An animation of elliptic curves

I thought it would be interesting to see what it wold look like if I created an animated GIF from graphs of elliptic curves as one of the coefficients in the Weierstrass form y2 = x3 + ax + b changed.

Here's what I got with the curve y2 = x3 – 2x + b for -4 ≤ b ≤ 8.

Ec 
 

It's actually easy to create animations like these in Mathematica. In the older version (5.1) that I have, here's how you do it:

e = Table[ImplicitPlot[y^2 == x^3 – 2 x + t, {x, -4, 4}, PlotRange->{{-4,4}, {-4,4}}, AspectRatio->1], {t, -4, 8, 0.1}];

Export["C:ec.gif", e, ConversionOptions->{"Loop"->True}]

It's even easier in the newer version, but I don't see a copy of Mathematica 8.0 as being in our budget any time soon.

Leave a Reply

Your email address will not be published. Required fields are marked *