The modular curve $X_{95b}$

Curve name $X_{95b}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 7 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $24$ $X_{27f}$
Meaning/Special name
Chosen covering $X_{95}$
Curves that $X_{95b}$ minimally covers
Curves that minimally cover $X_{95b}$
Curves that minimally cover $X_{95b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{8} + 24192t^{4} - 27648\] \[B(t) = 432t^{12} + 228096t^{8} - 3649536t^{4} - 1769472\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 452x - 6750$, with conductor $7872$
Generic density of odd order reductions $419/2688$

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