x = QQ['x'].0 for A in load("/sagedatafor2not4or4not8/li4"): E=EllipticCurve(A); rho=E.galois_representation(); if E.has_cm()==False and rho.is_surjective(2): F=factor(E.division_polynomial(4)); l=len([p for p,e in F if p.degree()==6]); if l!=0: for p,e in F: if p.degree()==6: g(x)=p(x/2)*2^6; K.=NumberField(g(x)); L.=K.galois_closure(); D=L.degree(); if D !=48: print E.label(),":", D; else: print E.label(),"division polynomial does not have a degree 6 factor, so maximum order of galois group is 36, which is not 48"; print 'done';