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!