## The modular curve $X_{94}$

Curve name $X_{94}$
Index $24$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 4 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$
Meaning/Special name
Chosen covering $X_{27}$
Curves that $X_{94}$ minimally covers $X_{27}$, $X_{34}$, $X_{45}$
Curves that minimally cover $X_{94}$ $X_{231}$, $X_{260}$, $X_{277}$, $X_{376}$, $X_{378}$, $X_{94a}$, $X_{94b}$, $X_{94c}$, $X_{94d}$, $X_{94e}$, $X_{94f}$
Curves that minimally cover $X_{94}$ and have infinitely many rational points. $X_{231}$, $X_{94a}$, $X_{94b}$, $X_{94c}$, $X_{94d}$, $X_{94e}$, $X_{94f}$
Model $\mathbb{P}^{1}, \mathbb{Q}(X_{94}) = \mathbb{Q}(f_{94}), f_{27} = \frac{\frac{1}{2}f_{94}^{2} - 4}{f_{94}^{2} + 8f_{94} + 8}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 5148x - 390528$, with conductor $10080$
Generic density of odd order reductions $289/1792$