Curve name  $X_{302}$  
Index  $48$  
Level  $16$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 13 & 7 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 13 & 10 \\ 2 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{63}$  
Curves that $X_{302}$ minimally covers  $X_{63}$, $X_{105}$, $X_{166}$  
Curves that minimally cover $X_{302}$  
Curves that minimally cover $X_{302}$ and have infinitely many rational points.  
Model  \[y^2 = x^3 + x^2  13x  21\]  
Info about rational points  $X_{302}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  7859386910x  268185327947856$, with conductor $30631008$  
Generic density of odd order reductions  $42979/172032$ 