## The modular curve $X_{211m}$

Curve name $X_{211m}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 5 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 9 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $48$ $X_{85l}$
Meaning/Special name
Chosen covering $X_{211}$
Curves that $X_{211m}$ minimally covers
Curves that minimally cover $X_{211m}$
Curves that minimally cover $X_{211m}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} - 12960t^{15} - 232416t^{14} - 1088640t^{13} - 1975104t^{12} + 1451520t^{11} + 5377536t^{10} + 22394880t^{9} + 48176640t^{8} - 89579520t^{7} + 86040576t^{6} - 92897280t^{5} - 505626624t^{4} + 1114767360t^{3} - 951975936t^{2} + 212336640t - 1769472$ $B(t) = 54t^{24} - 54432t^{23} - 3595104t^{22} - 50730624t^{21} - 316540224t^{20} - 838688256t^{19} - 733404672t^{18} + 2414168064t^{17} + 12561246720t^{16} + 20149420032t^{15} + 16335323136t^{14} + 1226244096t^{13} - 268429787136t^{12} - 4904976384t^{11} + 261365170176t^{10} - 1289562882048t^{9} + 3215679160320t^{8} - 2472108097536t^{7} - 3004025536512t^{6} + 13741068386304t^{5} - 20744780120064t^{4} + 13298728697856t^{3} - 3769739771904t^{2} + 228304355328t + 905969664$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 1920800x - 1024800150$, with conductor $210$
Generic density of odd order reductions $1/28$