LEADER 03489nam 22006854a 450 001 9910451756403321 005 20210524210605.0 010 $a1-282-19428-3 010 $a9786612194283 010 $a3-11-019801-0 024 7 $a10.1515/9783110198010 035 $a(CKB)1000000000520524 035 $a(EBL)314064 035 $a(OCoLC)232160036 035 $a(SSID)ssj0000145537 035 $a(PQKBManifestationID)11157522 035 $a(PQKBTitleCode)TC0000145537 035 $a(PQKBWorkID)10156991 035 $a(PQKB)10878980 035 $a(MiAaPQ)EBC314064 035 $a(DE-599)GBV587951869 035 $a(DE-B1597)32314 035 $a(OCoLC)979837887 035 $a(DE-B1597)9783110198010 035 $a(PPN)175506612$9sudoc 035 $a(PPN)140782052 035 $a(Au-PeEL)EBL314064 035 $a(CaPaEBR)ebr10194841 035 $a(CaONFJC)MIL219428 035 $a(EXLCZ)991000000000520524 100 $a20021210d2003 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic curves$b[electronic resource] $ea computational approach /$fSusanne Schmitt, Horst G. Zimmer ; with an appendix by Attila Petho? 210 $aBerlin ;$aNew York $cWalter de Gruyter$dc2003 215 $a1 online resource (377 p.) 225 1 $aDe Gruyter studies in mathematics ;$v31 300 $aDescription based upon print version of record. 311 0 $a3-11-016808-1 320 $aIncludes bibliographical references (p. [351]-363) and index. 327 $tFront matter --$tContents --$tChapter 1. Elliptic curves --$tChapter 2. Elliptic curves over the complex numbers --$tChapter 3. Elliptic curves over finite fields --$tChapter 4. Elliptic curves over local fields --$tChapter 5. The Mordell-Weil theorem and heights --$tChapter 6. Torsion group --$tChapter 7. The rank --$tChapter 8. Basis --$tChapter 9. S-integral points --$tAppendix A. Algorithmic theory of diophantine equations --$tAppendix B. Multiquadratic number fields --$tBack matter 330 $aThe purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available. 410 0$aGruyter studies in mathematics ;$v31. 606 $aCurves, Elliptic 608 $aElectronic books. 615 0$aCurves, Elliptic. 676 $a516.3/52 686 $aSK 240$2rvk 700 $aSchmitt$b Susanne$0241073 701 $aZimmer$b Horst G$055314 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451756403321 996 $aElliptic curves$91746872 997 $aUNINA