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Rational points on elliptic curves John Tate, Joseph H. Silverman
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

This process never repeats itself (and so infinitely many rational points may be generated in this way). The most general definition of an elliptic curve, is. By introducting a special point O (point is a rational function. Download Rational Points on Modular Elliptic Curves. [math.NT/0606003] We consider the structure of rational points on elliptic curves in Weierstrass form. In the language of elliptic curves, given a rational point P we are considering the new rational point -2P . Download Rational Points on Modular Elliptic Curves… eBook (PDF). Rational Points on Modular Elliptic Curves book download. Hmmm… The “parametrize by slopes of lines through the origin” is a standard trick to get rational or integral points on an elliptic curve. Rational Points on Elliptic Curves John Tate (Auteur), J.H. E is just a set of points fulfilling an equation that is quadratic in terms of y and cubic in x . Hey, now we know that this is a question in arithmetic statistics! Wei Ho delivered a very Ho talked about how Bhargava and his school are approaching different conjectures on the ranks of elliptic curves. Rational Points on Modular Elliptic Curves Henri Darmon. The Mordell-Weil theorem states that $C(mathbb{Q})$, the set of rational points on $C$, is a finitely generated abelian group. After a nice work lunch with two of my soon-to-be collaborators, I attended Wei Ho's talk in the Current Events Bulletin on “How many rational points does a random curve have?”. The first thing that we should do here is to reduce this equation to the Weierstrass normal form. Order of a pole is similar: b is a pole of order n if n is the largest integer, such that r(x)=\frac{s(x)}{(x-b . Let $C$ be an elliptic curve over $mathbb{Q}$. A very good book written on the subject is "Rational points on Elliptic Curves" by Silverman and Tate.