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

Let E/Q be an elliptic curve with no CM and a fixed modular parametrization and let be Heegner points attached to the rings of integers of distinct quadratic imaginary fields k1,…,kr. We prove that if the odd parts of the class numbers of k1,…,kr are larger than a constant C=C(E,ΦE) depending only on E and ΦE, then the points P1,…,Pr are independent in .