E:=EllipticCurveWithjInvariant(-3^3*13*479^3/2^14); Factorization(DivisionPolynomial(E,2)); R:=PolynomialRing(Rationals()); K:=NumberField(R![16384/38603997441, 65536/4289333049, 1/4, 1]); //K is the field extension over which E attains a point of order 2. _:=PolynomialRing(K); K1:=ext; //This is K(zeta_7). E1:=ChangeRing(E,K1); Factorization(DivisionPolynomial(E1,7)); //A similar argument can be made for an elliptic curve with j-invariant 3^3*13/2^2.