Curve name  $X_{20b}$  
Index  $16$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 0 \\ 3 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 1 & 0 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{20}$  
Curves that $X_{20b}$ minimally covers  
Curves that minimally cover $X_{20b}$  
Curves that minimally cover $X_{20b}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{8} + 648t^{7}  4212t^{6}  2376t^{5} + 60102t^{4} + 79704t^{3}  105732t^{2}  235224t  107811\] \[B(t) = 54t^{12}  1944t^{11} + 24300t^{10}  97848t^{9}  251262t^{8} + 1722384t^{7} + 4821768t^{6}  8697456t^{5}  64323558t^{4}  140447736t^{3}  157012020t^{2}  90561240t  21346578\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy + y = x^3  x^2 + 4x  1$, with conductor $162$  
Generic density of odd order reductions  $71/168$ 