The modular curve $X_{87f}$

Curve name $X_{87f}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{87}$
Curves that $X_{87f}$ minimally covers
Curves that minimally cover $X_{87f}$
Curves that minimally cover $X_{87f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -1728t^{8} - 3456t^{6} - 2160t^{4} - 432t^{2} - 108\] \[B(t) = -27648t^{12} - 82944t^{10} - 93312t^{8} - 48384t^{6} - 7776t^{4} + 2592t^{2} + 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 81x - 81$, with conductor $960$
Generic density of odd order reductions $635/5376$

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