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

Curve name $X_{187f}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 6 & 1 \end{matrix}\right]$
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 $X_{187f}$ minimally covers
Curves that minimally cover $X_{187f}$
Curves that minimally cover $X_{187f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{32} - 20736t^{24} + 718848t^{16} - 5308416t^{8} - 7077888$ $B(t) = 432t^{48} - 248832t^{40} + 7630848t^{32} - 1953497088t^{16} + 16307453952t^{8} - 7247757312$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 144300x + 9758000$, with conductor $14400$
Generic density of odd order reductions $51/448$