## The modular curve $X_{95}$

Curve name $X_{95}$
Index $24$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
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 $X_{95}$ minimally covers $X_{27}$, $X_{39}$, $X_{49}$
Curves that minimally cover $X_{95}$ $X_{221}$, $X_{222}$, $X_{259}$, $X_{260}$, $X_{379}$, $X_{381}$, $X_{95a}$, $X_{95b}$, $X_{95c}$, $X_{95d}$, $X_{95e}$, $X_{95f}$, $X_{95g}$, $X_{95h}$
Curves that minimally cover $X_{95}$ and have infinitely many rational points. $X_{221}$, $X_{222}$, $X_{95a}$, $X_{95b}$, $X_{95c}$, $X_{95d}$, $X_{95e}$, $X_{95f}$, $X_{95g}$, $X_{95h}$
Model $\mathbb{P}^{1}, \mathbb{Q}(X_{95}) = \mathbb{Q}(f_{95}), f_{27} = \frac{2}{f_{95}^{2}}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + 5899x + 478973$, with conductor $7275$
Generic density of odd order reductions $289/1792$