On the independence of Heegner points associated to distinct quadratic imaginary fields
Number Theory
2011-05-30 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0508259,
title = {On the independence of Heegner points associated to distinct quadratic imaginary fields},
author = {Michael Rosen and Joseph H. Silverman},
journal= {arXiv preprint arXiv:math/0508259},
year = {2011}
}
Comments
22 pages