Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.3190851810094053743.1	x^18 - 5x^17 + 15x^16 - 36x^15 + 75x^14 - 137x^13 + 221x^12 - 312x^11 + 384x^10 - 411x^9 + 384x^8 - 312x^7 + 221x^6 - 137x^5 + 75x^4 - 36x^3 + 15x^2 - 5x + 1	\( -\,11^{6}\cdot 23^{9} \)	18T221	Trivial
18.0.126459893166202412199.1	x^18 - x^17 - 2x^16 + x^15 + 6x^14 - 11x^13 + 5x^12 - 2x^11 + x^10 + 13x^9 - 2x^8 - 28x^7 + 14x^6 + 27x^5 - 19x^4 + x^3 + 8x^2 - 4x + 1	\( -\,3^{14}\cdot 31^{9} \)	18T221	Trivial
18.6.5323232862006353920000.1	x^18 - 5x^17 + 7x^16 + 6x^15 - 14x^14 - 26x^13 + 20x^12 + 72x^11 + 7x^10 - 107x^9 - 79x^8 + 172x^7 - 122x^6 + 210x^5 - 226x^4 + 94x^3 - 7x^2 - 5x + 1	\( 2^{16}\cdot 5^{4}\cdot 37^{9} \)	18T221	Trivial
18.6.71675758030642276007936.1	x^18 - 5x^17 + 15x^16 - 30x^15 + 48x^14 - 76x^13 + 80x^12 + 8x^11 - 169x^10 + 257x^9 - 169x^8 + 8x^7 + 80x^6 - 76x^5 + 48x^4 - 30x^3 + 15x^2 - 5x + 1	\( 2^{16}\cdot 101^{9} \)	18T221	Trivial
18.18.285528043884818109860965666161.1	x^18 - 9x^17 + 10x^16 + 124x^15 - 380x^14 - 224x^13 + 2242x^12 - 2246x^11 - 2595x^10 + 6155x^9 - 2595x^8 - 2246x^7 + 2242x^6 - 224x^5 - 380x^4 + 124x^3 + 10x^2 - 9x + 1	\( 3^{9}\cdot 53^{4}\cdot 107^{9} \)	18T221	Trivial (GRH)
18.18.3883935753586811556108815486976.2	x^18 - 45x^16 - 6x^15 + 774x^14 + 234x^13 - 6555x^12 - 3420x^11 + 29034x^10 + 23344x^9 - 64449x^8 - 76284x^7 + 53727x^6 + 111114x^5 + 21204x^4 - 49452x^3 - 37620x^2 - 10512x - 1052	\( 2^{12}\cdot 3^{25}\cdot 47^{9} \)	18T221	Trivial (GRH)