Curve name  $X_{259}$  
Index  $48$  
Level  $8$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{71}$  
Curves that $X_{259}$ minimally covers  $X_{71}$, $X_{91}$, $X_{92}$, $X_{95}$, $X_{134}$, $X_{137}$, $X_{144}$  
Curves that minimally cover $X_{259}$  $X_{453}$, $X_{544}$, $X_{592}$, $X_{593}$, $X_{671}$  
Curves that minimally cover $X_{259}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{53}$, 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 