Differences between revisions 4 and 5
 ⇤ ← Revision 4 as of 2010-06-30 15:22:13 → Size: 631 Editor: GaganSekhon Comment: ← Revision 5 as of 2010-06-30 15:24:24 → ⇥ Size: 702 Editor: GaganSekhon Comment: Deletions are marked like this. Additions are marked like this. 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:2not4galoisapproach.sage|2not4galoisapproach.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:2not4galoisapproach.sage|2not4galoisapproach.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

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 2not4galoisapproach.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)