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

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

The points P i subscript P i P_{i} generate E . 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. Be a set of generators of the free part of. Hyperbolic geometry: the metric of Minkowski space-time. In particular, you can take Q=P, so that the line PQ is the tangent at P. Be the group of rational points on the curve and let. 5,7 and 11 also have special significance because PSL(2,p) is “exceptional” for these primes. Be the Néron-Tate pairing: where. In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. The first proposition is that an elliptic curve $y^2 = x^3 + A x + B$, with $A,B in Z$, $A geq 0$, cannot contain a rational torsion point of order 5 or 7. The book surveys some recent developments in the arithmetic of modular elliptic curves. The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. Is the canonical height on the elliptic curve. Vector bundles over algebraic curves and counting rational points. Let E / ℚ E ℚ E/mathbb{Q} be an elliptic curve and let { P 1 , … , P r } subscript P 1 normal-… subscript P r {P_{1},ldots,P_{r}} be a set of generators of the free part of E ⁢ ( ℚ ) E ℚ E(mathbb{Q}) , i.e. Graphs of curves y2 = x3 − x and y2 = x3 − x + 1. If two points P, Q on an elliptic curve have rational coordinates then so does P*Q.