The modular curve $X_{236a}$

Curve name $X_{236a}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 0 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{13h}$
$8$ $48$ $X_{85p}$
Meaning/Special name
Chosen covering $X_{236}$
Curves that $X_{236a}$ minimally covers
Curves that minimally cover $X_{236a}$
Curves that minimally cover $X_{236a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -110592t^{24} + 1105920t^{22} + 2598912t^{20} - 46835712t^{18} + 121326336t^{16} - 30827520t^{14} - 131763456t^{12} - 7706880t^{10} + 7582896t^{8} - 731808t^{6} + 10152t^{4} + 1080t^{2} - 27\] \[B(t) = -14155776t^{36} + 212336640t^{34} - 3089498112t^{32} + 27377270784t^{30} - 111635988480t^{28} + 144845438976t^{26} + 269705576448t^{24} - 823468032000t^{22} + 200518447104t^{20} + 595708342272t^{18} + 50129611776t^{16} - 51466752000t^{14} + 4214149632t^{12} + 565802496t^{10} - 109019520t^{8} + 6683904t^{6} - 188568t^{4} + 3240t^{2} - 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 1053712x + 416675008$, with conductor $2352$
Generic density of odd order reductions $299/2688$

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