Code for Weights of Local Isomorphism Classes

This code is used to compute the weights in Tables 1-4 in an upcoming paper about counting D_4 quartic fields by conductor.

For each isomorphism class of quadratic extensions over Q_2, the code computes global representatives a of K_p^x/K_p^{x2} for each p|2. And, for each a computes the 2-part of the norm of the relative discriminant of K(\sqrt{a})/K and compares that to the 2-part of the discriminant of Q(\sqrt{Nm(a)}).

Running the Code

The code was written in Sage 9.1 but likely would work with earlier versions. To run from the command line:

sage local_weights.sage