The modular curve $X_{242a}$

Curve name $X_{242a}$
Index $96$
Level $32$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 9 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{32k}$
$16$ $48$ $X_{116k}$
Meaning/Special name
Chosen covering $X_{242}$
Curves that $X_{242a}$ minimally covers
Curves that minimally cover $X_{242a}$
Curves that minimally cover $X_{242a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{16} - 1728t^{8} - 1728\] \[B(t) = -432t^{24} - 10368t^{16} - 51840t^{8} + 27648\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 5804x - 170192$, with conductor $1088$
Generic density of odd order reductions $13411/86016$

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