Each $p$-adic family has a label of the form "p.f.e.cA", where
- p is the residue field characteristic,
- f is the residue field degree of $K$ over $\mathbb{Q}_p$,
- e is the ramification index of $K$ over $\mathbb{Q}_p$,
- c is the discriminant exponent of $K$ over $\mathbb{Q}_p$,
- A is a lower case letter code, with families sorted by their number of wild segments, then the list of lengths of the wild segments, then the rams.
Each $p$-adic field $K$ has a label of the form "p.f.e.cAi.j", where
- p.f.e.cA is the label of the family containing the field
- i is a positive integer code, shared among fields in the same family with equivalent residual polynomials, sorted lexicographically by coefficients of the residual polynomial.
- j is a positive integer code, ordering fields in a given family with the same residual polynomials by their defining polynomial, sorted lexicographically.
Prior to 2025, local fields in the LMFDB had a different label convention, of the form p.n.c.num, where n was the degree and num was an integer code from an unspecified ordering. If you have a field label in the old form, the website will translate it to the new label if you enter it in the "Find" box at the bottom of the browse page.