Elliptic curves

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]

Using `implicitcurve`

    const board = JXG.JSXGraph.initBoard('jxgbox', {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 c = board.create('implicitcurve', [(x, y) => x*x*x + a.Value() * x + b.Value() - y * y],
        {strokeWidth:3,strokeColor:'black'});

Using two function graphs

Use

[math]\displaystyle{ y^2=x^3+ax+b \quad\Longrightarrow\quad y=\pm\sqrt{x^3+ax+b} }[/math]

This approach is somewhat outdated.

    const board = JXG.JSXGraph.initBoard('jxgbox1', {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'});

References

• http://en.wikipedia.org/wiki/Elliptic_curves