Global number field search results

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

Results (displaying all 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.10834375376002294480896.1	x^18 + 3x^16 + 4x^14 + 6x^12 - 2x^10 - 4x^8 + 4x^6 - 6x^4 + x^2 + 1	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12} \)	18T175	Trivial
18.0.19408409961765342806016.1	x^18 + 3x^16 - 7x^12 - 3x^10 + 9x^8 + 3x^6 - 6x^4 + 1	\( -\,2^{36}\cdot 3^{24} \)	18T175	Trivial
18.6.155267279694122742448128.1	x^18 - 6x^16 + 12x^14 - 10x^12 + 21x^10 - 72x^8 + 117x^6 - 102x^4 + 48x^2 - 8	\( 2^{39}\cdot 3^{24} \)	18T175	Trivial
18.6.200129027320960098762752.1	x^18 - 8x^16 + 26x^14 - 58x^12 + 135x^10 - 256x^8 + 293x^6 - 190x^4 + 64x^2 - 8	\( 2^{33}\cdot 13^{12} \)	18T175	Trivial
18.8.80421398252924334225227776.1	x^18 - 2x^16 - 20x^14 + 41x^12 + 62x^10 - 120x^8 - 38x^6 + 60x^4 + 16x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T175	Trivial (GRH)
18.12.80421398252924334225227776.2	x^18 - 25x^14 + 3x^12 + 115x^10 - 50x^8 - 136x^6 + 115x^4 - 25x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T175	Trivial (GRH)
18.8.80421398252924334225227776.2	x^18 + 7x^16 + 6x^14 - 32x^12 - 23x^10 + 47x^8 + 18x^6 - 23x^4 - x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T175	Trivial (GRH)
18.12.80421398252924334225227776.3	x^18 - 3x^16 - 27x^14 + 62x^12 + 40x^10 - 133x^8 + 15x^6 + 73x^4 - 30x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T175	Trivial (GRH)
18.10.279992823820843547402730217.1	x^18 - 6x^17 + 11x^16 - 6x^15 - 21x^14 + 182x^13 - 493x^12 + 233x^11 + 1189x^10 - 1823x^9 - 580x^8 + 2290x^7 + 202x^6 - 1152x^5 - 959x^4 + 503x^3 + 670x^2 - 152x + 8	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T175	Trivial (GRH)
18.10.279992823820843547402730217.2	x^18 - x^17 - 10x^16 - 3x^15 + 36x^14 + 90x^13 - 146x^12 - 199x^11 + 509x^10 + 245x^9 - 388x^8 - 2643x^7 + 608x^6 + 3282x^5 + 96x^4 + 288x^3 - 1503x^2 - 547x + 293	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T175	Trivial (GRH)
18.6.23969878594169966578599985152.2	x^18 - 30x^14 - 33x^12 + 252x^10 + 504x^8 - 222x^6 - 1008x^4 - 522x^2 - 3	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T175	Trivial (GRH)
18.6.23969878594169966578599985152.3	x^18 - 36x^14 - 9x^12 + 270x^10 + 216x^8 - 540x^6 - 810x^4 - 324x^2 - 27	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T175	$[2]$ (GRH)
18.18.77197786955557097737493824000000.1	x^18 - 6x^17 - 38x^16 + 270x^15 + 400x^14 - 4437x^13 + 285x^12 + 34242x^11 - 27318x^10 - 132564x^9 + 162263x^8 + 262256x^7 - 407299x^6 - 256570x^5 + 489756x^4 + 116609x^3 - 275575x^2 - 20481x + 56647	\( 2^{12}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12}\cdot 61^{3} \)	18T175	Trivial (GRH)
18.0.89156963198142398832050176000000.1	x^18 + 38x^16 + 609x^14 + 5357x^12 + 28133x^10 + 89540x^8 + 166180x^6 + 159887x^4 + 57967x^2 + 2401	\( -\,2^{30}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12} \)	18T175	$[2, 1120]$ (GRH)
18.0.374995864672776683690097475584000.1	x^18 + 45x^16 + 708x^14 + 5093x^12 + 18705x^10 + 36303x^8 + 37039x^6 + 19110x^4 + 4500x^2 + 375	\( -\,2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6} \)	18T175	$[2, 2, 2, 182]$ (GRH)
18.18.374995864672776683690097475584000.1	x^18 - 45x^16 + 708x^14 - 5093x^12 + 18705x^10 - 36303x^8 + 37039x^6 - 19110x^4 + 4500x^2 - 375	\( 2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6} \)	18T175	Trivial (GRH)