## The modular curve $X_{121l}$

Curve name $X_{121l}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 5 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{36q}$
Meaning/Special name
Chosen covering $X_{121}$
Curves that $X_{121l}$ minimally covers
Curves that minimally cover $X_{121l}$
Curves that minimally cover $X_{121l}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{12} - 1296t^{10} - 6048t^{8} - 13824t^{6} - 15660t^{4} - 7344t^{2} - 432$ $B(t) = 432t^{18} + 7776t^{16} + 59616t^{14} + 254016t^{12} + 656424t^{10} + 1048464t^{8} + 1000944t^{6} + 510624t^{4} + 98496t^{2} - 3456$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 552x + 4984$, with conductor $2880$
Generic density of odd order reductions $41/336$