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

Curve name $X_{202h}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13h}$
Meaning/Special name
Chosen covering $X_{202}$
Curves that $X_{202h}$ minimally covers
Curves that minimally cover $X_{202h}$
Curves that minimally cover $X_{202h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -6912t^{16} - 801792t^{14} - 1264896t^{12} + 1029888t^{10} - 306720t^{8} + 257472t^{6} - 79056t^{4} - 12528t^{2} - 27$ $B(t) = -221184t^{24} + 57065472t^{22} + 638668800t^{20} + 70447104t^{18} - 75852288t^{16} - 481241088t^{14} + 404006400t^{12} - 120310272t^{10} - 4740768t^{8} + 1100736t^{6} + 2494800t^{4} + 55728t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 14624x + 669300$, with conductor $336$
Generic density of odd order reductions $53/896$