@article{727574,
      recid = {727574},
      author = {Silverman, Joseph H., and Tate, John Torrence,},
      title = {Rational points on elliptic curves [electronic resource]  /},
      pages = {1 online resource (xxii, 332 pages) :},
      abstract = {The theory of elliptic curves involves a pleasing blend of  algebra, geometry, analysis, and number theory. This book  stresses this interplay as it develops the basic theory,  thereby providing an opportunity for advanced  undergraduates to appreciate the unity of modern  mathematics. At the same time, every effort has been made  to use only methods and results commonly included in the  undergraduate curriculum. This accessibility, the informal  writing style, and a wealth of exercises make Rational  Points on Elliptic Curves an ideal introduction for  students at all levels who are interested in learning about  Diophantine equations and arithmetic geometry. Most  concretely, an elliptic curve is the set of zeroes of a  cubic polynomial in two variables. If the polynomial has  rational coefficients, then one can ask for a description  of those zeroes whose coordinates are either integers or  rational numbers. It is this number theoretic question that  is the main subject of this book. Topics covered include  the geometry and group structure of elliptic curves, the  Nagell-Lutz theorem describing points of finite order, the  Mordell-Weil theorem on the finite generation of the group  of rational points, the Thue-Siegel theorem on the  finiteness of the set of integer points, theorems on  counting points with coordinates in finite fields,  Lenstra's elliptic curve factorization algorithm, and a  discussion of complex multiplication and the Galois  representations associated to torsion points. Additional  topics new to the second edition include an introduction to  elliptic curve cryptography and a brief discussion of the  stunning proof of Fermat's Last Theorem by Wiles et al. via  the use of elliptic curves.},
      url = {http://library.usi.edu/record/727574},
      doi = {https://doi.org/10.1007/978-3-319-18588-0},
}