The modular curve $X_{192}$

Curve name $X_{192}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{85}$
Curves that $X_{192}$ minimally covers $X_{85}$, $X_{96}$, $X_{101}$
Curves that minimally cover $X_{192}$ $X_{451}$, $X_{458}$, $X_{482}$, $X_{483}$, $X_{504}$, $X_{505}$, $X_{506}$, $X_{519}$, $X_{192a}$, $X_{192b}$, $X_{192c}$, $X_{192d}$, $X_{192e}$, $X_{192f}$, $X_{192g}$, $X_{192h}$, $X_{192i}$, $X_{192j}$, $X_{192k}$, $X_{192l}$, $X_{192m}$, $X_{192n}$
Curves that minimally cover $X_{192}$ and have infinitely many rational points. $X_{192a}$, $X_{192b}$, $X_{192c}$, $X_{192d}$, $X_{192e}$, $X_{192f}$, $X_{192g}$, $X_{192h}$, $X_{192i}$, $X_{192j}$, $X_{192k}$, $X_{192l}$, $X_{192m}$, $X_{192n}$
Model $\mathbb{P}^{1}, \mathbb{Q}(X_{192}) = \mathbb{Q}(f_{192}), f_{85} = \frac{8f_{192}}{f_{192}^{2} + 4}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 - 14526053x + 21308093948$, with conductor $25410$
Generic density of odd order reductions $17/168$