## The modular curve $X_{200a}$

Curve name $X_{200a}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25n}$
Meaning/Special name
Chosen covering $X_{200}$
Curves that $X_{200a}$ minimally covers
Curves that minimally cover $X_{200a}$
Curves that minimally cover $X_{200a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -6912t^{16} + 27648t^{14} - 435456t^{12} + 822528t^{10} - 721440t^{8} + 205632t^{6} - 27216t^{4} + 432t^{2} - 27$ $B(t) = -221184t^{24} + 1327104t^{22} + 25546752t^{20} - 110702592t^{18} + 314316288t^{16} - 432470016t^{14} + 285562368t^{12} - 108117504t^{10} + 19644768t^{8} - 1729728t^{6} + 99792t^{4} + 1296t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 1664x - 9804$, with conductor $336$
Generic density of odd order reductions $53/896$