[smellybigbelly]

I think part of the reason why 3 is special is because you get a lot of bang for your buck. Order 3 is a low order polynomial that is relatively easy to analyse, but already gives tremendous mathematical properties.

For example, the points of elliptic curves form groups. The operation of combining the points is described in the article (draw a straight line through two points and mirror in x-axis).

That means that all the theorems that are proven for Groups, are also true for elliptic curves.

But I think there are many more exciting properties

Amateur here (just studying abstract algebra for hobby). I’m also very curious for more reasons.