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

Curve name $X_{87i}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 3 \end{matrix}\right]$
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 $X_{87i}$ minimally covers
Curves that minimally cover $X_{87i}$
Curves that minimally cover $X_{87i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -6912t^{12} - 20736t^{10} - 24192t^{8} - 13824t^{6} - 4320t^{4} - 864t^{2} - 108$ $B(t) = 221184t^{18} + 995328t^{16} + 1907712t^{14} + 2032128t^{12} + 1285632t^{10} + 456192t^{8} + 60480t^{6} - 12960t^{4} - 5184t^{2} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 183x + 182$, with conductor $720$
Generic density of odd order reductions $635/5376$