## The modular curve $X_{187h}$

Curve name $X_{187h}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 6 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{58}$
Meaning/Special name
Chosen covering $X_{187}$
Curves that $X_{187h}$ minimally covers
Curves that minimally cover $X_{187h}$
Curves that minimally cover $X_{187h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{24} - 216t^{20} - 6480t^{16} - 48384t^{12} - 103680t^{8} - 55296t^{4} - 110592$ $B(t) = 54t^{36} + 648t^{32} - 25920t^{28} - 338688t^{24} - 1824768t^{20} - 7299072t^{16} - 21676032t^{12} - 26542080t^{8} + 10616832t^{4} + 14155776$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 - 251x - 727$, with conductor $75$
Generic density of odd order reductions $11/112$