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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.250384196641554432.1	x^16 - 6x^14 + 10x^12 - 9x^8 + 9x^6 - 6x^5 + 10x^4 - 18x^3 + 15x^2 - 6x + 1	\( 2^{16}\cdot 3^{12}\cdot 193^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.4.451680665600000000.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 18x^12 + 10x^11 + 9x^10 + 8x^9 - 75x^8 + 128x^7 - 103x^6 + 34x^5 + 7x^4 - 4x^3 - 5x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.0.10962219134670077952.5	x^16 - 4x^14 + 21x^12 - 54x^10 + 129x^8 - 190x^6 + 221x^4 - 100x^2 + 73	\( 2^{32}\cdot 3^{8}\cdot 73^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.2.22563723673600000000.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 5x^12 - 18x^11 + 4x^10 - 28x^9 + 5x^8 - 28x^7 + 4x^6 - 18x^5 + 5x^4 - 10x^3 + 5x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 151^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.4.115630250393600000000.1	x^16 - 2x^14 - 4x^13 - 11x^12 + 48x^11 - 6x^10 - 72x^9 + 43x^8 - 8x^7 + 92x^6 - 168x^5 + 139x^4 - 72x^3 + 28x^2 - 8x + 1	\( 2^{32}\cdot 5^{8}\cdot 41^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.10.5617374084797634183168.2	x^16 - 12x^14 + 36x^12 + 40x^10 - 212x^8 - 120x^6 + 256x^4 + 80x^2 - 92	\( -\,2^{46}\cdot 3^{8}\cdot 23^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.2.5617374084797634183168.2	x^16 + 12x^14 + 36x^12 - 40x^10 - 212x^8 + 120x^6 + 256x^4 - 80x^2 - 92	\( -\,2^{46}\cdot 3^{8}\cdot 23^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial
16.10.5776313260441600000000.3	x^16 - 18x^14 - 4x^13 + 114x^12 + 64x^11 - 312x^10 - 380x^9 + 299x^8 + 968x^7 + 132x^6 - 1060x^5 - 102x^4 + 496x^3 - 110x^2 - 8x + 1	\( -\,2^{32}\cdot 5^{8}\cdot 151^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.16.66874197993062400000000.1	x^16 - 24x^14 - 6x^13 + 180x^12 + 78x^11 - 527x^10 - 210x^9 + 741x^8 + 210x^7 - 527x^6 - 78x^5 + 180x^4 + 6x^3 - 24x^2 + 1	\( 2^{24}\cdot 3^{6}\cdot 5^{8}\cdot 241^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.0.133195802142310400000000.1	x^16 - 2x^15 + 9x^14 + 4x^13 - 3x^12 + 90x^11 - 37x^10 + 40x^9 + 401x^8 - 924x^7 + 1565x^6 - 2090x^5 + 1938x^4 - 1690x^3 + 1076x^2 - 768x + 431	\( 2^{24}\cdot 5^{8}\cdot 2729^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	$[3]$ (GRH)
16.16.1805152587776000000000000.1	x^16 - 32x^14 - 34x^13 + 287x^12 + 446x^11 - 889x^10 - 1762x^9 + 670x^8 + 2018x^7 - 302x^6 - 1002x^5 + 182x^4 + 196x^3 - 57x^2 - 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 761^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.8.1805152587776000000000000.1	x^16 - 4x^15 - 8x^14 + 38x^13 + 7x^12 - 54x^11 - 103x^10 + 274x^9 - 185x^8 - 1844x^7 + 5544x^6 - 6442x^5 + 5462x^4 + 72x^3 - 6578x^2 + 2860x - 479	\( 2^{24}\cdot 5^{12}\cdot 761^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.0.5416810037438054400000000.1	x^16 - 2x^15 + 13x^14 - 6x^13 + 57x^12 + 98x^11 + 192x^10 + 376x^9 + 1521x^8 + 1056x^7 + 3316x^6 + 5558x^5 + 6361x^4 + 6498x^3 + 5619x^2 + 2862x + 639	\( 2^{24}\cdot 3^{10}\cdot 5^{8}\cdot 241^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	$[2, 2, 6]$ (GRH)
16.8.41796373745664000000000000.1	x^16 - 10x^14 - 2x^13 + 21x^12 + 120x^11 - 201x^10 - 294x^9 + 571x^8 - 808x^7 + 5387x^6 - 12576x^5 + 8552x^4 + 9078x^3 - 20281x^2 + 14002x - 3559	\( 2^{24}\cdot 3^{6}\cdot 5^{12}\cdot 241^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	$[2]$ (GRH)