Titlebook: Rational Points on Elliptic Curves; Joseph H. Silverman,John T. Tate Textbook 2015Latest edition Springer International Publishing Switzer

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Textbook 2015Latest editionnal numbers. It is this number theoretic question that is the main subject of .Rational Points on Elliptic Curves.. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation

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Complex Multiplication,d to use some basic theorems about extension fields and Galois groups, but nothing very fancy. We start by reminding you of most of the facts that we need, and you can look in any basic algebra text such as [14, 23, 26] for the proofs and additional background material.

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Points of Finite Order, study of points of finite order on cubic curves by looking at points of order two and order three. As usual, we will assume that our non-singular cubic curve is given by a Weierstrass equation . and that the point at infinity . is taken to be the zero element for the group law.

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Integer Points on Cubic Curves,), then the set of all rational points on . forms a finitely generated abelian group. So we can get every rational point on . by starting from some finite set and adding points using the geometrically defined group law.

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Complex Multiplication,ean points of finite order with arbitrary complex coordinates, not just the ones with rational coordinates that we studied in Chapter 2 So we will need to use some basic theorems about extension fields and Galois groups, but nothing very fancy. We start by reminding you of most of the facts that we

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