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

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

The arithmetic of elliptic curves (GTM 106, Springer, 1986)(L)(T)(ISBN 0387962034)(208s).djvuhttp://www.box.net/shared/ks3hlb3evjSilverman J., Tate J. Hyperbolic geometry: the metric of Minkowski space-time. Sub Child Category 1; Sub Child Category 2; Sub Child Category 3. Be the group of rational points on the curve and let. Is the canonical height on the elliptic curve. Count the number of minimisations of a genus one curve defined over a Henselian discrete valuation field. Challenge 4 is a large rational function calculating the "multiply-by-m" map of a point on an elliptic curve. Be a set of generators of the free part of. 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. Vector bundles over algebraic curves and counting rational points. We perform explicit computations on the special fibers of minimal proper regular models of elliptic curves. Be the Néron-Tate pairing: where. 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. This number depends only on the Kodaira symbol of the Jacobian and on an auxiliary rational point. 5,7 and 11 also have special significance because PSL(2,p) is “exceptional” for these primes. 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.