01648nam a2200265 a 4500999001700000020002700017020003000044100002500074245004000099250001800139260003100157300001300188490003500201520081800236650001501054650002401069650002101093650002201114650001801136650001201154650001601166856007001182942000701252952012301259  c13546d13546  a0387094938 (hardcover)  a9780387094939 (hardcover)1 aSilverman, Joseph H.14aThe Arithmetic of Elliptic Curves /  a2nd ed. 2009.  a[S.l.] :bSpringer,c2009.  a514 p. ;1 aGraduate texts in mathematics.  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 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.  aArithmetic  aGeometry, Algebraic  aCurves, Elliptic  aCurves, Algebraic  aNumber theory  aAlgebra  aMathematics40uhttp://www.amazon.com/exec/obidos/ASIN/0387094938/chopaconline-20  cBK  00104070aQUESTCLbQUESTCLd2015-07-28g7984.00l1o516.3SILp52190r2025-04-25 00:00:00s2020-01-29w2015-07-28yBK