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: | Yes | |
Index: | ||
Inessential primes: | None |
Class group and class number
Ideal class group: | Trivial group, which has order |
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Narrow class group: | Trivial group, which has order |
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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: |
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Class number formula
Galois group
(as 10T45):
A non-solvable group of order 3628800 |
The 42 conjugacy class representatives for |
Character table for |
Intermediate fields
The extension is primitive: there are no intermediate fields between this field and . |
Sibling fields
Degree 20 sibling: | data not computed |
Degree 45 sibling: | data not computed |
Minimal sibling: | This field is its own minimal sibling |
Frobenius cycle types
Cycle type | 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 | ||||
---|---|---|---|---|---|---|---|
| 17.1.2.1a1.1 | ||||||
17.8.1.0a1.1 | |||||||
| Trivial | ||||||
Trivial | |||||||
103.1.2.1a1.2 | |||||||
103.6.1.0a1.1 | |||||||
| Trivial | ||||||
Trivial | |||||||
Trivial | |||||||
Trivial | |||||||
Deg | |||||||
Deg | |||||||
| Trivial | ||||||
Trivial | |||||||
Deg | |||||||
Deg |