The modular curve $X_{228g}$

Curve name $X_{228g}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{84j}$
Meaning/Special name
Chosen covering $X_{228}$
Curves that $X_{228g}$ minimally covers
Curves that minimally cover $X_{228g}$
Curves that minimally cover $X_{228g}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 216t^{16} + 10368t^{15} + 200448t^{14} + 2073600t^{13} + 11943936t^{12} + 28532736t^{11} - 97763328t^{10} - 1088225280t^{9} - 4255580160t^{8} - 8705802240t^{7} - 6256852992t^{6} + 14608760832t^{5} + 48922361856t^{4} + 67947724800t^{3} + 52546240512t^{2} + 21743271936t + 3623878656\] \[B(t) = 1512t^{24} + 62208t^{23} + 891648t^{22} - 497664t^{21} - 211921920t^{20} - 3762339840t^{19} - 37545984000t^{18} - 247892410368t^{17} - 1105883725824t^{16} - 3052041928704t^{15} - 2647413227520t^{14} + 17094288605184t^{13} + 81972361691136t^{12} + 136754308841472t^{11} - 169434446561280t^{10} - 1562645467496448t^{9} - 4529699740975104t^{8} - 8122938502938624t^{7} - 9842454429696000t^{6} - 7890198520135680t^{5} - 3555459826974720t^{4} - 66795331387392t^{3} + 957399749885952t^{2} + 534362651099136t + 103903848824832\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 + 3x + 3$, with conductor $192$
Generic density of odd order reductions $271/2688$

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