## The modular curve $X_{305}$

Curve name $X_{305}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$ $8$ $24$ $X_{92}$
Meaning/Special name
Chosen covering $X_{92}$
Curves that $X_{305}$ minimally covers $X_{92}$, $X_{118}$, $X_{168}$
Curves that minimally cover $X_{305}$ $X_{478}$, $X_{479}$, $X_{544}$, $X_{603}$, $X_{636}$, $X_{638}$
Curves that minimally cover $X_{305}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{168}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None