Curve name  $X_{32d}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 3 & 3 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{32}$  
Curves that $X_{32d}$ minimally covers  
Curves that minimally cover $X_{32d}$  
Curves that minimally cover $X_{32d}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 108t^{8}  5184t^{6}  84672t^{4}  497664t^{2}  442368\] \[B(t) = 432t^{12}  31104t^{10}  881280t^{8}  12192768t^{6}  80953344t^{4}  191102976t^{2} + 113246208\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  12008x  502488$, with conductor $2400$  
Generic density of odd order reductions  $289/1792$ 