The modular curve $X_{195b}$

Curve name $X_{195b}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 14 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{27}$
$8$ $48$ $X_{195}$
Meaning/Special name
Chosen covering $X_{195}$
Curves that $X_{195b}$ minimally covers
Curves that minimally cover $X_{195b}$
Curves that minimally cover $X_{195b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -110592t^{24} + 1603584t^{20} - 103680t^{16} - 255744t^{12} - 6480t^{8} + 6264t^{4} - 27\] \[B(t) = -14155776t^{36} - 456523776t^{32} + 583925760t^{28} + 216760320t^{24} - 69341184t^{20} - 17335296t^{16} + 3386880t^{12} + 570240t^{8} - 27864t^{4} - 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 + 13992x + 334512$, with conductor $1200$
Generic density of odd order reductions $5/42$

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