Integral points on elliptic curves over function fields
نویسندگان
چکیده
منابع مشابه
Higher Heegner points on elliptic curves over function fields
Let E be a modular elliptic curve defined over a rational function field k of odd characteristic. We construct a sequence of Heegner points on E, defined over a Zp -tower of finite extensions of k, and show that these Heegner points generate a group of infinite rank. This is a function field analogue of a result of C. Cornut and V. Vatsal.
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Let F be a number field and let K be a quadratic extension of F . The goal of the theory of Stark-Heegner points is to generalize the construction of Heegner points on elliptic curves over quadratic imaginary fields. If F is totally real and K is totally complex (i.e., a CM field), then under fairly general hypotheses, there is a notion of Heegner points on E defined over suitable ring class fi...
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-We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large; it is based on Shanks’s baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2004
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700013586