///////////////////////////////////////////////////////////////////////////
//
// 		"An algorithm for determining torsion growth of elliptic curves"
// 		Enrique González-Jiménez & Filip Najman
//
//      Magma script related to Lemma 2.9 case without 7-isogeny
// 		
//      file: Lemma_2_9_order49.txt
//
///////////////////////////////////////////////////////////////////////////
// 25/3/2019 - Magma 2.24
//////////////////////////////////////////////////////////////////////////


L:=<>;
for j in [-15^3,255^3] do
	E:=MinimalQuadraticTwist(EllipticCurveFromjInvariant(j));
	fac:=Factorization(DivisionPolynomial(E,49) div DivisionPolynomial(E,7));
	deg49:=[ Degree(f[1]) : f in fac];
	printf "j=%o, label=%o, degrees=%o\n",j,CremonaReference(E),deg49;
	L:=Append(L,<j,deg49>);
end for;
assert L eq <<-15^3,[147, 1029 ]>,<255^3,[ 147, 1029 ]>>;
print "Done";
quit;