The modular curve $X_{92i}$

Curve name	$X_{92i}$
Index	$48$
Level	$8$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$
Meaning/Special name
Chosen covering	$X_{92}$
Curves that $X_{92i}$ minimally covers
Curves that minimally cover $X_{92i}$
Curves that minimally cover $X_{92i}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -27t^{10} + 1620t^{8} - 3618t^{6} + 1620t^{4} - 27t^{2}$$ $$B(t) = 54t^{15} + 6804t^{13} - 56214t^{11} + 95256t^{9} - 56214t^{7} + 6804t^{5} + 54t^{3}$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy = x^3 + x^2 + 15125x - 2468750$, with conductor $975$
Generic density of odd order reductions	$25/224$

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