## The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

### Joseph H. Silverman

4.22 avg rating
( 32 ratings by Goodreads )

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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

"synopsis" may belong to another edition of this title.

From the Back Cover:

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.

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.

The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.

Dr. Joseph Silverman is a professor at Brown University and has been an instructor or professors since 1982. He was the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards, as well as being a frequently invited lecturer. He is currently a member of the Council of the American Mathematical Society. His research areas of interest are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has co-authored over 120 publications and has had over 20 doctoral students under his tutelage. He has published 9 highly successful books with Springer, including the recently released, An Introduction to Mathematical Cryptography, for Undergraduate Texts in Mathematics.

List Price: US\$ 59.95
US\$ 47.26

Shipping: US\$ 4.15
From India to U.S.A.

Destination, Rates & Speeds

## 1.The Arithmetic Of Elliptic Curves 2Ed (Hb 2009)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 10
Seller:
bookscollection
(Delhi, DELHI, India)
Rating

Book Description Book Condition: Brand New. HARDCOVER, Book Condition New, U.S. EDITION. We Do not Ship APO FPO AND PO BOX. . Printing in English language.NO CD AND ACCESS CODE. Quick delivery by USPS/UPS/DHL/FEDEX/ARAMEX ,Customer satisfaction guaranteed. We may ship the books from Asian regions for inventory purpose. Bookseller Inventory # ABE ORG##CB12379

US\$ 47.26
Convert Currency
Shipping: US\$ 4.15
From India to U.S.A.
Destination, Rates & Speeds

## 2.The Arithmetic of Elliptic Curves (Hardback)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 1
Seller:
The Book Depository US
(London, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., United States, 2009. Hardback. Book Condition: New. 2nd ed. 2009. Language: English . Brand New Book. 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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics. Bookseller Inventory # AAZ9780387094939

US\$ 54.14
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 3.The Arithmetic of Elliptic Curves (Hardback)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 1
Seller:
The Book Depository
(London, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., United States, 2009. Hardback. Book Condition: New. 2nd ed. 2009. Language: English . Brand New Book. 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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics. Bookseller Inventory # AAZ9780387094939

US\$ 55.69
Convert Currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 4.The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 3
Seller:
Chiron Media
(Wallingford, United Kingdom)
Rating

Book Description Springer, 2009. Hardcover. Book Condition: New. Bookseller Inventory # NU-GRD-00659868

US\$ 52.69
Convert Currency
Shipping: US\$ 3.98
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 5.The Arithmetic of Elliptic Curves

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Quantity Available: > 20
Print on Demand
Seller:
Pbshop
(Wood Dale, IL, U.S.A.)
Rating

Book Description Springer-Verlag New York Inc., 2009. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9780387094939

US\$ 53.13
Convert Currency
Shipping: US\$ 3.99
Within U.S.A.
Destination, Rates & Speeds

## 6.The Arithmetic of Elliptic Curves

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Quantity Available: 3
Seller:
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating

Book Description Springer-Verlag New York Inc., 2009. HRD. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # GB-9780387094939

US\$ 47.45
Convert Currency
Shipping: US\$ 11.98
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 7.The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (Hardcover)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Quantity Available: 3
Seller:
Speedy Hen LLC
(Sunrise, FL, U.S.A.)
Rating

Book Description Book Condition: New. Bookseller Inventory # ST0387094938. Bookseller Inventory # ST0387094938

US\$ 59.45
Convert Currency
Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

## 8.The Arithmetic of Elliptic Curves

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: > 20
Seller:
Blackwell's
(Oxford, OX, United Kingdom)
Rating

Book Description Springer New York 2009-05-29, Dordrecht |London, 2009. hardback. Book Condition: New. Bookseller Inventory # 9780387094939

US\$ 52.55
Convert Currency
Shipping: US\$ 7.98
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 9.The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 1
Seller:
THE SAINT BOOKSTORE
(Southport, United Kingdom)
Rating

Book Description Springer. Hardcover. Book Condition: New. New copy - Usually dispatched within 2 working days. Bookseller Inventory # B9780387094939

US\$ 53.13
Convert Currency
Shipping: US\$ 9.23
From United Kingdom to U.S.A.
Destination, Rates & Speeds

## 10.The Arithmetic of Elliptic Curves

ISBN 10: 0387094938 ISBN 13: 9780387094939
New Hardcover Quantity Available: 3
Rating

Book Description Springer-Verlag New York Inc., 2009. Book Condition: New. 2009. 2nd ed. 2009. Hardcover. The theory of elliptic curves is distinguished by the diversity of the methods 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. Series: Graduate Texts in Mathematics. Num Pages: 514 pages, 14 black & white illustrations, 2 black & white tables, biography. BIC Classification: PBF; PBMW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 245 x 165 x 25. Weight in Grams: 912. . . . . . . Bookseller Inventory # V9780387094939