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Elliptic curves (with two function graphs)
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<iframe 
    src="http://jsxgraph.org/share/iframe/elliptic-curves" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Elliptic curves (with two function graphs)" 
    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: 3 / 2; width: 100%;" data-ar="3 / 2"></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.axis.strokeColor = '#cccccc';
    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-15, 10, 15, -10],
        axis: true
    });
    
    var b = board.create('slider', [[1, -3], [10, -3], [-10, 2.10, 10]], {name: 'a'});
    var a = board.create('slider', [[1, -4], [10, -4], [-10, -9.52, 10]], {name: 'b'});
    
    var c1 = board.create('functiongraph', [function(x) {
        return Math.sqrt(x * x * x + a.Value() * x + b.Value());
    }], {strokeWidth: 3, strokeColor: 'black'});
    var c2 = board.create('functiongraph', [function(x) {
        return -Math.sqrt(x * x * x + a.Value() * x + b.Value());
    }], {strokeWidth: 3, strokeColor: 'black'});
 </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.axis.strokeColor = '#cccccc';
const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-15, 10, 15, -10],
    axis: true
});

var b = board.create('slider', [[1, -3], [10, -3], [-10, 2.10, 10]], {name: 'a'});
var a = board.create('slider', [[1, -4], [10, -4], [-10, -9.52, 10]], {name: 'b'});

var c1 = board.create('functiongraph', [function(x) {
    return Math.sqrt(x * x * x + a.Value() * x + b.Value());
}], {strokeWidth: 3, strokeColor: 'black'});
var c2 = board.create('functiongraph', [function(x) {
    return -Math.sqrt(x * x * x + a.Value() * x + b.Value());
}], {strokeWidth: 3, strokeColor: 'black'});
<jsxgraph width="100%" aspect-ratio="3 / 2" title="Elliptic curves (with two function graphs)" 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.axis.strokeColor = '#cccccc';
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-15, 10, 15, -10],
       axis: true
   });
   
   var b = board.create('slider', [[1, -3], [10, -3], [-10, 2.10, 10]], {name: 'a'});
   var a = board.create('slider', [[1, -4], [10, -4], [-10, -9.52, 10]], {name: 'b'});
   
   var c1 = board.create('functiongraph', [function(x) {
       return Math.sqrt(x * x * x + a.Value() * x + b.Value());
   }], {strokeWidth: 3, strokeColor: 'black'});
   var c2 = board.create('functiongraph', [function(x) {
       return -Math.sqrt(x * x * x + a.Value() * x + b.Value());
   }], {strokeWidth: 3, strokeColor: 'black'});
</jsxgraph>

Elliptic curves (with two function graphs)

Curves
An elliptic curve can be written as a plane algebraic curve defined by an equation of the form $$y^2=x^3+ax+b\,.$$ Here, simply the two branches $$ y = \pm \sqrt{x^3+ax+b} $$ are plotted with two function graphs. 
// Define the id of your board in BOARDID

JXG.Options.axis.strokeColor = '#cccccc';
const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-15, 10, 15, -10],
    axis: true
});

var b = board.create('slider', [[1, -3], [10, -3], [-10, 2.10, 10]], {name: 'a'});
var a = board.create('slider', [[1, -4], [10, -4], [-10, -9.52, 10]], {name: 'b'});

var c1 = board.create('functiongraph', [function(x) {
    return Math.sqrt(x * x * x + a.Value() * x + b.Value());
}], {strokeWidth: 3, strokeColor: 'black'});
var c2 = board.create('functiongraph', [function(x) {
    return -Math.sqrt(x * x * x + a.Value() * x + b.Value());
}], {strokeWidth: 3, strokeColor: 'black'});

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.