Rational points on elliptic curves John Tate, Joseph H. Silverman
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

We give geometric criteria which relate these models to the minimal proper regular models of the Jacobian elliptic curves of the genus one curves above. This number depends only on the Kodaira symbol of the Jacobian and on an auxiliary rational point. For elliptic curves, one has the Birch and Swinner-Dyer(BSD) conjecture which related the. Mordell-Weil group and the central values of L-Series arsing from counting rational points over finite fields. Elliptic Curves, Modular Forms,. Henri Poincaré studied them in the early years of the 20th century. Similarly, if P is constrained to lie on one of the sides of the square, it becomes equivalent to showing that there are no non-trivial rational points on the elliptic curve y^2 = x^3 - 7x - 6 . Buy Book Elliptic Curves: Number Theory and Cryptography. Rational Points on Elliptic Curves - Google Books The theory of elliptic curves involves a blend of algebra,. Count the number of minimisations of a genus one curve defined over a Henselian discrete valuation field. Kinsey, L.Christine, Topology of Surfaces, 1993 65. Devlin, Keith, The Joy of Sets – Fundamentals of Contemporary Set Theory, 1993 64. Rational Points on Modular Elliptic Curves book download Download Rational Points on Modular Elliptic Curves Request a Print Examination Copy. Elliptic curves have been a focus of intense scrutiny for decades. Home » Book » Elliptic Curves:. Silverman, Joseph H., Tate, John, Rational Points on Elliptic Curves, 1992 63. We perform explicit computations on the special fibers of minimal proper regular models of elliptic curves. This is precisely to look for rational points on the modular surface S parametrizing pairs (E,E',C,C',φ), where E and E' are elliptic curves, C and C' are cyclic 13-subgroups, and φ is an isomorphism between C and C'.