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

Curve name $X_{183f}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 4 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
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 $X_{183f}$ minimally covers
Curves that minimally cover $X_{183f}$
Curves that minimally cover $X_{183f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{32} - 1296t^{24} + 2808t^{16} - 1296t^{8} - 108$ $B(t) = 432t^{48} - 15552t^{40} + 29808t^{32} - 29808t^{16} + 15552t^{8} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 + x^2 - 2360545125x - 43782192871875$, with conductor $252150$
Generic density of odd order reductions $51/448$