The modular curve $X_{195j}$

Curve name $X_{195j}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 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 $X_{195}$
Curves that $X_{195j}$ minimally covers
Curves that minimally cover $X_{195j}$
Curves that minimally cover $X_{195j}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -442368t^{24} + 6856704t^{20} - 7050240t^{16} + 2681856t^{12} - 440640t^{8} + 26784t^{4} - 108\] \[B(t) = 113246208t^{36} + 3482320896t^{32} - 10022289408t^{28} + 9314500608t^{24} - 4238770176t^{20} + 1059692544t^{16} - 145539072t^{12} + 9787392t^{8} - 212544t^{4} - 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 20148x + 586096$, with conductor $2880$
Generic density of odd order reductions $73/672$

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