Elliptic curve arithmetic [closed]

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the below code is performed mod arithmetic of two polynomial fE and fL over prime field P= 5 and the extension is 5^2. the mod of two polynomial is always third degree polynomial. My fE polynomial is always 3p degree and fL polynomial is p degree. my question is whatever p(large p = 112 bit ,128 bit 160 bit) I will take my mod is always third degree. is it because of any polynomial property.

p=5 A=4 B=4 print"\n p=",p print"\n A=",A print"\n B=",B

F = GF(p) E = EllipticCurve( F, [A,B] );E

S. = PolynomialRing( F ) K. = GF( p**2);#K.modulus#, modulus=W^2+W+1 ) print "\n Modulus of K is =", K.modulus()