\documentclass[border=1px]{standalone}

\usepackage{pgfplots}
\usepackage{amsmath}
\begin{document}
	\begin{tikzpicture}
		\begin{axis}[legend columns=2,enlarge x limits=false,enlarge y limits=false,xmax=16,ymin=0.04,ymax=0.11,axis on top, xlabel=$N$, ylabel=$\omega_s / \omega_x$,width=6.5cm,height=5.5cm,legend style={overlay, at={(1,0)},anchor=south east},legend cell align=left,tick label style={/pgf/number format/fixed}]
			\addplot[only marks,color=red,mark=x,mark options={scale=1.5}] coordinates { 
(1,0.044256)
(3,0.061453)
   		}; 
   		\addplot[only marks,color=blue,mark=triangle,mark options={scale=1.5}] coordinates { 
(1,0.043986)
(3,0.057571)
(5,0.068645)
(7,0.083195)
(9,0.099472)
	};
	\addplot[only marks,color=orange!90!black,mark=star,mark options={scale=1.5}] coordinates { 
(1,0.043985)
(3,0.0574)
(5,0.068148)
(7,0.077145)
(9,0.085024)
(11,0.092139)
(13,0.099921)
(15,0.10564)
};
	\addplot[style=dashed,color=black,mark options={scale=1.5}] coordinates { 
(1,0.043634)
(3,0.057036)
(5,0.06774)
(7,0.076692)
(9,0.084505)
(11,0.091533)
(13,0.097972)
(15,0.10395)
};
		\legend{$M=4$,$M=8$,$M=16$,GPE};
  		\end{axis}
	\end{tikzpicture}
\end{document}