Geodesic
The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1133-1147
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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.
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.
DOI : 10.21136/CMJ.2021.0238-20
Classification : 11D59, 11G05
Keywords: elliptic curve; Mordell-Weil group; canonical height 
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Rout, Sudhansu Sekhar; Juyal, Abhishek. The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1133-1147. doi: 10.21136/CMJ.2021.0238-20

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