## The modular curve $X_{490}$

Curve name $X_{490}$
Index $96$
Level $32$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 9 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 16 & 3 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 24 & 1 \end{matrix}\right], \left[ \begin{matrix} 13 & 13 \\ 16 & 5 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{85}$ $16$ $48$ $X_{211}$
Meaning/Special name
Chosen covering $X_{211}$
Curves that $X_{490}$ minimally covers $X_{211}$, $X_{243}$, $X_{354}$
Curves that minimally cover $X_{490}$ $X_{720}$, $X_{721}$, $X_{726}$, $X_{727}$
Curves that minimally cover $X_{490}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{354}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None