## The modular curve $X_{208j}$

Curve name $X_{208j}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$ $8$ $48$ $X_{96k}$
Meaning/Special name
Chosen covering $X_{208}$
Curves that $X_{208j}$ minimally covers
Curves that minimally cover $X_{208j}$
Curves that minimally cover $X_{208j}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{16} + 108t^{8} - 108$ $B(t) = -432t^{24} + 648t^{16} + 648t^{8} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 87041x - 9854559$, with conductor $16320$
Generic density of odd order reductions $299/2688$