## The modular curve $X_{87a}$

Curve name $X_{87a}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{87}$
Curves that $X_{87a}$ minimally covers
Curves that minimally cover $X_{87a}$
Curves that minimally cover $X_{87a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -6912t^{16} - 34560t^{14} - 72576t^{12} - 82944t^{10} - 56160t^{8} - 23328t^{6} - 6156t^{4} - 1080t^{2} - 108$ $B(t) = 221184t^{24} + 1658880t^{22} + 5557248t^{20} + 10962432t^{18} + 14100480t^{16} + 12317184t^{14} + 7318080t^{12} + 2822688t^{10} + 593568t^{8} + 5616t^{6} - 29808t^{4} - 6480t^{2} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 4575x + 22750$, with conductor $3600$
Generic density of odd order reductions $635/5376$