## The modular curve $X_{183}$

Curve name $X_{183}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 6 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{58}$
Meaning/Special name
Chosen covering $X_{58}$
Curves that $X_{183}$ minimally covers $X_{58}$, $X_{87}$, $X_{101}$
Curves that minimally cover $X_{183}$ $X_{446}$, $X_{447}$, $X_{450}$, $X_{452}$, $X_{454}$, $X_{458}$, $X_{183a}$, $X_{183b}$, $X_{183c}$, $X_{183d}$, $X_{183e}$, $X_{183f}$, $X_{183g}$, $X_{183h}$, $X_{183i}$, $X_{183j}$, $X_{183k}$, $X_{183l}$
Curves that minimally cover $X_{183}$ and have infinitely many rational points. $X_{183a}$, $X_{183b}$, $X_{183c}$, $X_{183d}$, $X_{183e}$, $X_{183f}$, $X_{183g}$, $X_{183h}$, $X_{183i}$, $X_{183j}$, $X_{183k}$, $X_{183l}$
Model $\mathbb{P}^{1}, \mathbb{Q}(X_{183}) = \mathbb{Q}(f_{183}), f_{58} = -f_{183}^{2}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - x^2 - 12960x - 453200$, with conductor $1530$
Generic density of odd order reductions $25/224$