## The modular curve $X_{493}$

Curve name $X_{493}$
Index $96$
Level $32$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 16 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 16 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 16 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{86}$ $16$ $48$ $X_{212}$
Meaning/Special name
Chosen covering $X_{212}$
Curves that $X_{493}$ minimally covers $X_{212}$, $X_{240}$, $X_{353}$
Curves that minimally cover $X_{493}$
Curves that minimally cover $X_{493}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{353}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None