The modular curve $X_{94d}$

Curve name $X_{94d}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 4 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $24$ $X_{27h}$
Meaning/Special name
Chosen covering $X_{94}$
Curves that $X_{94d}$ minimally covers
Curves that minimally cover $X_{94d}$
Curves that minimally cover $X_{94d}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 324t^{8} + 5184t^{7} + 13824t^{6} - 124416t^{5} - 732672t^{4} - 995328t^{3} + 884736t^{2} + 2654208t + 1327104\] \[B(t) = 31104t^{11} + 684288t^{10} + 5446656t^{9} + 15925248t^{8} - 14598144t^{7} - 167215104t^{6} - 116785152t^{5} + 1019215872t^{4} + 2788687872t^{3} + 2802843648t^{2} + 1019215872t\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 572x + 14464$, with conductor $1120$
Generic density of odd order reductions $307/2688$

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