The modular curve $X_{87n}$

Curve name $X_{87n}$
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} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \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 $X_{87n}$ minimally covers
Curves that minimally cover $X_{87n}$
Curves that minimally cover $X_{87n}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -1728t^{12} - 6912t^{10} - 10800t^{8} - 8208t^{6} - 3132t^{4} - 648t^{2} - 108\] \[B(t) = 27648t^{18} + 165888t^{16} + 425088t^{14} + 604800t^{12} + 515808t^{10} + 259200t^{8} + 63504t^{6} - 1296t^{4} - 3888t^{2} - 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 2033x + 6063$, with conductor $4800$
Generic density of odd order reductions $635/5376$

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