In order to refresh my Java skills, I implemented an Applet that visualizes an Elliptic Curve over the real numbers. You can change the parameters of the short Weierstrass equation by moving the two sliders. You can start the animation by pressing the “resume” button. Furthermore, if you click on the curve, you can see the result of the point doubling or point addition operation.
I implemented the Edwards model for Edwards curves. Formulas taken from the EFD. Edwards curves have some nice properties: Fast arithmetic and unified group law (same formula for point addition as point doubling).