The modular curve $X_{87j}$

Curve name $X_{87j}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 3 \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 $X_{87j}$ minimally covers
Curves that minimally cover $X_{87j}$
Curves that minimally cover $X_{87j}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -6912t^{12} - 20736t^{10} - 24192t^{8} - 13824t^{6} - 4320t^{4} - 864t^{2} - 108\] \[B(t) = -221184t^{18} - 995328t^{16} - 1907712t^{14} - 2032128t^{12} - 1285632t^{10} - 456192t^{8} - 60480t^{6} + 12960t^{4} + 5184t^{2} + 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 183x - 182$, with conductor $360$
Generic density of odd order reductions $691/5376$

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