Hasse invariant of a quadratic form

The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt.

The invariant may be computed for a specific symbol φ taking values in the group C2 = {±1}.

[2] In the context of quadratic forms over a local field, the Hasse invariant may be defined using the Hilbert symbol, the unique symbol taking values in C2.

[4] For quadratic forms over a number field, there is a Hasse invariant ±1 for every finite place.

The invariants of a form over a number field are precisely the dimension, discriminant, all local Hasse invariants and the signatures coming from real embeddings.