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Answer by Noam D. Elkies for The action of a subgroup of the torsion group of...

The subgroup $\hat T$ cannot contain any integral points because each $t \in \hat T$ is the $t$-translate of the origin which is not an integral point.Therefore by Nagell-Lutz $\hat T$ is either...

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Answer by user6671 for The action of a subgroup of the torsion group of...

I will try to answer question 1. on my own as good as I can:Consider two cases:1.) $\hat{T} \cap E(\mathbb{Z}) \neq \emptyset$Let $Q$ be an element in this intersection. Then $-Q \in \hat{T}$ and...

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The action of a subgroup of the torsion group of elliptic curves on integral...

Let $E$ be an elliptic curve given in long Weierstraß form with all coefficients $a_1,a_2,a_3,a_4,a_6 \in \mathbb{Z}$. It is known that the rational points $E(\mathbb{Q})$ form a group which has a...

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