The modular curve $X_{92k}$

Curve name $X_{92k}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{27}$
$8$ $24$ $X_{92}$
Meaning/Special name
Chosen covering $X_{92}$
Curves that $X_{92k}$ minimally covers
Curves that minimally cover $X_{92k}$
Curves that minimally cover $X_{92k}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -27t^{12} + 1566t^{10} - 405t^{8} - 3996t^{6} - 405t^{4} + 1566t^{2} - 27\] \[B(t) = -54t^{18} - 6966t^{16} + 35640t^{14} + 52920t^{12} - 67716t^{10} - 67716t^{8} + 52920t^{6} + 35640t^{4} - 6966t^{2} - 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 + 1635864x + 2783551536$, with conductor $40560$
Generic density of odd order reductions $41/336$

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