Curve name  $X_{62b}$  
Index  $48$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 5 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{62}$  
Curves that $X_{62b}$ minimally covers  
Curves that minimally cover $X_{62b}$  
Curves that minimally cover $X_{62b}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{8}  1512t^{4}  432\] \[B(t) = 54t^{12}  7128t^{8}  28512t^{4} + 3456\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  3704x  29184$, with conductor $1848$  
Generic density of odd order reductions  $65/896$ 