The modular curve $X_{235n}$

Curve name	$X_{235n}$
Index	$96$
Level	$32$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 16 & 15 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{102}$ $16$ $48$ $X_{235}$
Meaning/Special name
Chosen covering	$X_{235}$
Curves that $X_{235n}$ minimally covers
Curves that minimally cover $X_{235n}$
Curves that minimally cover $X_{235n}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -27t^{26} - 108t^{25} + 108t^{24} + 756t^{23} + 378t^{22} - 324t^{21} - 324t^{20} - 2916t^{19} - 1701t^{18} + 648t^{17} - 1512t^{16} + 2376t^{15} - 756t^{14} - 2376t^{13} - 1512t^{12} - 648t^{11} - 1701t^{10} + 2916t^{9} - 324t^{8} + 324t^{7} + 378t^{6} - 756t^{5} + 108t^{4} + 108t^{3} - 27t^{2}$$ $$B(t) = 54t^{39} + 324t^{38} - 3132t^{36} - 4374t^{35} + 5184t^{34} + 12096t^{33} + 15552t^{32} + 25272t^{31} - 19440t^{30} - 51840t^{29} - 19440t^{28} - 56376t^{27} + 36288t^{26} + 108864t^{25} + 46656t^{24} + 155844t^{23} + 48600t^{22} + 48600t^{20} - 155844t^{19} + 46656t^{18} - 108864t^{17} + 36288t^{16} + 56376t^{15} - 19440t^{14} + 51840t^{13} - 19440t^{12} - 25272t^{11} + 15552t^{10} - 12096t^{9} + 5184t^{8} + 4374t^{7} - 3132t^{6} + 324t^{4} - 54t^{3}$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy + y = x^3 - x^2 - 3390755x - 2401706253$, with conductor $3150$
Generic density of odd order reductions	$11/112$

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