The modular curve $X_{1}$

Curve name $X_{1}$
Index $1$
Level $1$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices
Images in lower levels
Meaning/Special name $X(1)$
Chosen covering
Curves that $X_{1}$ minimally covers
Curves that minimally cover $X_{1}$ $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$
Curves that minimally cover $X_{1}$ and have infinitely many rational points. $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$
Model $\mathbb{P}^{1} \cong \mathbb{Q}(f_{1})$, where $f_{1} = j$
Info about rational points None
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + y = x^3 - x^2 - 10x - 20$, with conductor $11$
Generic density of odd order reductions $11/21$

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