Curve name  $X_{202f}$  
Index  $96$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{202}$  
Curves that $X_{202f}$ minimally covers  
Curves that minimally cover $X_{202f}$  
Curves that minimally cover $X_{202f}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27648t^{16}  3207168t^{14}  5059584t^{12} + 4119552t^{10}  1226880t^{8} + 1029888t^{6}  316224t^{4}  50112t^{2}  108\] \[B(t) = 1769472t^{24}  456523776t^{22}  5109350400t^{20}  563576832t^{18} + 606818304t^{16} + 3849928704t^{14}  3232051200t^{12} + 962482176t^{10} + 37926144t^{8}  8805888t^{6}  19958400t^{4}  445824t^{2} + 432\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  58497x  5412897$, with conductor $1344$  
Generic density of odd order reductions  $271/2688$ 