Abstract
In this paper, we study the Heegner points on more general modular curves other than X 0 ( N ) X_0(N) , which generalizes Gross’ work “Heegner points on X 0 ( N ) X_0(N) ”. The explicit Gross-Zagier formula and the Euler system property are stated in this case. Using such a kind of Heegner points, we construct certain families of quadratic twists of X 0 ( 36 ) X_0(36) , with the ranks of Mordell-Weil groups being zero and one respectively, and show that the 2 2 -part of their BSD conjectures hold.
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