Curve name  $X_{167}$  
Index  $24$  
Level  $16$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 2 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{30}$  
Curves that $X_{167}$ minimally covers  $X_{30}$  
Curves that minimally cover $X_{167}$  $X_{295}$, $X_{297}$, $X_{419}$, $X_{423}$  
Curves that minimally cover $X_{167}$ and have infinitely many rational points.  $X_{295}$, $X_{297}$  
Model  \[y^2 = x^3 + x^2 + x + 1\]  
Info about rational points  $X_{167}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  None. All the rational points lift to covering modular curves.  
Generic density of odd order reductions  N/A 