## The modular curve $X_{202f}$

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
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$
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 $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27648t^{16} - 3207168t^{14} - 5059584t^{12} + 4119552t^{10} - 1226880t^{8} + 1029888t^{6} - 316224t^{4} - 50112t^{2} - 108$ $B(t) = 1769472t^{24} - 456523776t^{22} - 5109350400t^{20} - 563576832t^{18} + 606818304t^{16} + 3849928704t^{14} - 3232051200t^{12} + 962482176t^{10} + 37926144t^{8} - 8805888t^{6} - 19958400t^{4} - 445824t^{2} + 432$
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 $271/2688$