Curve name  $X_{120c}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 5 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{120}$  
Curves that $X_{120c}$ minimally covers  
Curves that minimally cover $X_{120c}$  
Curves that minimally cover $X_{120c}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 108t^{8} + 1728t^{6}  8640t^{4} + 13824t^{2}  1728\] \[B(t) = 432t^{12}  10368t^{10} + 93312t^{8}  387072t^{6} + 715392t^{4}  414720t^{2}  27648\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2 + 63x  63$, with conductor $1344$  
Generic density of odd order reductions  $635/5376$ 