The modular curve $X_{193f}$

Curve name	$X_{193f}$
Index	$96$
Level	$16$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 0 & 9 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$ $8$ $48$ $X_{193}$
Meaning/Special name
Chosen covering	$X_{193}$
Curves that $X_{193f}$ minimally covers
Curves that minimally cover $X_{193f}$
Curves that minimally cover $X_{193f}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -452984832t^{26} - 905969664t^{25} + 452984832t^{24} + 1585446912t^{23} + 396361728t^{22} - 169869312t^{21} - 84934656t^{20} - 382205952t^{19} - 536150016t^{18} - 828112896t^{17} - 449445888t^{16} - 192872448t^{15} - 162349056t^{14} + 48218112t^{13} - 28090368t^{12} + 12939264t^{11} - 2094336t^{10} + 373248t^{9} - 20736t^{8} + 10368t^{7} + 6048t^{6} - 6048t^{5} + 432t^{4} + 216t^{3} - 27t^{2}$$ $$B(t) = 3710851743744t^{39} + 11132555231232t^{38} - 26903675142144t^{36} - 18786186952704t^{35} + 11132555231232t^{34} + 12987981103104t^{33} + 8349416423424t^{32} - 521838526464t^{31} - 24526410743808t^{30} - 18090402250752t^{29} + 8479876055040t^{28} + 12295820279808t^{27} + 13089449705472t^{26} + 13241652609024t^{25} + 5120540540928t^{24} + 3302599163904t^{23} + 1566534795264t^{22} + 391633698816t^{20} - 206412447744t^{19} + 80008445952t^{18} - 51725205504t^{17} + 12782665728t^{16} - 3001909248t^{15} + 517570560t^{14} + 276037632t^{13} - 93560832t^{12} + 497664t^{11} + 1990656t^{10} - 774144t^{9} + 165888t^{8} + 69984t^{7} - 25056t^{6} + 648t^{4} - 54t^{3}$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy = x^3 + x^2 - 26750x + 976500$, with conductor $1050$
Generic density of odd order reductions	$1091/10752$

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