The modular curve $X_{119b}$

Curve name	$X_{119b}$
Index	$48$
Level	$16$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 1 & 1 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 3 \end{matrix}\right]$
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	$X_{119}$
Curves that $X_{119b}$ minimally covers
Curves that minimally cover $X_{119b}$
Curves that minimally cover $X_{119b}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -27t^{8} - 432t^{6} - 2160t^{4} - 3456t^{2} - 432$$ $$B(t) = -54t^{12} - 1296t^{10} - 11664t^{8} - 48384t^{6} - 89424t^{4} - 51840t^{2} + 3456$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 = x^3 + x^2 - 3200x - 70752$, with conductor $120$
Generic density of odd order reductions	$47/672$

Back to the 2-adic image homepage.