A rational diagonal is easier to draw, c=ab means a line b on the x axis and a up on the y axis; a line through cutting the both axes at these point is c. But what else?
The effect of not allowing other numbers for c is an incomplete set of spaced ellipses.
But what look like a ellipse is an ellipse. Since every ellipse can be drawn on a pixelized computer screen, there are finite number of rational points on every ellipse. Birch and Swinnerton-Dyer conjecture is half proven!
The latter part of the Conjecture, "...and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K", suggests an irrational coefficient, possibly involving √2 and π.
Dithering is after the ellipse has been drawn. A kind of fuzz to made the lines smooth.
A made-up question to plot ellipse on cartesian points. Not fun.
Note: c is used to general the ellipse; rational c, plots rational points on the ellipse. If c not rational move diagonal to next rational points and start there.
