## The modular curve $X_{142}$

Curve name $X_{142}$
Index $24$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{25}$
Curves that $X_{142}$ minimally covers $X_{25}$, $X_{30}$, $X_{51}$
Curves that minimally cover $X_{142}$ $X_{244}$, $X_{245}$, $X_{247}$, $X_{249}$, $X_{271}$, $X_{272}$, $X_{273}$, $X_{274}$, $X_{409}$, $X_{410}$, $X_{423}$, $X_{424}$
Curves that minimally cover $X_{142}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{51}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None