The modular curve $X_{223h}$

Curve name	$X_{223h}$
Index	$96$
Level	$16$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $48$ $X_{102o}$
Meaning/Special name
Chosen covering	$X_{223}$
Curves that $X_{223h}$ minimally covers
Curves that minimally cover $X_{223h}$
Curves that minimally cover $X_{223h}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -452984832t^{16} - 452984832t^{14} - 84934656t^{12} + 7077888t^{10} + 1105920t^{8} + 110592t^{6} - 20736t^{4} - 1728t^{2} - 27$$ $$B(t) = -3710851743744t^{24} - 5566277615616t^{22} - 2435246456832t^{20} - 202937204736t^{18} + 51640270848t^{16} + 8153726976t^{14} - 396361728t^{12} + 127401984t^{10} + 12607488t^{8} - 774144t^{6} - 145152t^{4} - 5184t^{2} - 54$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 = x^3 - x^2 - 544x - 4352$, with conductor $816$
Generic density of odd order reductions	$215/2688$

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