The modular curve $X_{27f}$

Curve name $X_{27f}$
Index $24$
Level $4$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 2 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
Meaning/Special name
Chosen covering $X_{27}$
Curves that $X_{27f}$ minimally covers
Curves that minimally cover $X_{27f}$
Curves that minimally cover $X_{27f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -432t^{6} + 1512t^{4} - 27t^{2}\] \[B(t) = 3456t^{9} + 28512t^{7} - 7128t^{5} - 54t^{3}\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 1221x - 13210$, with conductor $936$
Generic density of odd order reductions $13/84$

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