Curve name  $X_{185l}$  
Index  $96$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{185}$  
Curves that $X_{185l}$ minimally covers  
Curves that minimally cover $X_{185l}$  
Curves that minimally cover $X_{185l}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 110592t^{24}  1714176t^{20}  1762560t^{16}  670464t^{12}  110160t^{8}  6696t^{4}  27\] \[B(t) = 14155776t^{36} + 435290112t^{32} + 1252786176t^{28} + 1164312576t^{24} + 529846272t^{20} + 132461568t^{16} + 18192384t^{12} + 1223424t^{8} + 26568t^{4}  54\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  54008x + 4846512$, with conductor $1200$  
Generic density of odd order reductions  $5/42$ 