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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|2not4galoisapproachv2.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]]

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 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)