Curve name  $X_{24}$  
Index  $12$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 2 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{8}$  
Curves that $X_{24}$ minimally covers  $X_{8}$, $X_{9}$, $X_{11}$  
Curves that minimally cover $X_{24}$  $X_{58}$, $X_{59}$, $X_{61}$, $X_{66}$, $X_{67}$, $X_{132}$, $X_{141}$, $X_{24a}$, $X_{24b}$, $X_{24c}$, $X_{24d}$, $X_{24e}$, $X_{24f}$, $X_{24g}$, $X_{24h}$  
Curves that minimally cover $X_{24}$ and have infinitely many rational points.  $X_{58}$, $X_{61}$, $X_{66}$, $X_{67}$, $X_{24a}$, $X_{24b}$, $X_{24c}$, $X_{24d}$, $X_{24e}$, $X_{24f}$, $X_{24g}$, $X_{24h}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{24}) = \mathbb{Q}(f_{24}), f_{8} = 2f_{24}^{2}  1\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  240x  469$, with conductor $1845$  
Generic density of odd order reductions  $9/56$ 