The modular curve $X_{118g}$

Curve name $X_{118g}$
Index $48$
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 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{36i}$
Meaning/Special name
Chosen covering $X_{118}$
Curves that $X_{118g}$ minimally covers
Curves that minimally cover $X_{118g}$
Curves that minimally cover $X_{118g}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{8} + 1728t^{4} - 1728\] \[B(t) = -432t^{12} + 10368t^{8} - 51840t^{4} - 27648\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 8320001x - 9234274815$, with conductor $12480$
Generic density of odd order reductions $307/2688$

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