Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 1133-1147, 2021
The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$
Sudhansu Sekhar Rout, Abhishek Juyal
Received June 7, 2020. Published online March 22, 2021.
Abstract: Let $D_m$ be an elliptic curve over $\mathbb{Q}$ of the form $y^2 = x^3 -m^2x +m^2$, where $m$ is an integer. In this paper we prove that the two points $P_{-1}=(-m, m)$ and $P_0 = (0, m)$ on $D_m$ can be extended to a basis for $D_m(\mathbb{Q})$ under certain conditions described explicitly.
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Affiliations: Sudhansu Sekhar Rout, Institute of Mathematics & Applications, Andharua, Bhubaneswar 751029, India, e-mail: lbs.sudhansu@gmail.com, sudhansu@iomaorissa.ac.in; Abhishek Juyal (corresponding author), Institute of Mathematical Sciences (HBNI), CIT Campus, Taramani, Chennai 600 113, India, e-mail: abhinfo1402@gmail.com
