The modular curve $X_{227j}$

Curve name $X_{227j}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{84i}$
Meaning/Special name
Chosen covering $X_{227}$
Curves that $X_{227j}$ minimally covers
Curves that minimally cover $X_{227j}$
Curves that minimally cover $X_{227j}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -7077888t^{16} + 212336640t^{14} - 238878720t^{12} + 92897280t^{10} - 30246912t^{8} + 5806080t^{6} - 933120t^{4} + 51840t^{2} - 108\] \[B(t) = 7247757312t^{24} + 456608710656t^{22} - 1883510931456t^{20} + 1740820709376t^{18} - 942689746944t^{16} + 346023788544t^{14} - 103004504064t^{12} + 21626486784t^{10} - 3682381824t^{8} + 425005056t^{6} - 28740096t^{4} + 435456t^{2} + 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 + 419199x - 493911585$, with conductor $16320$
Generic density of odd order reductions $299/2688$

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