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arXiv · 1805.04046

Arithmetic of quaternion origami

Rachel Davis·Edray Herber Goins
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Abstract

We study origami $f: C \rightarrow E$ with $G$-Galois cover $Q_8$. For a point $P \in E(\mathbb{Q}) \backslash \left\{ \mathcal{O} \right\}$, we study the field obtained by adjoining to $\mathbb{Q}$ the coordinates of all of the preimages of $P$ under $f$. We find a defining polynomial, $f_{E, Q_8,P}$, for this field and study its Galois group. We give an isomorphism depending on $P$ between a certain subfield of this field and a certain subfield of the 4-division field of the elliptic curve.

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Rachel Davis, Edray Herber Goins. 2018-05-10. Arithmetic of quaternion origami. https://arxiv.org/abs/1805.04046

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