The modular curve $X_{195e}$

Curve name $X_{195e}$
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 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 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 $X_{195e}$ minimally covers
Curves that minimally cover $X_{195e}$
Curves that minimally cover $X_{195e}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -442368t^{24} + 6414336t^{20} - 414720t^{16} - 1022976t^{12} - 25920t^{8} + 25056t^{4} - 108\] \[B(t) = -113246208t^{36} - 3652190208t^{32} + 4671406080t^{28} + 1734082560t^{24} - 554729472t^{20} - 138682368t^{16} + 27095040t^{12} + 4561920t^{8} - 222912t^{4} - 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 + 55967x + 2732063$, with conductor $4800$
Generic density of odd order reductions $271/2688$

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