Curve name  $X_{115}$  
Index  $24$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 12 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{32}$  
Curves that $X_{115}$ minimally covers  $X_{32}$  
Curves that minimally cover $X_{115}$  $X_{314}$, $X_{334}$, $X_{115a}$, $X_{115b}$, $X_{115c}$, $X_{115d}$, $X_{115e}$, $X_{115f}$, $X_{115g}$, $X_{115h}$  
Curves that minimally cover $X_{115}$ and have infinitely many rational points.  $X_{115a}$, $X_{115b}$, $X_{115c}$, $X_{115d}$, $X_{115e}$, $X_{115f}$, $X_{115g}$, $X_{115h}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{115}) = \mathbb{Q}(f_{115}), f_{32} = \frac{2}{f_{115}^{2}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  18x  27$, with conductor $360$  
Generic density of odd order reductions  $13/84$ 