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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.121285501930583761.1	x^16 - 3x^15 + x^14 + 2x^13 + x^12 - 2x^11 + 3x^10 + 8x^9 - 20x^8 - 15x^7 + 20x^6 + 15x^5 - 6x^4 - 5x^3 + 4x^2 + 4x + 1	\( 29^{2}\cdot 229^{6} \)	16T1537	Trivial
16.0.148462392804296041.1	x^16 - x^15 - 3x^14 - x^13 + 9x^12 + 7x^11 - 10x^10 - 6x^9 - 2x^8 + 9x^7 + 12x^6 - 10x^5 - 14x^4 - 3x^3 + 7x^2 + 5x + 1	\( 17^{2}\cdot 283^{6} \)	16T1537	Trivial
16.0.222256600452006289.1	x^16 - 2x^15 + 4x^14 - 3x^13 + 9x^12 - 19x^11 + 44x^10 - 56x^9 + 61x^8 - 52x^7 + 56x^6 - 52x^5 + 47x^4 - 23x^3 + 10x^2 - 3x + 1	\( 13^{2}\cdot 331^{6} \)	16T1537	Trivial
16.0.686611503794898081.1	x^16 - 3x^15 + x^14 + 3x^13 - x^12 + 5x^11 - 7x^10 + x^9 + 16x^8 + 4x^7 + x^6 + x^5 + 7x^3 + 12x^2 + 5x + 1	\( 3^{2}\cdot 23^{2}\cdot 229^{6} \)	16T1537	Trivial
16.4.1788226952774237089.1	x^16 - 4x^15 + 6x^14 - 7x^13 + 9x^12 + 9x^11 - 50x^10 + 30x^9 + 42x^8 - 53x^7 + 12x^6 - 7x^5 - 10x^4 + 17x^3 - 8x^2 - 5x + 1	\( 59^{2}\cdot 283^{6} \)	16T1537	Trivial
16.4.2431671326838814369.1	x^16 - 2x^15 - 2x^14 + 12x^13 - 8x^12 - 23x^11 + 44x^10 + 7x^9 - 64x^8 + 22x^7 + 47x^6 - 32x^5 - 48x^4 - 11x^3 + 8x^2 + 5x + 1	\( 43^{2}\cdot 331^{6} \)	16T1537	Trivial
16.0.56175242250280047049.1	x^16 - 4x^15 + 11x^14 - 20x^13 + 33x^12 - 44x^11 + 51x^10 - 49x^9 + 49x^8 - 43x^7 + 29x^6 - 8x^5 + 16x^4 - 14x^3 - 4x^2 + 6x + 9	\( 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.0.505577180252520423441.1	x^16 + 8x^14 - 14x^13 + 14x^12 - 37x^11 + 86x^10 + 76x^9 + 162x^8 - 42x^7 - 173x^6 - 310x^5 - 20x^4 + 118x^3 + 158x^2 + 7x + 49	\( 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	$[2]$
16.8.505577180252520423441.1	x^16 - 4x^15 + 19x^13 - 33x^12 + 27x^11 - 30x^10 + 23x^9 + 96x^8 - 115x^7 - 90x^6 + 122x^5 + 54x^4 - 75x^3 - 36x^2 + 3x + 1	\( 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.4.2752586870263722305401.1	x^16 - 5x^15 + 18x^14 - 45x^13 + 48x^12 + 22x^11 - 236x^10 + 353x^9 - 222x^8 - 134x^7 + 258x^6 + 66x^5 + 180x^4 - 80x^3 - 130x^2 - 38x - 37	\( 7^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.4.2752586870263722305401.2	x^16 - x^15 + 6x^13 + 7x^12 - 54x^11 + 20x^10 + 46x^9 - 225x^8 - 215x^7 + 105x^6 + 162x^5 - 116x^4 - 120x^3 + 214x^2 + 224x + 49	\( 7^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.0.7337958667162225175824.1	x^16 - 19x^14 + 172x^12 - 943x^10 + 3387x^8 - 8051x^6 + 12164x^4 - 10427x^2 + 3844	\( 2^{4}\cdot 2777^{6} \)	16T1537	$[9]$
16.0.29351834668648900703296.1	x^16 - 5x^15 + 25x^14 - 92x^13 + 286x^12 - 790x^11 + 1906x^10 - 3972x^9 + 7288x^8 - 11440x^7 + 16018x^6 - 19693x^5 + 21633x^4 - 20304x^3 + 15479x^2 - 8164x + 2038	\( 2^{6}\cdot 2777^{6} \)	16T1537	$[9]$
16.8.40951751600454154298721.1	x^16 - 5x^15 + 2x^14 + 7x^13 + 4x^12 - 9x^11 + 9x^10 + 568x^9 + 266x^8 - 893x^7 - 367x^6 + 393x^5 - 159x^4 - 411x^3 + 157x^2 + 231x + 49	\( 3^{6}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.4.99516037292441516747025.1	x^16 - 4x^15 + 12x^14 - 32x^13 + 71x^12 - 97x^11 - 384x^10 + 2007x^9 - 4716x^8 + 7397x^7 - 12084x^6 + 11477x^5 - 11794x^4 + 8833x^3 - 4347x^2 + 2626x - 227	\( 3^{6}\cdot 5^{2}\cdot 1327^{6} \)	16T1537	Trivial (GRH)
