Curve name  $X_{185j}$  
Index  $96$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{185}$  
Curves that $X_{185j}$ minimally covers  
Curves that minimally cover $X_{185j}$  
Curves that minimally cover $X_{185j}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27648t^{16}  414720t^{12}  231552t^{8}  25920t^{4}  108\] \[B(t) = 1769472t^{24} + 55738368t^{20} + 115126272t^{16} + 48771072t^{12} + 7195392t^{8} + 217728t^{4}  432\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  8641x + 311905$, with conductor $960$  
Generic density of odd order reductions  $299/2688$ 