## The modular curve $X_{140}$

Curve name $X_{140}$
Index $24$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 3 & 1 \\ 6 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{26}$
Meaning/Special name
Chosen covering $X_{26}$
Curves that $X_{140}$ minimally covers $X_{26}$, $X_{45}$, $X_{53}$
Curves that minimally cover $X_{140}$ $X_{275}$, $X_{277}$, $X_{387}$, $X_{403}$
Curves that minimally cover $X_{140}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{53}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None
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