The modular curve $X_{116l}$

Curve name $X_{116l}$
Index $48$
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} 3 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 12 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{13h}$
$8$ $24$ $X_{32l}$
Meaning/Special name
Chosen covering $X_{116}$
Curves that $X_{116l}$ minimally covers
Curves that minimally cover $X_{116l}$
Curves that minimally cover $X_{116l}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -27t^{8} - 432t^{4} - 432\] \[B(t) = 54t^{12} + 1296t^{8} + 6480t^{4} - 3456\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 164x + 740$, with conductor $291$
Generic density of odd order reductions $307/2688$

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