Curve name  $X_{23}$  
Index  $12$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 2 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  $X_{s}^{+}(4)$  
Chosen covering  $X_{11}$  
Curves that $X_{23}$ minimally covers  $X_{11}$  
Curves that minimally cover $X_{23}$  $X_{58}$, $X_{60}$, $X_{64}$, $X_{65}$, $X_{68}$, $X_{69}$, $X_{76}$, $X_{80}$, $X_{127}$, $X_{136}$, $X_{146}$, $X_{148}$  
Curves that minimally cover $X_{23}$ and have infinitely many rational points.  $X_{58}$, $X_{60}$, $X_{64}$, $X_{65}$, $X_{68}$, $X_{69}$, $X_{76}$, $X_{80}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{23}) = \mathbb{Q}(f_{23}), f_{11} = \frac{8}{f_{23}^{2}  1}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  128x + 540$, with conductor $1176$  
Generic density of odd order reductions  $25/112$ 