The modular curve $X_{235p}$

Curve name	$X_{235p}$
Index	$96$
Level	$32$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 5 & 0 \\ 16 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 0 & 15 \end{matrix}\right]$
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 $X_{235p}$ minimally covers
Curves that minimally cover $X_{235p}$
Curves that minimally cover $X_{235p}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -108t^{26} - 432t^{25} + 432t^{24} + 3024t^{23} + 1512t^{22} - 1296t^{21} - 1296t^{20} - 11664t^{19} - 6804t^{18} + 2592t^{17} - 6048t^{16} + 9504t^{15} - 3024t^{14} - 9504t^{13} - 6048t^{12} - 2592t^{11} - 6804t^{10} + 11664t^{9} - 1296t^{8} + 1296t^{7} + 1512t^{6} - 3024t^{5} + 432t^{4} + 432t^{3} - 108t^{2}$$ $$B(t) = 432t^{39} + 2592t^{38} - 25056t^{36} - 34992t^{35} + 41472t^{34} + 96768t^{33} + 124416t^{32} + 202176t^{31} - 155520t^{30} - 414720t^{29} - 155520t^{28} - 451008t^{27} + 290304t^{26} + 870912t^{25} + 373248t^{24} + 1246752t^{23} + 388800t^{22} + 388800t^{20} - 1246752t^{19} + 373248t^{18} - 870912t^{17} + 290304t^{16} + 451008t^{15} - 155520t^{14} + 414720t^{13} - 155520t^{12} - 202176t^{11} + 124416t^{10} - 96768t^{9} + 41472t^{8} + 34992t^{7} - 25056t^{6} + 2592t^{4} - 432t^{3}$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy = x^3 + x^2 + 5250x + 112500$, with conductor $1050$
Generic density of odd order reductions	$1091/10752$

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