Tables of Fields With Prescribed Ramification

Note: At some point in the future, the data included here will also be found on the website of Dr. Jones (my thesis advisor, not to be confused with Indiana Jones).

The tables require some explanation. Let S be a finite set of primes. We are interested in the fields which are unramified outside of the set S, and this is what we mean by "prescribed ramification". A classical result from number theory tells us that the number of such fields is finite. Unless stated otherwise, the tables presented below are complete in the sense that every field is listed.

The field data is partitioned by Galois group. Each row in a table gives the numbers of each type of field and the total number of fields. The last two columns give links to the actual field data in two different formats: text and gp.

In some cases, to reduce the width of the tables, we partition the results into new and old fields. A field is said to be old if it's Galois closure is the compositum of smaller degree fields; otherwise, it is said to be new. Note that this definition differs slightly from that in the literature. The key point here is that old fields can be easily generated from tables of smaller degree fields by forming compositums and then computing the subfields of the compositums.