Elliptic curves: Difference between revisions

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An elliptic curve can be written as a plane algebraic curve defined by an equation of the form
An elliptic curve can be written as a plane algebraic curve defined by an equation of the form
:<math>    y^2=x^3+ax+b\,. </math>
:<math>    y^2=x^3+ax+b\,. </math>
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<source lang="html4strict">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
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var c1 = brd.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],
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===References===
* [http://en.wikipedia.org/wiki/Elliptic_curves http://en.wikipedia.org/wiki/Elliptic_curves]


[[Category:Examples]]
[[Category:Examples]]
[[Category:Curves]]

Latest revision as of 11:42, 28 February 2014

An elliptic curve can be written as a plane algebraic curve defined by an equation of the form

[math]\displaystyle{ y^2=x^3+ax+b\,. }[/math]

JXG.Options.axis.strokeColor = '#cccccc';
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true});
brd.suspendUpdate();
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});
var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'});

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

References