Basic invariants
Defining polynomial
f(x) | = |
x6+10x4+25x2+32
. |
The roots of f are computed in an extension of Q17 to precision 8.
Minimal polynomial of a generator a of K over Q17:
x2+16x+3
Generators of the action on the roots
r1,…,r6
Cycle notation |
(2,6)(3,5) |
(1,2)(3,6)(4,5) |
Size | Order | Action on
r1,…,r6
| Character value | Complex conjugation |
1 | 1 | () | 2 |
|
1 | 2 | (1,4)(2,5)(3,6) | −2 |
|
3 | 2 | (1,2)(3,6)(4,5) | 0 |
✓ |
3 | 2 | (1,3)(4,6) | 0 |
|
2 | 3 | (1,5,3)(2,6,4) | −1 |
|
2 | 6 | (1,6,5,4,3,2) | 1 |
|