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