## The modular curve $X_{102l}$

Curve name $X_{102l}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$
Meaning/Special name
Chosen covering $X_{102}$
Curves that $X_{102l}$ minimally covers
Curves that minimally cover $X_{102l}$
Curves that minimally cover $X_{102l}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{12} - 216t^{11} + 216t^{10} + 3456t^{9} - 3888t^{8} - 19008t^{7} + 45792t^{6} - 19008t^{5} - 62640t^{4} + 120960t^{3} - 100224t^{2} + 41472t - 6912$ $B(t) = -54t^{18} - 648t^{17} - 648t^{16} + 14688t^{15} + 18144t^{14} - 181440t^{13} - 18144t^{12} + 1259712t^{11} - 1686096t^{10} - 2158272t^{9} + 8589888t^{8} - 12752640t^{7} + 16232832t^{6} - 21772800t^{5} + 23680512t^{4} - 17252352t^{3} + 7796736t^{2} - 1990656t + 221184$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 1912x - 32782$, with conductor $147$
Generic density of odd order reductions $25/224$