On the independence of Heegner points associated to distinct quadratic imaginary fields

Details On the independence of Heegner points associated to distinct quadratic imaginary fields On the independence of Heegner points associated to distinct quadratic imaginary fields

2005-08-15

arxiv.org/abs/math/0508259v2

Journal of Number Theory 127 (2007), 10--36

Mathematics

Number Theory

22 pages

Scientific paper

Let E/Q be an elliptic curve with a fixed modular parametrization F : X_0(N) --> E and let P_1,...,P_r be Heegner points on E attached to the rings of integers of distinct quadratic imaginary field k_1,...,k_r. We prove that if the odd parts of the class numbers of k_1,...,k_r are larger than a constant C=C(E,F) depending only on E and F, then the points P_1,...,P_r are independent in E/(torsion). We also discuss a possible application to the elliptic curve discrete logarithm problem.

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