The modular curve $X_{102b}$

Curve name $X_{102b}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{102}$
Meaning/Special name
Chosen covering $X_{102}$
Curves that $X_{102b}$ minimally covers
Curves that minimally cover $X_{102b}$
Curves that minimally cover $X_{102b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{14} - 648t^{13} + 2484t^{12} + 11232t^{11} - 42336t^{10} - 31104t^{9} + 319680t^{8} - 518400t^{7} + 84672t^{6} + 908928t^{5} - 1619136t^{4} + 1451520t^{3} - 760320t^{2} + 221184t - 27648\] \[B(t) = 432t^{21} + 3888t^{20} - 9072t^{19} - 117936t^{18} + 217728t^{17} + 1529280t^{16} - 4527360t^{15} - 6013440t^{14} + 42705792t^{13} - 53578368t^{12} - 69973632t^{11} + 346488192t^{10} - 659349504t^{9} + 938552832t^{8} - 1203600384t^{7} + 1358760960t^{6} - 1218945024t^{5} + 806547456t^{4} - 374685696t^{3} + 115458048t^{2} - 21233664t + 1769472\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 1101324x + 442162672$, with conductor $28224$
Generic density of odd order reductions $635/5376$

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