Abstract
In this paper, we give the method of constructing non-torsion points on elliptic curves, which generalizes the classical Birch lemma. As an application, we get more quadratic twist families of the elliptic curve \(X_0(49)\), which have rank one. This report is a combination of the two joint works (Coates, Li, Tian, Zhai, Proc Lond Math Soc 110(2), 357–394, 2015, [4]; Cai, Li, Wang, Sci China Math 59(7), 1307–1326, 2016, [2]).
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Acknowledgements
The author would like to thank Ye Tian to give him a chance to present the joint work in the conference which was hold at Beijing university in the year 2014. The author would also like to thank the organizers of that conference for their hospitality.
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Li, Y. (2019). Quadratic Twists of Elliptic Curves. In: Liang, Z., Aribam, C. (eds) The Computational and Theoretical Aspects of Elliptic Curves. Mathematical Lectures from Peking University. Springer, Singapore. https://doi.org/10.1007/978-981-13-6664-2_4
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DOI: https://doi.org/10.1007/978-981-13-6664-2_4
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