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

Curve name $X_{87g}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
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 $X_{87g}$ minimally covers
Curves that minimally cover $X_{87g}$
Curves that minimally cover $X_{87g}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1728t^{16} - 8640t^{14} - 18144t^{12} - 20736t^{10} - 14040t^{8} - 5832t^{6} - 1539t^{4} - 270t^{2} - 27$ $B(t) = 27648t^{24} + 207360t^{22} + 694656t^{20} + 1370304t^{18} + 1762560t^{16} + 1539648t^{14} + 914760t^{12} + 352836t^{10} + 74196t^{8} + 702t^{6} - 3726t^{4} - 810t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 18300x + 182000$, with conductor $14400$
Generic density of odd order reductions $89/672$