The modular curve $X_{241c}$

Curve name	$X_{241c}$
Index	$96$
Level	$32$
Genus	$0$
Does the subgroup contain $-I$?	No
Generating matrices	$\left[ \begin{matrix} 5 & 20 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 21 \\ 12 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 21 \\ 4 & 1 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $24$ $X_{32i}$ $16$ $48$ $X_{116i}$
Meaning/Special name
Chosen covering	$X_{241}$
Curves that $X_{241c}$ minimally covers
Curves that minimally cover $X_{241c}$
Curves that minimally cover $X_{241c}$ and have infinitely many rational points.
Model	$\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $$y^2 = x^3 + A(t)x + B(t), \text{ where}$$ $$A(t) = -27t^{16} - 432t^{8} - 432$$ $$B(t) = 54t^{24} - 1620t^{16} - 5184t^{8} - 3456$$
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	$y^2 + xy + y = x^3 - x^2 - 21931x - 1244565$, with conductor $514$
Generic density of odd order reductions	$9827/86016$

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