Curve name  $X_{102p}$  
Index  $48$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  $X_1(8)$  
Chosen covering  $X_{102}$  
Curves that $X_{102p}$ minimally covers  
Curves that minimally cover $X_{102p}$  
Curves that minimally cover $X_{102p}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{8} + 432t^{6}  864t^{5} + 1728t^{3}  2592t^{2} + 1728t  432\] \[B(t) = 54t^{12}  1296t^{10} + 2592t^{9} + 5184t^{8}  25920t^{7} + 42336t^{6}  46656t^{5} + 58320t^{4}  69120t^{3} + 51840t^{2}  20736t + 3456\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  39x + 90$, with conductor $21$  
Generic density of odd order reductions  $5/84$ 