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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
Format: djvu
Page: 296
ISBN: 3540978259, 9783540978251
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Program of Literka "Elliptic Curve Method" is mainly for illustration of addition of rational points on an elliptic curve. Position: Location: Field of Science: Science - Math - Number Theory - Elliptic Curves and Modular Forms. Since it is a degree two cover, it is necessarily Galois, and {C} has a hyperelliptic involution {\iota: C \rightarrow C} over {\mathbb{ P}^1} with those is an elliptic curve (once one chooses an origin on {C} ), and the hyperelliptic . Heavily on the fact that E has a rational point of finite rank. We discuss its resolved elliptic fibrations over a general base B. 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. Name: Institution: Rational Points on Elliptic Curves. It can be downloaded from www.literka.addr.com/mathcountry/numth/ecm.zip. 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. This number depends only on the Kodaira symbol of the Jacobian and on an auxiliary rational point. Count the number of minimisations of a genus one curve defined over a Henselian discrete valuation field. Website / Blog: www.math.rutgers.edu/~tunnell/math574.html. In other words, it is a two-sheeted cover of {\mathbb{P}^1} , and the sheets come together at {2g + 2} points. We perform explicit computations on the special fibers of minimal proper regular models of elliptic curves. Moreover, it is a unirational variety: it admits a dominant rational map from a projective space. The book surveys some recent developments in the arithmetic of modular elliptic curves.