# How to define a polynomial A(x,y) that (x,y) satisfying y^2+y=x^3

I am working on a elliptic curve like `y^2+y=x^3`

over `GF(2^6)`

and i want to define a polynomial `A(x,y)`

over `GF(2^6)`

that `x,y`

satisfying `y^2+y=x^3`

Hope to get your help, thank you!

Please describe mathematically the situation. It is hard to figure out the "map between variables", so maybe we have a map $f$ from a polynomial ring $R$ to some other ring $S$, and the map $f:R\to S$ is determined by the images through $f$ of the generators of $R$.

I have reorganize my language. Thank you a lot for your attention

A polynomial function on your curve is given by an element in the quotient K[x,y] / (y^2 + y - x^3). The answer to your question really depends on what you want to do with such function.

This is what i need! thank you!