TITLE: How do I draw an elliptic curve?
QUESTION [6 upvotes]: I can draw a circle using a compass.
I can draw an ellipse using two focal points and a loop of string.
I think that you can draw an arbitrary conic with a "generalized" compass for which the pencil can slide in and out as it is rotated.
What instruments and devices can draw elliptic curves?

REPLY [3 votes]: I have an answer, for a limited case, and it is not pretty. Elliptic curves have the form:
$y^2= x^3 + ax +b$ 
Suppose $b=0$ and $a < 0$
$y^2= x(x^2 + a)$ 
$y= \sqrt{x}\sqrt{x^2 + a}$  
You can construct $\sqrt{x}$ as shown here.

And, $\sqrt{x^2 + a}$  with $a < 0$ is the distance from (x, -a) to the origin.
We have two constructible lengths so just construct their product:

...and you have y.