On the independence of Heegner points associated to distinct quadratic imaginary fields
Abstract
Let E/Q be an elliptic curve with a fixed modular parametrization F : X0(N) --> E and let P1,...,Pr be Heegner points on E attached to the rings of integers of distinct quadratic imaginary field k1,...,kr. We prove that if the odd parts of the class numbers of k1,...,kr are larger than a constant C=C(E,F) depending only on E and F, then the points P1,...,Pr are independent in E/(torsion). We also discuss a possible application to the elliptic curve discrete logarithm problem.
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