Curve name  $X_{36h}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{36}$  
Curves that $X_{36h}$ minimally covers  
Curves that minimally cover $X_{36h}$  
Curves that minimally cover $X_{36h}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{8} + 1296t^{6}  21168t^{4} + 124416t^{2}  110592\] \[B(t) = 54t^{12}  3888t^{10} + 110160t^{8}  1524096t^{6} + 10119168t^{4}  23887872t^{2}  14155776\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  27081x + 1667790$, with conductor $1287$  
Generic density of odd order reductions  $19/168$ 