Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\Q$

Abstract

Associated to an open subgroup $G$ of $\GL_2(\Zhat)$ satisfying conditions $-I\in G$ and $\det(G) \subsetneq (\Zhat)^{\times}$ there is a modular curve $X_G$ which is a smooth compact curve defined over an extension of $\Q.$ In this article, we give a complete list of all such prime power level genus $0$ modular curves with a point.

arXiv admin note: substantial text overlap with arXiv:2105.14623