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Rational points on elliptic curves book download

Rational points on elliptic curves by John Tate, Joseph H. Silverman

Rational points on elliptic curves

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Rational points on elliptic curves John Tate, Joseph H. Silverman ebook
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
ISBN: 3540978259, 9783540978251
Format: djvu
Page: 296

It also has It has no dependencies (instead of PARI), because Mark didn't want to have to license sympow under the GPL. We discuss its resolved elliptic fibrations over a general base B. This library is very, very good and fast for doing computations of many functions relevant to number theory, of "class groups of number fields", and for certain computations with elliptic curves. Ratpoints (C library): Michael Stoll's highly optimized C program for searching for certain rational points on hyperelliptic curves (i.e. 5,7 and 11 also have special significance because PSL(2,p) is “exceptional” for these primes. Vector bundles over algebraic curves and counting rational points. We prove that the presentation of a general elliptic curve E with two rational points and a zero point is the generic Calabi-Yau onefold in dP_2. For example the supersingular primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71 are important to moonshine theory as factors of the size of the monster group and as special cases for elliptic curves modulo p. An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring ZN , N=pq for two distinct odd primes p and q. Silverman, John Tate, Rational Points on Elliptic Curves, Springer 1992. Heavily on the fact that E has a rational point of finite rank. Rational Points on Elliptic Curves - Silverman, Tate.pdf. These finite étale coverings admit various symmetry properties arising from the additive and multiplicative structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve. Through Bhargava's work with Arul Shankar and Chris Skinner, he has proven that a positive proportion of elliptic curves have infinitely many rational points and a positive proportion have no rational points. 106, Springer 1986; Advanced Topics in the Arithmetic of Elliptic Curves Graduate Texts in Mathl. Update: also, opinions on books on elliptic curves solicited, for the four or five of you who might have some! Hyperbolic geometry: the metric of Minkowski space-time.

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