. The Geometry of Elliptic Curves<br/>4. The Formal Group of an Elliptic Curve<br/>5. Elliptic Curves over Finite Fields<br/>6. Elliptic Curves over C<br/>7. Elliptic Curves over Local Fields<br/>8. Elliptic Curves over Global Fields<br/>9. Integral Points on Elliptic Curves<br/>10. Computing the Mordell–Weil Group<br/>11. Algorithmic Aspects of Elliptic Curves |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell–Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points.<br/><br/>For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. --- summary provided by publisher |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
<a href="https://link.springer.com/book/10.1007/978-0-387-09494-6#toc">https://link.springer.com/book/10.1007/978-0-387-09494-6#toc</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Koha item type |
Book |
