# Difference between revisions of "Elliptic curves"

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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 13:42, 28 February 2014

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]

```
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();
```