## The modular curve $X_{118i}$

Curve name $X_{118i}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $24$ $X_{36l}$
Meaning/Special name
Chosen covering $X_{118}$
Curves that $X_{118i}$ minimally covers
Curves that minimally cover $X_{118i}$
Curves that minimally cover $X_{118i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{8} + 432t^{4} - 432$ $B(t) = -54t^{12} + 1296t^{8} - 6480t^{4} - 3456$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 130000x - 18051943$, with conductor $195$
Generic density of odd order reductions $5/84$