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

Curve name $X_{187b}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 4 \\ 0 & 5 \end{matrix}\right]$
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 $X_{187b}$ minimally covers
Curves that minimally cover $X_{187b}$
Curves that minimally cover $X_{187b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{24} + 864t^{20} - 25920t^{16} + 193536t^{12} - 414720t^{8} + 221184t^{4} - 442368$ $B(t) = 432t^{36} - 5184t^{32} - 207360t^{28} + 2709504t^{24} - 14598144t^{20} + 58392576t^{16} - 173408256t^{12} + 212336640t^{8} + 84934656t^{4} - 113246208$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 5772x + 78064$, with conductor $2880$
Generic density of odd order reductions $73/672$