The modular curve $X_{223d}$

Curve name $X_{223d}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{13h}$
$8$ $48$ $X_{102p}$
Meaning/Special name
Chosen covering $X_{223}$
Curves that $X_{223d}$ minimally covers
Curves that minimally cover $X_{223d}$
Curves that minimally cover $X_{223d}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -452984832t^{16} - 452984832t^{14} - 84934656t^{12} + 7077888t^{10} + 1105920t^{8} + 110592t^{6} - 20736t^{4} - 1728t^{2} - 27\] \[B(t) = 3710851743744t^{24} + 5566277615616t^{22} + 2435246456832t^{20} + 202937204736t^{18} - 51640270848t^{16} - 8153726976t^{14} + 396361728t^{12} - 127401984t^{10} - 12607488t^{8} + 774144t^{6} + 145152t^{4} + 5184t^{2} + 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 34x + 68$, with conductor $102$
Generic density of odd order reductions $53/896$

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