The modular curve $X_{92f}$

Curve name $X_{92f}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \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 $X_{92f}$ minimally covers
Curves that minimally cover $X_{92f}$
Curves that minimally cover $X_{92f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -27t^{14} + 1566t^{12} - 405t^{10} - 3996t^{8} - 405t^{6} + 1566t^{4} - 27t^{2}\] \[B(t) = 54t^{21} + 6966t^{19} - 35640t^{17} - 52920t^{15} + 67716t^{13} + 67716t^{11} - 52920t^{9} - 35640t^{7} + 6966t^{5} + 54t^{3}\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 58891092x + 601364913968$, with conductor $486720$
Generic density of odd order reductions $307/2688$

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