% edwards-conic1.tex
%
% Group law on an Edwards curve
%
% Author: Michael Naehrig
% Public domain

\psset{unit=3cm} 
\begin{pspicture}(-1.5,-1.5)(1.5,1.5) 
\psaxes[labels=none, ticks=none, linewidth=.2pt]{->}(0,0)(-1.5,-1.5)(1.5,1.5)  
\psplot[plotstyle=curve]{-1}{1}{1 x x mul sub 1 30 x mul x mul add div sqrt}
\psplot[plotstyle=curve]{-1}{1}{1 x x mul sub 1 30 x mul x mul add div sqrt neg}
\psdots(0,1)(0,-1)(-0.6,0.233)(0.1, 0.873)(-0.366306,0.415076)(0.366306,0.415076)
\psline[linestyle=dashed]{-}(-1.5,0.415076)(1.5,0.415076)
\uput[-55](-0.62,0.28){$P_1$}
\uput[45](0.1,0.873){$P_2$}
\uput[135](-0.366306,0.415076){$P_3$}
\uput[45](0.366306,0.415076){$-P_3$}
\uput[135](-1,0.415076){$L_{1,P_3}$}
\uput[-45](-1.4,0.26){$C$}
\uput[-45](0.4,-0.4){$E_{-30}$}
\uput[135](0,1){$\mathcal{O}$}
\uput[-45](0,-1){$\mathcal{O}'$}
\psplot[plotstyle=curve, linestyle=dashed, dash=10pt 1pt]{-1.5}{0.005}
{0.038386 0.369263 x mul add -0.038386 1.246886 x mul add div}
\psplot[plotstyle=curve, linestyle=dashed, dash=10pt 1pt]{0.065}{1.5}
{0.038386 0.369263 x mul add -0.038386 1.246886 x mul add div}
\end{pspicture}