The modular curve $X_{215g}$

Curve name	$X_{215g}$
Index	$96$
Level	$16$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 1 & 0 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25i}$ $8$ $48$ $X_{96g}$
Meaning/Special name
Chosen covering	$X_{215}$
Curves that $X_{215g}$ minimally covers
Curves that minimally cover $X_{215g}$
Curves that minimally cover $X_{215g}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -27t^{32} + 1296t^{24} - 27648t^{16} + 331776t^{8} - 1769472$$ $$B(t) = 54t^{48} - 3888t^{40} + 82944t^{32} - 21233664t^{16} + 254803968t^{8} - 905969664$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy + y = x^3 - x^2 - 1130x - 14128$, with conductor $225$
Generic density of odd order reductions	$299/2688$

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