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Keywords:
elliptic curve; Mordell-Weil group; canonical height
elliptic curve; Mordell-Weil group; canonical height
Summary:
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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