The modular curve $X_{94b}$

Curve name $X_{94b}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $24$ $X_{27f}$
Meaning/Special name
Chosen covering $X_{94}$
Curves that $X_{94b}$ minimally covers
Curves that minimally cover $X_{94b}$
Curves that minimally cover $X_{94b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 81t^{16} + 2592t^{15} + 29376t^{14} + 96768t^{13} - 718848t^{12} - 7188480t^{11} - 16478208t^{10} + 49987584t^{9} + 324919296t^{8} + 399900672t^{7} - 1054605312t^{6} - 3680501760t^{5} - 2944401408t^{4} + 3170893824t^{3} + 7700742144t^{2} + 5435817984t + 1358954496\] \[B(t) = 3888t^{23} + 178848t^{22} + 3480192t^{21} + 35997696t^{20} + 191351808t^{19} + 196466688t^{18} - 3765657600t^{17} - 21297364992t^{16} - 19382796288t^{15} + 225650147328t^{14} + 854697443328t^{13} - 6837579546624t^{11} - 14441609428992t^{10} + 9923991699456t^{9} + 87234007007232t^{8} + 123393068236800t^{7} - 51502563459072t^{6} - 401293826850816t^{5} - 603941121294336t^{4} - 467103463243776t^{3} - 192036577738752t^{2} - 33397665693696t\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 7007x + 620144$, with conductor $15680$
Generic density of odd order reductions $419/2688$

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