Curve name  $X_{60}$  
Index  $24$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{23}$  
Curves that $X_{60}$ minimally covers  $X_{20}$, $X_{23}$, $X_{26}$, $X_{27}$  
Curves that minimally cover $X_{60}$  $X_{277}$, $X_{278}$, $X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$  
Curves that minimally cover $X_{60}$ and have infinitely many rational points.  $X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{60}) = \mathbb{Q}(f_{60}), f_{23} = \frac{f_{60}^{2} + \frac{1}{2}}{f_{60}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + 117x + 918$, with conductor $360$  
Generic density of odd order reductions  $13/84$ 