Curve name  $X_{272}$  
Index  $48$  
Level  $8$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{98}$  
Curves that $X_{272}$ minimally covers  $X_{98}$, $X_{99}$, $X_{142}$  
Curves that minimally cover $X_{272}$  $X_{448}$, $X_{460}$, $X_{462}$, $X_{465}$  
Curves that minimally cover $X_{272}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{51}$, 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 