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

Curve name $X_{87p}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
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 $X_{87p}$ minimally covers
Curves that minimally cover $X_{87p}$
Curves that minimally cover $X_{87p}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1728t^{12} - 5184t^{10} - 6048t^{8} - 3456t^{6} - 1080t^{4} - 216t^{2} - 27$ $B(t) = 27648t^{18} + 124416t^{16} + 238464t^{14} + 254016t^{12} + 160704t^{10} + 57024t^{8} + 7560t^{6} - 1620t^{4} - 648t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 732x + 1456$, with conductor $2880$
Generic density of odd order reductions $41/336$