Curve name  $X_{58}$  
Index  $24$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 2 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{23}$  
Curves that $X_{58}$ minimally covers  $X_{23}$, $X_{24}$, $X_{25}$  
Curves that minimally cover $X_{58}$  $X_{183}$, $X_{186}$, $X_{187}$, $X_{189}$, $X_{248}$, $X_{249}$, $X_{251}$, $X_{255}$, $X_{357}$, $X_{58a}$, $X_{58b}$, $X_{58c}$, $X_{58d}$, $X_{58e}$, $X_{58f}$, $X_{58g}$, $X_{58h}$, $X_{58i}$, $X_{58j}$, $X_{58k}$  
Curves that minimally cover $X_{58}$ and have infinitely many rational points.  $X_{183}$, $X_{187}$, $X_{189}$, $X_{58a}$, $X_{58b}$, $X_{58c}$, $X_{58d}$, $X_{58e}$, $X_{58f}$, $X_{58g}$, $X_{58h}$, $X_{58i}$, $X_{58j}$, $X_{58k}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{58}) = \mathbb{Q}(f_{58}), f_{23} = \frac{f_{58}^{2} + 2f_{58}  1}{f_{58}^{2} + 1}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  40807260x  94524898325$, with conductor $6435$  
Generic density of odd order reductions  $19/168$ 