# elliptic curve equation for F2^m field

what will be the elliptic curve equation for the following code after executing in sagemath.` for the equation

E: y^2+xy=x^3+ax^2+b

R.<x> = PolynomialRing( GF(2) ) K.<x> = GF( 2**113, modulus = X^113 + X^9 + 1 ); a=003088250CA6E7C7FE649CE85820F7 b=00e8bee4d3e2260744188be0e9c723

E = EllipticCurve( K, [ 1,a, 0, 0, b ] );E

The given code cannot be executed since:

`X`

, not defined in advance as a generator of the polynomial ring over $\mathbb F_2 =$`GF(2)`

.`a, b`

should be elements of`K`

(supposed to be already defined with characteristic two), but as they come there is no immediate coercion.Note on the human readability. Using

`x`

as the name of the generator for`K`

will be confusing when asking for the equation of the curve, which by default uses`x,y`

as variables, so i will use`u`

. So:Which is now the question?