Heegner Points on Modular Curves
Cai, Li · Chen, Yihua · Liu, Yu
Original · EN
In this paper, we study the Heegner points on more general modular curves other than X₀(N), which generalizes Gross' work "Heegner points on X₀(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 X₀(36), with the ranks of Mordell-Weil groups being zero and one respectively, and show that the 2-part of their BSD conjectures hold.
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