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

Curve name $X_{183b}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 4 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 4 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 4 \\ 6 & 3 \end{matrix}\right]$
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 $X_{183b}$ minimally covers
Curves that minimally cover $X_{183b}$
Curves that minimally cover $X_{183b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{24} + 216t^{20} - 1620t^{16} + 3024t^{12} - 1620t^{8} + 216t^{4} - 108$ $B(t) = 432t^{36} - 1296t^{32} - 12960t^{28} + 42336t^{24} - 57024t^{20} + 57024t^{16} - 42336t^{12} + 12960t^{8} + 1296t^{4} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 89872033x + 325211684063$, with conductor $196800$
Generic density of odd order reductions $299/2688$