The modular curve $X_{92c}$

Curve name	$X_{92c}$
Index	$48$
Level	$8$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$
Meaning/Special name
Chosen covering	$X_{92}$
Curves that $X_{92c}$ minimally covers
Curves that minimally cover $X_{92c}$
Curves that minimally cover $X_{92c}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -108t^{14} + 6696t^{12} - 27540t^{10} + 41904t^{8} - 27540t^{6} + 6696t^{4} - 108t^{2}$$ $$B(t) = 432t^{21} + 53136t^{19} - 611712t^{17} + 2274048t^{15} - 4139424t^{13} + 4139424t^{11} - 2274048t^{9} + 611712t^{7} - 53136t^{5} - 432t^{3}$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy + y = x^3 - x^2 + 136120x + 66792372$, with conductor $2925$
Generic density of odd order reductions	$307/2688$

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