Attachment '2not4galoisapproach.sage'
Download 1 x = QQ['x'].0
2 for A in load("/sagedatafor2not4or4not8/li4"):
3 E=EllipticCurve(A);
4 rho=E.galois_representation();
5 if E.has_cm()==False and rho.is_surjective(2):
6 F=factor(E.division_polynomial(4));
7 l=len([p for p,e in F if p.degree()==6]);
8 if l!=0:
9 for p,e in F:
10 if p.degree()==6:
11 g(x)=p(x/2)*2^6;
12 K.<a>=NumberField(g(x));
13 L.<b>=K.galois_closure();
14 D=L.degree();
15 if D !=48:
16 print E.label(),":", D;
17
18 else:
19 print E.label(),"division polynomial does not have a degree 6 factor, so maximum order of galois group is 36, which is not 48";
20 print 'done';
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