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arXiv · 1601.04415

Heegner Points on Modular Curves

Li Cai·Yihua Chen·Yu Liu
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Abstract

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.

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Li Cai, Yihua Chen, Yu Liu. 2016-01-18. Heegner Points on Modular Curves. https://arxiv.org/abs/1601.04415

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