ELLIPTIC CURVES (SECOND EDITION)Author(s): James S Milne\nFormat: Paperback\nPublisher: World Scientific Publishing Co Pte Ltd, Singapore\nImprint: World Scientific Publishing Co Pte Ltd\nISBN-13: 9789811274039, 978-9811274039\nSynopsis\nThis book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate [url] elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers .