Curve name  $X_{326}$  
Index  $48$  
Level  $16$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 15 & 13 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 13 & 10 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{70}$  
Curves that $X_{326}$ minimally covers  $X_{70}$, $X_{112}$, $X_{153}$  
Curves that minimally cover $X_{326}$  
Curves that minimally cover $X_{326}$ and have infinitely many rational points.  
Model  \[y^2 = x^3 + x^2  13x  21\]  
Info about rational points  $X_{326}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  7802175025x + 272281984973281$, with conductor $30631008$  
Generic density of odd order reductions  $42979/172032$ 