The modular curve $X_{227f}$

Curve name $X_{227f}$
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 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{84n}$
Meaning/Special name
Chosen covering $X_{227}$
Curves that $X_{227f}$ minimally covers
Curves that minimally cover $X_{227f}$
Curves that minimally cover $X_{227f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -452984832t^{24} + 13589544960t^{22} - 15344861184t^{20} + 7644119040t^{18} - 3848601600t^{16} + 1167851520t^{14} - 361414656t^{12} + 72990720t^{10} - 15033600t^{8} + 1866240t^{6} - 234144t^{4} + 12960t^{2} - 27\] \[B(t) = 3710851743744t^{36} + 233783659855872t^{34} - 963661812203520t^{32} + 935134639423488t^{30} - 663430713311232t^{28} + 347022620098560t^{26} - 154536681406464t^{24} + 54793045278720t^{22} - 17665389232128t^{20} + 4587490639872t^{18} - 1104086827008t^{16} + 214035333120t^{14} - 37728681984t^{12} + 5295144960t^{10} - 632696832t^{8} + 55738368t^{6} - 3589920t^{4} + 54432t^{2} + 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 + 1892944x - 4740612030$, with conductor $8670$
Generic density of odd order reductions $271/2688$

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