## Heegner points on modular curves

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- by Li Cai, Yihua Chen and Yu Liu PDF
- Trans. Amer. Math. Soc.
**370**(2018), 3721-3743 Request permission

## 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 a 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.## References

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## Additional Information

**Li Cai**- Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
- MR Author ID: 1093027
- Email: lcai@math.tsinghua.edu.cn
**Yihua Chen**- Affiliation: Academy of Mathematics and Systems Science, Morningside center of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- Email: yihuachenamss@163.com
**Yu Liu**- Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: yliu@math.tsinghua.edu.cn
- Received by editor(s): May 31, 2016
- Received by editor(s) in revised form: August 18, 2016, and August 21, 2016
- Published electronically: December 14, 2017
- Additional Notes: The first author was supported by the Special Financial Grant from the China Postdoctoral Science Foundation 2014T70067.
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 3721-3743 - MSC (2010): Primary 11G05, 11G07
- DOI: https://doi.org/10.1090/tran/7053
- MathSciNet review: 3766864