# 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 | |||

<math> | :<math> y^2=x^3+ax+b\,. </math> | ||

<jsxgraph width="600" height="400" box="jxgbox"> | |||

</ | 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],[-10,2.10,10]],{name:'a'}); | |||

var a = brd.create('slider',[[1,-4],[10,-4],[-10,-9.52,10]],{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(); | |||

</jsxgraph> | |||

<source lang="javascript"> | |||

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(); | |||

</source> | |||

===References=== | |||

* [http://en.wikipedia.org/wiki/Elliptic_curves http://en.wikipedia.org/wiki/Elliptic_curves] | |||

[[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();
```