03557nam 22007334a 450 991114286030332120260415134150.09786612194283978128219428112821942839783110198010311019801010.1515/9783110198010(CKB)1000000000520524(EBL)314064(OCoLC)232160036(SSID)ssj0000145537(PQKBManifestationID)11157522(PQKBTitleCode)TC0000145537(PQKBWorkID)10156991(PQKB)10878980(MiAaPQ)EBC314064(DE-599)GBV587951869(DE-B1597)32314(OCoLC)979837887(DE-B1597)9783110198010(Au-PeEL)EBL314064(CaPaEBR)ebr10194841(CaONFJC)MIL219428(PPN)175506612(PPN)140782052(Perlego)652762(EXLCZ)99100000000052052420021210d2003 uy 0engurun#---|u||utxtccrElliptic curves a computational approach /Susanne Schmitt, Horst G. Zimmer ; with an appendix by Attila Petho1st ed.Berlin ;New York Walter de Gruyterc20031 online resource (377 p.)De Gruyter studies in mathematics ;31Description based upon print version of record.9783110168082 3110168081 Includes bibliographical references (p. [351]-363) and index.Front matter --Contents --Chapter 1. Elliptic curves --Chapter 2. Elliptic curves over the complex numbers --Chapter 3. Elliptic curves over finite fields --Chapter 4. Elliptic curves over local fields --Chapter 5. The Mordell-Weil theorem and heights --Chapter 6. Torsion group --Chapter 7. The rank --Chapter 8. Basis --Chapter 9. S-integral points --Appendix A. Algorithmic theory of diophantine equations --Appendix B. Multiquadratic number fields --Back matterThe purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.Gruyter studies in mathematics ;31.Curves, EllipticCurves, Elliptic.516.3/52SK 240rvkSchmitt Susanne241073Zimmer Horst G55314MiAaPQMiAaPQMiAaPQBOOK9911142860303321Elliptic curves1746872UNINA