Attachment '2not4Galoisapproach.sage'

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   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';

Attached Files

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  • [get | view] (2010-07-02 15:46:50, 20.8 KB) [[attachment:2not4 output.txt]]
  • [get | view] (2010-06-30 15:14:30, 0.8 KB) [[attachment:2not4Galoisapproach.sage]]
  • [get | view] (2010-06-30 16:32:36, 0.8 KB) [[attachment:2not4Galoisapproachv2.sage]]
  • [get | view] (2010-06-30 15:22:48, 0.8 KB) [[attachment:2not4galoisapproach.sage]]
  • [get | view] (2010-06-30 15:14:49, 11.3 KB) [[attachment:2not4or4not8v3.sage]]
  • [get | view] (2010-06-30 15:15:11, 1.7 KB) [[attachment:li4.sobj]]
  • [get | view] (2010-06-30 15:15:27, 1.6 KB) [[attachment:li8.sobj]]
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