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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.367709590087890625.1	x^16 - x^15 + 2x^14 - 2x^13 + 7x^12 - 10x^11 + 8x^10 - 9x^9 + 10x^8 - 16x^7 + 18x^6 - 10x^5 + 7x^4 - 8x^3 + 7x^2 - 4x + 1	\( 5^{12}\cdot 197^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial
16.0.3790869843994140625.1	x^16 - 5x^15 + 5x^14 + 10x^13 - 12x^12 - 15x^11 - 10x^10 + 50x^9 + 79x^8 - 240x^7 + 160x^6 + 15x^5 - 58x^4 + 20x^3 + 5x^2 - 5x + 1	\( 5^{12}\cdot 353^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2]$
16.0.28398241000000000000.1	x^16 - 2x^15 + x^14 + 7x^13 - 16x^12 + 17x^11 + 7x^10 - 39x^9 + 51x^8 - 30x^7 - 18x^6 + 16x^5 - 16x^4 + 16x + 16	\( 2^{12}\cdot 5^{12}\cdot 73^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial
16.0.29986576000000000000.1	x^16 - 8x^15 + 26x^14 - 36x^13 - 9x^12 + 106x^11 - 134x^10 - 28x^9 + 309x^8 - 480x^7 + 432x^6 - 294x^5 + 181x^4 - 90x^3 + 30x^2 - 10x + 5	\( 2^{16}\cdot 5^{12}\cdot 37^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial
16.0.160979497422684160000.1	x^16 - 4x^15 + 6x^14 - 13x^12 + 16x^11 + 22x^10 - 100x^9 + 179x^8 - 232x^7 + 284x^6 - 344x^5 + 348x^4 - 240x^3 + 112x^2 - 32x + 4	\( 2^{44}\cdot 5^{4}\cdot 11^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial
16.0.221533456000000000000.4	x^16 - 6x^15 + 13x^14 - 6x^13 - 10x^12 - 16x^11 + 83x^10 - 132x^9 + 149x^8 - 158x^7 + 177x^6 - 156x^5 + 106x^4 - 46x^3 + 13x^2 - 2x + 1	\( 2^{16}\cdot 5^{12}\cdot 61^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial
16.0.973214788027587890625.1	x^16 + x^14 - 7x^12 + 26x^8 - 45x^6 + 17x^4 + 52x^2 + 16	\( 3^{8}\cdot 5^{12}\cdot 157^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[4]$
16.0.6987834057851806640625.1	x^16 - 5x^15 + 17x^14 - 57x^13 + 166x^12 - 388x^11 + 730x^10 - 1177x^9 + 1833x^8 - 2840x^7 + 3933x^6 - 4345x^5 + 3587x^4 - 2141x^3 + 890x^2 - 234x + 31	\( 3^{8}\cdot 5^{12}\cdot 257^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2]$
16.8.6987834057851806640625.1	x^16 - 2x^15 - 4x^14 + 5x^13 + x^12 + 14x^11 + 20x^10 - 46x^9 - 43x^8 + 8x^7 + 5x^6 + 52x^5 + 66x^4 - 16x^2 - x + 1	\( 3^{8}\cdot 5^{12}\cdot 257^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)
16.8.7676563456000000000000.1	x^16 - 2x^15 - 2x^14 + 10x^13 - 16x^12 - 4x^11 + 54x^10 - 28x^9 - 39x^8 - 8x^7 - 46x^6 + 84x^5 + 86x^4 - 30x^3 - 30x^2 - 10x + 5	\( 2^{24}\cdot 5^{12}\cdot 37^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)
16.8.18339659776000000000000.1	x^16 - 2x^15 - 10x^14 + 14x^13 + 36x^12 - 28x^11 - 64x^10 + 10x^9 + 139x^8 - 100x^7 - 116x^6 + 126x^5 + 46x^4 - 42x^3 - 10x^2 + 4x + 1	\( 2^{28}\cdot 5^{12}\cdot 23^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)
16.8.18339659776000000000000.2	x^16 - 8x^14 - 14x^13 - 22x^12 - 6x^11 + 70x^10 + 140x^9 + 161x^8 + 66x^7 - 150x^6 - 312x^5 - 340x^4 - 250x^3 - 102x^2 - 14x + 1	\( 2^{28}\cdot 5^{12}\cdot 23^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)
16.0.61320934176347900390625.1	x^16 - 3x^15 + 4x^13 + 12x^12 - 49x^11 + 47x^10 + 9x^9 + 92x^8 - 343x^7 + 423x^6 - 208x^5 - 164x^4 + 265x^3 - 60x^2 - 50x + 25	\( 3^{4}\cdot 5^{12}\cdot 1327^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2, 2]$ (GRH)
16.0.807985254400000000000000.1	x^16 - 4x^15 + 16x^14 - 48x^13 + 144x^12 - 320x^11 + 688x^10 - 1116x^9 + 1748x^8 - 2104x^7 + 2448x^6 - 2160x^5 + 1844x^4 - 1112x^3 + 656x^2 - 216x + 76	\( 2^{24}\cdot 5^{14}\cdot 53^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2]$ (GRH)
16.0.1166177856221725962879121.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 33x^12 + 16x^11 + 149x^10 - 272x^9 + 148x^8 + 72x^7 - 4x^6 - 339x^5 + 613x^4 - 563x^3 + 283x^2 - 71x + 9	\( 11^{4}\cdot 13^{12}\cdot 43^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2]$ (GRH)
16.0.4966995668284179931640625.1	x^16 - 2x^15 + 8x^14 + 10x^13 - 18x^12 + 34x^11 + 184x^10 - 244x^9 + 246x^8 + 800x^7 - 634x^6 - 1760x^5 + 3797x^4 - 1320x^3 - 1444x^2 - 418x + 21901	\( 3^{8}\cdot 5^{12}\cdot 1327^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2, 2]$ (GRH)
16.0.6169143218176000000000000.1	x^16 - 6x^15 + 20x^14 - 32x^13 + 72x^12 - 16x^11 + 200x^10 + 56x^9 + 136x^8 - 64x^7 + 896x^6 + 672x^5 + 616x^4 + 496x^3 + 384x^2 + 64x + 16	\( 2^{24}\cdot 5^{12}\cdot 197^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2, 12]$ (GRH)
16.16.6743454497573300933103616.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 193x^12 - 116x^11 + 774x^10 - 185x^9 - 1358x^8 + 690x^7 + 1192x^6 - 669x^5 - 511x^4 + 236x^3 + 86x^2 - 19x - 1	\( 2^{12}\cdot 17^{12}\cdot 41^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)
16.0.64545232525865114587365376.1	x^16 + 32x^14 + 360x^12 + 1744x^10 + 3604x^8 + 3456x^6 + 1488x^4 + 224x^2 + 4	\( 2^{56}\cdot 173^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	$[2, 10]$ (GRH)
16.16.64545232525865114587365376.1	x^16 - 32x^14 + 360x^12 - 1744x^10 + 3604x^8 - 3456x^6 + 1488x^4 - 224x^2 + 4	\( 2^{56}\cdot 173^{4} \)	$C_2^4.(C_4\times S_3)$ (as 16T725)	Trivial (GRH)