02830cam a22002655i 4500999001500000005001700015008004100032020001800073041000800091082001800099100002500117245007700142250000600219260003100225300001400256490004000270505046500310520144300775650002402218650002402242700001602266942000702282952013202289952014302421  c4012d401220210924164341.0130321s1992    xxu|||| o    |||| 0|eng    a9783319185873  aeng04a516.35bSIL/R1 aSilverman, Joseph H,10aRational Points on Elliptic Curves /cby Joseph H. Silverman, John Tate.  a2  aHeidelbergbSpringerc2015  axxii, 3321 aUndergraduate Texts in Mathematics,0 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.  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. 0aAlgebraic geometry.14aAlgebraic Geometry.1 aTate, John,  cBK  001040708MATaIITTPbIITTPcREFd2021-09-24iIN29380/21-22l0oREF 516.35 SilR2p07949r2021-09-24 00:00:00w2021-08-17yREF  001040708MATaIITTPbIITTPcGENd2021-09-24eShankar's BookiIN29380/21-22l0o516.35 SIL/Rp07950r2021-09-24 00:00:00w2021-08-17yBK