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arXiv · 1902.08801

On the $\text{PGL}_{2}$-invariant quadruples of torsion points of elliptic curves

Fedor Bogomolov·Hang Fu
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Abstract

Let $E$ be an elliptic curve and $\pi:E\to\mathbb{P}^{1}$ a standard double cover identifying $\pm P\in E$. It is known that for some torsion points $P_{i}\in E$, $1\leq i\leq4$, the cross ratio of $\{\pi(P_{i})\}_{i=1}^{4}$ is independent of $E$. In this article, we will give a complete classification of such quadruples.

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Fedor Bogomolov, Hang Fu. 2019-02-23. On the $\text{PGL}_{2}$-invariant quadruples of torsion points of elliptic curves. https://doi.org/10.1007/s40879-019-00377-w

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