Is there any place to go on line for good graphics of how a complex elliptic curve sits as an affine curve in $\mathbb{C}^2$?
The mathematics is well discussed in Drawing elliptic curve and Is the real locus of an elliptic curve the intersection of a torus with a plane?. But I'd like to find graphics.
Mercio asks for pointers. Of course we are all accustomed to drawing 3 real dimensions on a 2-d screen or paper. And the big help here is that the curve has only 2 real dimensions.
So the most direct approach would be to give a 2-d drawing of how the curve would look projected into 3-d. The value of this would depend on finding an good pair of angles to show what is going on. See any number of drawings of tessaracts and other regular 4-d solids online done this way -- some interactive to allow rotation. A graphically simpler approach would be to draw a few intersections of the curve with flat 3-dim sections of $\mathbb{C}^2$, using gradation of colors to indicate successive sections.
For more discussion and great graphics of shapes in 4-d space see https://en.wikipedia.org/wiki/Four-dimensional_space and https://en.wikipedia.org/wiki/3-sphere
http://www.math.purdue.edu/~dvb/ graphs the Weierstrass function of an elliptic curve, and its derivative, using three spatial dimensions plus one color dimension. He gives similar graphics for nodal and cuspidal cubics.
He even gives Maple code for it. Color graphics as four dimensional paper!