The modular curve $X_{60}$

Curve name $X_{60}$
Index $24$
Level $4$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
Meaning/Special name
Chosen covering $X_{23}$
Curves that $X_{60}$ minimally covers $X_{20}$, $X_{23}$, $X_{26}$, $X_{27}$
Curves that minimally cover $X_{60}$ $X_{277}$, $X_{278}$, $X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$
Curves that minimally cover $X_{60}$ and have infinitely many rational points. $X_{60a}$, $X_{60b}$, $X_{60c}$, $X_{60d}$
Model \[\mathbb{P}^{1}, \mathbb{Q}(X_{60}) = \mathbb{Q}(f_{60}), f_{23} = \frac{f_{60}^{2} + \frac{1}{2}}{f_{60}}\]
Info about rational points None
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 117x + 918$, with conductor $360$
Generic density of odd order reductions $13/84$

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