## The modular curve $X_{183h}$

Curve name $X_{183h}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{58}$
Meaning/Special name
Chosen covering $X_{183}$
Curves that $X_{183h}$ minimally covers
Curves that minimally cover $X_{183h}$
Curves that minimally cover $X_{183h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{24} - 54t^{20} - 405t^{16} - 756t^{12} - 405t^{8} - 54t^{4} - 27$ $B(t) = 54t^{36} + 162t^{32} - 1620t^{28} - 5292t^{24} - 7128t^{20} - 7128t^{16} - 5292t^{12} - 1620t^{8} + 162t^{4} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 416166x + 83020500$, with conductor $8670$
Generic density of odd order reductions $271/2688$