Differences between revisions 3 and 11 (spanning 8 versions)
 ⇤ ← Revision 3 as of 2010-06-30 15:19:30 → Size: 645 Editor: GaganSekhon Comment: ← Revision 11 as of 2011-02-12 05:15:41 → ⇥ Size: 759 Editor: GaganSekhon Comment: Deletions are marked like this. Additions are marked like this. Line 4: Line 4: The results of the above program for 2not4 curves is [[attachment:li4.sobj|li4.sobj]] The results of the above program for 2not4 curves is [[attachment:li4.sobj|li4.sobj]] [[attachment:2not4 output.txt|2not4 output.txt]] Line 7: Line 7: I have verified the results of 2not4 list, using a galois approach, which involves compute the order of the Gal(Q(E[4])/Q). The program I used is [[attachment:2not4or4not8galoisapproach.sage|2not4or4not8galoisapproach.sage]] I have verified the results of 2not4 list, using a Galois approach, which involves compute the order of the Gal(Q(E[4])/Q). The program I used is [[attachment:2not4galoisapproachv2.sage|2not4galoisapproachv2.sage]] Line 10: Line 10: The results of the above program for 2not4 curves is [[attachment:li8.sobj|li8.sobj]] The results of the above program for 4not8 curves is [[attachment:li8.sobj|li8.sobj]]I am working on verifying this result using the Galois approach.

I used a Heuristic approach to narrow down the list of elliptic curves for which \rho_{2,E} is surjective mod 2 but not mod 4 or \rho_{2,E} is surjective mod 4 but not mod. 2not4or4not8v3.sage

The results of the above program for 2not4 curves is li4.sobj 2not4 output.txt

I have verified the results of 2not4 list, using a Galois approach, which involves compute the order of the Gal(Q(E[4])/Q). The program I used is 2not4galoisapproachv2.sage

The results of the above program for 4not8 curves is li8.sobj

I am working on verifying this result using the Galois approach.

GaganSekhon (last edited 2011-02-12 05:15:41 by GaganSekhon)