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

Curve name $X_{87l}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25i}$
Meaning/Special name
Chosen covering $X_{87}$
Curves that $X_{87l}$ minimally covers
Curves that minimally cover $X_{87l}$
Curves that minimally cover $X_{87l}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -432t^{12} - 1728t^{10} - 2700t^{8} - 2052t^{6} - 783t^{4} - 162t^{2} - 27$ $B(t) = -3456t^{18} - 20736t^{16} - 53136t^{14} - 75600t^{12} - 64476t^{10} - 32400t^{8} - 7938t^{6} + 162t^{4} + 486t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 508x - 1012$, with conductor $1200$
Generic density of odd order reductions $25/224$