The modular curve $X_{102i}$

Curve name $X_{102i}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
Meaning/Special name
Chosen covering $X_{102}$
Curves that $X_{102i}$ minimally covers
Curves that minimally cover $X_{102i}$
Curves that minimally cover $X_{102i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{12} - 864t^{11} + 864t^{10} + 13824t^{9} - 15552t^{8} - 76032t^{7} + 183168t^{6} - 76032t^{5} - 250560t^{4} + 483840t^{3} - 400896t^{2} + 165888t - 27648\] \[B(t) = 432t^{18} + 5184t^{17} + 5184t^{16} - 117504t^{15} - 145152t^{14} + 1451520t^{13} + 145152t^{12} - 10077696t^{11} + 13488768t^{10} + 17266176t^{9} - 68719104t^{8} + 102021120t^{7} - 129862656t^{6} + 174182400t^{5} - 189444096t^{4} + 138018816t^{3} - 62373888t^{2} + 15925248t - 1769472\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 1195616x + 502673184$, with conductor $5880$
Generic density of odd order reductions $635/5376$

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