Curve name  $X_{86j}$  
Index  $48$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 5 & 5 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{86}$  
Curves that $X_{86j}$ minimally covers  
Curves that minimally cover $X_{86j}$  
Curves that minimally cover $X_{86j}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{8}  216t^{6} + 1080t^{4} + 6048t^{2}  432\] \[B(t) = 54t^{12}  648t^{10}  9720t^{8}  60480t^{6}  85536t^{4} + 114048t^{2} + 3456\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2 + 80x  80$, with conductor $240$  
Generic density of odd order reductions  $9/112$ 