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 ΦE:X0(N)→E and let P1,…,Pr∈E(Q¯) 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 E(Q¯)/Etors.