Curve name  $X_{185g}$  
Index  $96$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 3 & 6 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{185}$  
Curves that $X_{185g}$ minimally covers  
Curves that minimally cover $X_{185g}$  
Curves that minimally cover $X_{185g}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 6912t^{16}  103680t^{12}  57888t^{8}  6480t^{4}  27\] \[B(t) = 221184t^{24} + 6967296t^{20} + 14390784t^{16} + 6096384t^{12} + 899424t^{8} + 27216t^{4}  54\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  2160x + 37908$, with conductor $240$  
Generic density of odd order reductions  $19/336$ 