Normalized defining polynomial
Invariants
Degree: |
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Signature: |
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Discriminant: |
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Root discriminant: |
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Galois root discriminant: | |||
Ramified primes: |
,
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Discriminant root field: | |||
: |
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This field is not Galois over . | |||
This is not a CM field. | |||
This field has no CM subfields. |
Integral basis (with respect to field generator )
, , , , , , , , , , , , , , , , , , , , , , , , , ,
Monogenic: | Not computed | |
Index: | ||
Inessential primes: | None |
Class group and class number
Ideal class group: | , which has order (assuming GRH) |
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Narrow class group: | , which has order (assuming GRH) |
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Unit group
Rank: |
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Torsion generator: |
(order )
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Fundamental units: |
, , , , , , , , , , , , ,
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Regulator: | (assuming GRH) |
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Class number formula
Galois group
(as 27T211):
A solvable group of order 648 |
The 14 conjugacy class representatives for |
Character table for |
Intermediate fields
3.1.6075.2 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Sibling fields
Degree 9 sibling: | data not computed |
Degree 12 siblings: | data not computed |
Degree 18 siblings: | data not computed |
Degree 24 siblings: | data not computed |
Degree 27 sibling: | data not computed |
Degree 36 siblings: | data not computed |
Minimal sibling: | 9.1.151336128515625.2 |
Frobenius cycle types
Cycle type | R | R |
In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.
Local algebras for ramified primes
Label | Polynomial | Galois group | Slope content | ||||
---|---|---|---|---|---|---|---|
| 3.1.9.18b1.4 | ||||||
3.1.9.18b1.4 | |||||||
3.1.9.18b1.4 | |||||||
| Deg |