Curve name  $X_{126}$  
Index  $24$  
Level  $8$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 1 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{30}$  
Curves that $X_{126}$ minimally covers  $X_{30}$, $X_{40}$, $X_{52}$  
Curves that minimally cover $X_{126}$  $X_{265}$, $X_{266}$, $X_{419}$, $X_{420}$  
Curves that minimally cover $X_{126}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{52}$, which only has finitely many rational points.  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  None  
Generic density of odd order reductions  N/A 