• $$d$$ 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.