03346cam a22004215i 45000010009000000050017000090060019000260070015000450080041000600200018001010200026001190240035001450350026001800400011002060500023002170720017002400720023002570820015002801000034002952100039003292450100003683000022004684900051004905050465005415060043010065201437010496500017024866500025025036500017025286500024025457000016025697100034025857730020026197730063026397760036027028300040027388560146027781131878720190904111254.0m        d        cr  n         130321s1992    xxu|    s    |||| 0|eng d  a9781475742527  a9781441931016 (print)7 a10.1007/978-1-4757-4252-72doi  a(WaSeSS)ssj0000899291  dWaSeSS 4aQA567.2bSIL 2010. 7aPBMW2bicssc 7aMAT0120102bisacsh04a516.352231 aSilverman, Joseph H.eauthor.10aRational Points on Elliptic Curves10aRational Points on Elliptic Curvesh[electronic resource] /cby Joseph H. Silverman, John Tate.  ax, 281 p.:bill.;1 aUndergraduate Texts in Mathematics,x0172-60560 aI Geometry and Arithmetic -- II Points of Finite Order -- III The Group of Rational Points -- IV Cubic Curves over Finite Fields -- V Integer Points on Cubic Curves -- VI Complex Multiplication -- Appendix A Projective Geometry -- 1. Homogeneous Coordinates and the Projective Plane -- 2. Curves in the Projective Plane -- 3. Intersections of Projective Curves -- 4. Intersection Multiplicities and a Proof of Bezout's Theorem -- Exercises -- List of Notation.  aLicense restrictions may limit access.  aIn 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. 0aMathematics. 0aGeometry, algebraic.14aMathematics.24aAlgebraic Geometry.1 aTate, John.2 aSpringerLink (Online service)0 tSpringer eBooks 0tSpringerLink ebooks - Mathematics and Statistics (Archive)08iPrinted edition:z9781441931016 0aUndergraduate Texts in Mathematics,40uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio11318787zFull text available from SpringerLink ebooks - Mathematics and Statistics (Archive)