Curve name  $X_{27}$  
Index  $12$  
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], \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{10}$  
Curves that $X_{27}$ minimally covers  $X_{10}$, $X_{11}$, $X_{13}$  
Curves that minimally cover $X_{27}$  $X_{60}$, $X_{92}$, $X_{94}$, $X_{95}$, $X_{134}$, $X_{135}$, $X_{27a}$, $X_{27b}$, $X_{27c}$, $X_{27d}$, $X_{27e}$, $X_{27f}$, $X_{27g}$, $X_{27h}$  
Curves that minimally cover $X_{27}$ and have infinitely many rational points.  $X_{60}$, $X_{92}$, $X_{94}$, $X_{95}$, $X_{27a}$, $X_{27b}$, $X_{27c}$, $X_{27d}$, $X_{27e}$, $X_{27f}$, $X_{27g}$, $X_{27h}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{27}) = \mathbb{Q}(f_{27}), f_{10} = \frac{f_{27}}{f_{27}^{2}  \frac{1}{4}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2 + 885x  4294$, with conductor $1845$  
Generic density of odd order reductions  $9/56$ 