The modular curve $X_{212i}$

Curve name $X_{212i}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{13h}$
$8$ $48$ $X_{86l}$
Meaning/Special name
Chosen covering $X_{212}$
Curves that $X_{212i}$ minimally covers
Curves that minimally cover $X_{212i}$
Curves that minimally cover $X_{212i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -452984832t^{16} + 6794772480t^{14} - 3822059520t^{12} + 743178240t^{10} - 120987648t^{8} + 11612160t^{6} - 933120t^{4} + 25920t^{2} - 27\] \[B(t) = -3710851743744t^{24} - 116891829927936t^{22} + 241089399226368t^{20} - 111412525400064t^{18} + 30166071902208t^{16} - 5536380616704t^{14} + 824036032512t^{12} - 86505947136t^{10} + 7364763648t^{8} - 425005056t^{6} + 14370048t^{4} - 108864t^{2} - 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 1760x + 52788$, with conductor $240$
Generic density of odd order reductions $19/336$

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