Another graph of an elliptic curve

After playing with the graphing program on my son's iPad for a while, I tried using it to plot a few 3-dimensional graphs. The first thing that I tried was to look at the elliptic curve

y² = x³ - 2x +2

When you graph this curve it looks like this:

Another way to think of this curve is as the intersection of the surfaces defined by

z = y² - x³

and

z = 2x - 2

When I plotted those surfaces on the iPad, here's what I got (roughly looking down the y-axis):

Here's another point of view that shows a better view the intersection of the two surfaces (roughly looking down the x-axis):

 

And here's another point of view that's roughly looking down the z-axis:

I'm not sure that point of view really provides any useful insight into elliptic curves, but it seemed sort of interesting.