## The modular curve $X_{101l}$

Curve name $X_{101l}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25i}$
Meaning/Special name
Chosen covering $X_{101}$
Curves that $X_{101l}$ minimally covers
Curves that minimally cover $X_{101l}$
Curves that minimally cover $X_{101l}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1769472t^{12} + 1769472t^{10} - 691200t^{8} + 131328t^{6} - 12528t^{4} + 648t^{2} - 27$ $B(t) = -905969664t^{18} + 1358954496t^{16} - 870580224t^{14} + 309657600t^{12} - 66023424t^{10} + 8294400t^{8} - 508032t^{6} - 2592t^{4} + 1944t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 7059x - 227950$, with conductor $1008$
Generic density of odd order reductions $25/224$