Curve name  $X_{3a}$  
Index  $4$  
Level  $4$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 2 & 3 \\ 3 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 3 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{3}$  
Curves that $X_{3a}$ minimally covers  
Curves that minimally cover $X_{3a}$  
Curves that minimally cover $X_{3a}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 108t^{6} + 559872t^{4}  967458816t^{2} + 557256278016\] \[B(t) = 432t^{9}  2985984t^{7} + 7739670528t^{5}  8916100448256t^{3} + 3851755393646592t\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy + y = x^3 + 253x  26862$, with conductor $1058$  
Generic density of odd order reductions  $179/336$ 