?

For fun I came up with the idea of programming an ai that plays qwop. For all those that haven't played that excellent game yet:

http://www.foddy.net/Athletics.html

I have 2 main problems here:

1. How do I make my program play in the first place. Is there an easy way to simulate keyboard inputs for example.

2. Is there a way to find out if the game is over and what score it got? If it was in html you could somehow read the sourcecode and find your answer, but I am not even sure there is a way with flash ...

I run often run cpu and memory intensive programs on my pc.

But my pc is not the newest and I don't want it to run overnight all the time.

So what would be the cheapest way to do so?

A second pc that is heavy on cpu and neglects things like graphic card etc.

Or are there better/cheaper way?

I'm working through a paper and at some point it says:

"x²y-xy²+x²z+y²+z+5xz²-10z³=0

is birationally equivalent to the elliptic curve

Y² = X³-2X+1

with rational rank 0."

I have a book about elliptic curves here, but it didn't help much ...

How do I get to the elliptic curve from the equation? Is it (mainly) guesswork or is there another way?

Also it would be nice if you could tell me if there is an easy way to show that is has rational rank 0.

I don't need the complete calculations, just some hints or nudges in the right direction would probably help :)