Number field label (reviewed)

Each (global) number field has a unique label of the form d.r.D.i where

• \(d\) is the degree;
• \(r\) is the real signature; the full signature is therefore \([r,(d-r)/2]\);
• \(D\) is the absolute value of the discriminant;
• \(i\) is the index, counting from 1. This is in case there is more than one field with the same signature and absolute value of the discriminant: for example 4.0.1008.1 and 4.0.1008.2.

The discriminant portion of the label can take the form \(a_1\) e \(\epsilon_1\) _ \(a_2\) e \(\epsilon_2\) _ \(\cdots\) _ \(a_k\) e \(\epsilon_k\) to mean the absolute value of the discriminant equals \(a_1^{\epsilon_1}a_2^{\epsilon_2}\cdots a_k^{\epsilon_k}\). The separators are the letter e and the underscore symbol.