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

Curve name $X_{183i}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 6 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 6 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 2 & 5 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $48$ $X_{58i}$
Meaning/Special name
Chosen covering $X_{183}$
Curves that $X_{183i}$ minimally covers
Curves that minimally cover $X_{183i}$
Curves that minimally cover $X_{183i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} - 378t^{8} - 27$ $B(t) = -54t^{24} + 1782t^{16} + 1782t^{8} - 54$
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 56170x - 5105305$, with conductor $1230$
Generic density of odd order reductions $19/336$