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Elliptic curves: group law
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/elliptic-curves-group-law" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Elliptic curves: group law" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
 
<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';
 
    JXG.Options.label.autoposition = true;
    
    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        axis: true
    });
    
    var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], {strokeWidth: 2});
    var A = board.create('glider', [-1.5, 0, curve]);
    var B = board.create('glider', [0, 1, curve]);
    var line = board.create('line', [A, B], {color: 'black', strokeWidth: 1});
    var C = board.create('otherintersection', [line, curve, [A, B]], {color: 'blue'});
    var D = board.create('point', [() => C.X(), () => -C.Y()], {name: '-C = A + B', color: 'blue'});
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
 
Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/
 
const BOARDID = 'your_div_id'; // Insert your id here!
 
JXG.Options.label.autoposition = true;
 
const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: true
});
 
var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], {strokeWidth: 2});
var A = board.create('glider', [-1.5, 0, curve]);
var B = board.create('glider', [0, 1, curve]);
var line = board.create('line', [A, B], {color: 'black', strokeWidth: 1});
var C = board.create('otherintersection', [line, curve, [A, B]], {color: 'blue'});
var D = board.create('point', [() => C.X(), () => -C.Y()], {name: '-C = A + B', color: 'blue'});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Elliptic curves: group law" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   JXG.Options.label.autoposition = true;
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       axis: true
   });
   
   var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], {strokeWidth: 2});
   var A = board.create('glider', [-1.5, 0, curve]);
   var B = board.create('glider', [0, 1, curve]);
   var line = board.create('line', [A, B], {color: 'black', strokeWidth: 1});
   var C = board.create('otherintersection', [line, curve, [A, B]], {color: 'blue'});
   var D = board.create('point', [() => C.X(), () => -C.Y()], {name: '-C = A + B', color: 'blue'});
</jsxgraph>

Visualization of the group law of points on an elliptic curve.

Attention: The curve intersection algorithm always determines CC as the third intersection point. In some constellations CC will coincide with AA or BB. In that cases the result is wrong.

1234−1−2−3−41234−1−2−3−4
A
B
C
-C = A + B
// Define the id of your board in BOARDID
 
JXG.Options.label.autoposition = true;
 
const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: true
});
 
var curve = board.create('implicitcurve', ['-(y**2) + x**3 - 2 * x + 1'], {strokeWidth: 2});
var A = board.create('glider', [-1.5, 0, curve]);
var B = board.create('glider', [0, 1, curve]);
var line = board.create('line', [A, B], {color: 'black', strokeWidth: 1});
var C = board.create('otherintersection', [line, curve, [A, B]], {color: 'blue'});
var D = board.create('point', [() => C.X(), () => -C.Y()], {name: '-C = A + B', color: 'blue'});

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.