Summary Tables for 2-adic Fields of Degree 14
By Discriminant and Ramification Index
| e=1 | e=2 | e=7 | e=14 | Total
|
---|
d=0 | 1 | | | | 1
|
---|
12 | | | 1 | | 1
|
---|
14 | | 38 | | 2 | 40
|
---|
16 | | | | 4 | 4
|
---|
18 | | | | 8 | 8
|
---|
20 | | | | 16 | 16
|
---|
21 | | 40 | | | 40
|
---|
22 | | | | 32 | 32
|
---|
24 | | | | 64 | 64
|
---|
26 | | | | 128 | 128
|
---|
27 | | | | 256 | 256
|
---|
Total | 1 | 78 | 1 | 510 | 590
|
---|
By Galois Group and Ramification Index
| e=1 | e=2 | e=7 | e=14 | Total
|
---|
g=1 | 1 | 6 | | | 7
|
---|
5 | | | 1 | 6 | 7
|
---|
6 | | 2 | | | 2
|
---|
9 | | 14 | | | 14
|
---|
11 | | | | 14 | 14
|
---|
18 | | | | 98 | 98
|
---|
21 | | 7 | | | 7
|
---|
29 | | 49 | | | 49
|
---|
35 | | | | 49 | 49
|
---|
44 | | | | 343 | 343
|
---|
Total | 1 | 78 | 1 | 510 | 590
|
---|
By Galois Group and Discriminant
Ramification Index = 1
| d=0 | Total
|
---|
g=1 | 1 | 1
|
---|
Total | 1 | 1
|
---|
Ramification Index = 2
| d=14 | 21 | Total
|
---|
g=1 | 2 | 4 | 6
|
---|
6 | 2 | | 2
|
---|
9 | 6 | 8 | 14
|
---|
21 | 7 | | 7
|
---|
29 | 21 | 28 | 49
|
---|
Total | 38 | 40 | 78
|
---|
Ramification Index = 7
| d=12 | Total
|
---|
g=5 | 1 | 1
|
---|
Total | 1 | 1
|
---|
Ramification Index = 14
| d=14 | 16 | 18 | 20 | 22 | 24 | 26 | 27 | Total
|
---|
g=5 | | | | 2 | | | | 4 | 6
|
---|
11 | 1 | 1 | 2 | | 2 | 4 | 4 | | 14
|
---|
18 | 1 | 1 | 2 | 8 | 6 | 12 | 12 | 56 | 98
|
---|
35 | | 1 | 2 | | 6 | 12 | 28 | | 49
|
---|
44 | | 1 | 2 | 6 | 18 | 36 | 84 | 196 | 343
|
---|
Total | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 510
|
---|