The modular curve $X_{187}$

Curve name $X_{187}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 6 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 6 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $24$ $X_{58}$
Meaning/Special name
Chosen covering $X_{58}$
Curves that $X_{187}$ minimally covers $X_{58}$, $X_{98}$, $X_{99}$
Curves that minimally cover $X_{187}$ $X_{449}$, $X_{454}$, $X_{457}$, $X_{459}$, $X_{460}$, $X_{465}$, $X_{187a}$, $X_{187b}$, $X_{187c}$, $X_{187d}$, $X_{187e}$, $X_{187f}$, $X_{187g}$, $X_{187h}$, $X_{187i}$, $X_{187j}$, $X_{187k}$, $X_{187l}$
Curves that minimally cover $X_{187}$ and have infinitely many rational points. $X_{187a}$, $X_{187b}$, $X_{187c}$, $X_{187d}$, $X_{187e}$, $X_{187f}$, $X_{187g}$, $X_{187h}$, $X_{187i}$, $X_{187j}$, $X_{187k}$, $X_{187l}$
Model \[\mathbb{P}^{1}, \mathbb{Q}(X_{187}) = \mathbb{Q}(f_{187}), f_{58} = \frac{-2}{f_{187}^{2}}\]
Info about rational points None
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 491x + 1896$, with conductor $735$
Generic density of odd order reductions $25/224$

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