tikz-gallery-generator

01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34

% This picture represents the group structure of the points of an elliptic
% curve
\begin{tikzpicture}[yscale=.7]
  % The axis
  \draw[->] (-3,    0) -- (3.5,   0);
  \draw[->] ( 0, -3.2) -- (  0, 3.2);

  \clip(-3., -3.2) rectangle (3.5, 3.2);

  % The curve
  \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] 
    plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)});
  \draw[thick, smooth, samples=100, domain=2.0762:3.5] 
    plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)});
  \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] 
    plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)});
  \draw[thick, smooth, samples=100, domain=2.0762:3.5] 
    plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)});

  % The intersection lines
  \draw[thick, color=violet] (     -3, 1.2218) -- (    3.5, 2.5105);
  \draw[thick, color=violet] (-2.5534,   -3.2) -- (-2.5534,    3.2);

  % The intersection points
  \filldraw (                  0,  1.8165902124584950) circle (1.0pt);
  \filldraw ( 2.5927223574355067,  2.3306137033629240) circle (1.0pt);
  \filldraw (-2.5534168046838945,  1.3103592942448403) circle (1.0pt);
  \filldraw (-2.5534168046838945, -1.3103592942526257) circle (1.0pt);

  % The labels
  \draw ( 0,  2.2346057845515620) node[right]{$P$};
  \draw ( 3,  2.6354835353265860) node {$Q$};
  \draw (-2, -1.0195783099751021) node {$P+Q$};
\end{tikzpicture}