000			02054 a2200253 4500
003			OSt
005			20210707103157.0
008			210204b xxu||||| |||| 00| 0 eng d
020			_a9780387094946
040			_cIIT Kanpur
041			_aeng
082			_a512 _bSi39a2
100			_aSilverman, Joseph H.
245			_aThe arithmetic of elliptic curves [2nd ed.] [Perpetual] _cJoseph H. Silverman
250			_a2nd ed.
260			_bSpringer _c2009 _aNew York
440			_aGraduate texts in mathematics; v.106
490			_a/ edited by S. Axler and K. A. Ribet
520			_aThe 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.
650			_aArithmetic
650			_aCurves, Algebraic
856			_uhttps://link.springer.com/book/10.1007/978-0-387-09494-6
942			_cEBK
999			_c563587 _d563587