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Quadratic twists of χ_0(14)

Junhwa Choi School of Mathematics, Korea Institute for Advanced Study, 85 Hoegi-ro, Dongdaemun-gu, Seoul 02455, Republic of Korea Yongxiong Li Yau Mathematical Science Center, Tsinghua University, Beijing, China

Number Theory mathscidoc:2204.24003

Journal of Number Theory, 224, 142-164, 2021.7
In the present paper, we prove the 2-part of Birch and Swinnerton-Dyer conjecture for an explicit infinite family of rank 0 quadratic twists of the modular elliptic curve χ_0(14), using an explicit form of the Waldspurger formula. We also give an explicit infinite family of rank 1 quadratic twists of χ_0(14) whose Tate–Shafarevich group is of odd cardinality.
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@inproceedings{junhwa2021quadratic,
  title={Quadratic twists of χ_0(14)},
  author={Junhwa Choi, and Yongxiong Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422143646354410103},
  booktitle={Journal of Number Theory},
  volume={224},
  pages={142-164},
  year={2021},
}
Junhwa Choi, and Yongxiong Li. Quadratic twists of χ_0(14). 2021. Vol. 224. In Journal of Number Theory. pp.142-164. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422143646354410103.
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