The previous tables of number fields have been replaced by the searchable
database below. For the time being, the previous tables are
still accessible here.
Entry blanks for a variable x can be filled in with
- Warning: the most common error is to treat an
entry blank as a bound. All entry blanks describe sets as described
below. So, entering "101" for "|D|" means that D
must equal 101 (so not many fields will be found).
- rd(K) is the root discriminant of the field K,
- grd(K) is the Galois root discriminant of the field K,
i.e., root discriminant of the Galois closure of K.
- Galois groups are entered by T-numbers.
- For ramifying primes, ci is the exponent of
pi in the discriminant of the field.
- r1 and r2 are the number of real
and pairs of complex embeddings for the field
- pmin refers to the smallest ramifying prime
- pmax refers to the largest ramifying prime
- The check box "Only listed primes can ramify" only has meaning if some of
the prime entry blanks pi are filled in, and each such entry
blank is a specific prime. (In general, such a blank could contain "2..11" meaning
that the condition has to be satisfied by any prime between 2 and 11. A query with
an entry of this type will ignore the "Only listed primes can ramify".)
- single values, such as "4", meaning that x = 4.
- ranges, as in "3..7", meaning 3 ≤ x ≤ 7. You can
use I to represent infinity, so "3..I" means x≥ 3.
- combinations of the above separated by commas. So,
"2, 3, 6..11" means x = 2 or x = 3 or 6 ≤ x ≤ 11.
- All values must be non-negative. Including negative values will
likely lead to unexpected results.
- Entry blanks will not do arithmetic for you, so "10^5" will not
produce a meaningful result.
Most fields here were computed by J. Jones and D. Roberts. In addition,
there are fields computed by
J. Voight, as
well as those
from the Bordeaux