16.8.124091110130868623931241.1	x^16 - 4x^15 - 3x^14 + 7x^13 + 11x^12 + 115x^11 - 152x^10 - 165x^9 - 251x^8 + 49x^7 + 1451x^6 + 108x^5 - 669x^4 - 480x^3 - 673x^2 + 273x + 49	\( 19^{6}\cdot 47^{2}\cdot 103^{6} \)	16T1537	Trivial
16.4.195546018273224843777569.1	x^16 - 3x^15 + 5x^14 + 5x^13 - 39x^12 - 5x^11 - 67x^10 - 213x^9 - 112x^8 + 96x^7 - 61x^6 + 307x^5 - 264x^4 - 149x^3 + 292x^2 - 175x + 49	\( 19^{6}\cdot 59^{2}\cdot 103^{6} \)	16T1537	$[4]$
16.4.214501813959024741484449.1	x^16 - 5x^15 + 11x^14 - 13x^13 - 16x^12 + 111x^11 - 221x^10 + 79x^9 + 149x^8 - 585x^7 + 1190x^6 - 157x^5 - 1075x^4 + 997x^3 - 255x^2 - 294x + 196	\( 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial
16.0.242611258433051069875681.1	x^16 - 3x^15 + 14x^14 - 42x^13 + 62x^12 - 135x^11 - 19x^10 - 286x^9 - 236x^8 + 1077x^7 + 5599x^6 + 7170x^5 + 10773x^4 + 3877x^3 - 1953x^2 - 5586x + 2819	\( 23^{2}\cdot 2777^{6} \)	16T1537	$[9]$
16.8.368565764404087388688489.1	x^16 - 17x^14 + 88x^12 - 326x^10 + 1204x^8 - 3236x^6 + 4753x^4 - 2915x^2 + 529	\( 3^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial
16.12.3432029023344395863751184.1	x^16 - 5x^14 - 3x^12 + 49x^10 - 85x^8 + 49x^6 - 3x^4 - 5x^2 + 1	\( 2^{4}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial (GRH)
16.8.3432029023344395863751184.1	x^16 - 6x^14 - 140x^12 - 67x^10 + 1151x^8 - 728x^6 - 207x^4 + 136x^2 + 1	\( 2^{4}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial
16.0.3681500676114353163403264.1	x^16 + 15x^14 + 81x^12 + 225x^10 + 497x^8 + 852x^6 + 627x^4 + 632x^2 + 49	\( 2^{16}\cdot 19^{6}\cdot 103^{6} \)	16T1537	$[6]$
16.0.3681500676114353163403264.2	x^16 + 12x^14 + 65x^12 + 207x^10 + 411x^8 + 495x^6 + 324x^4 + 81x^2 + 1	\( 2^{16}\cdot 19^{6}\cdot 103^{6} \)	16T1537	$[12]$
16.0.4315178318708086042458001.1	x^16 - 4x^15 - x^14 + 26x^13 + 56x^12 - 414x^11 + 566x^10 + 893x^9 - 1952x^8 - 317x^7 + 7122x^6 + 3134x^5 - 6448x^4 - 5022x^3 + 1647x^2 + 4360x + 3749	\( 97^{2}\cdot 2777^{6} \)	16T1537	$[9]$
16.16.10510588883992212332738001.1	x^16 - 23x^14 + 207x^12 - 940x^10 + 2317x^8 - 3051x^6 + 1896x^4 - 369x^2 + 9	\( 3^{6}\cdot 7^{2}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial (GRH)
16.4.10510588883992212332738001.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 15x^12 - 92x^11 + 164x^10 + 643x^9 - 1478x^8 - 102x^7 - 391x^6 + 6462x^5 - 7540x^4 + 1781x^3 + 761x^2 - 194x + 113	\( 3^{6}\cdot 7^{2}\cdot 17^{8}\cdot 59^{6} \)	16T1537	$[2]$
16.0.13567885575582954350098576.1	x^16 - 8x^15 + 44x^14 - 168x^13 + 587x^12 - 1702x^11 + 4239x^10 - 8644x^9 + 15457x^8 - 23538x^7 + 30978x^6 - 33521x^5 + 31435x^4 - 23817x^3 + 13277x^2 - 4620x + 6466	\( 2^{4}\cdot 43^{2}\cdot 2777^{6} \)	16T1537	$[2, 90]$
16.8.13728116093377583455004736.1	x^16 - 15x^14 + 22x^12 + 422x^10 - 1020x^8 - 1768x^6 + 793x^4 + 918x^2 + 4	\( 2^{6}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial (GRH)
16.12.17374646930681004060240369.1	x^16 - 28x^14 + 246x^12 - 607x^10 - 1193x^8 + 8022x^6 - 13077x^4 + 7074x^2 + 81	\( 3^{10}\cdot 17^{8}\cdot 59^{6} \)	16T1537	Trivial (GRH)
16.0.33133506085029178470629376.1	x^16 + 30x^14 + 368x^12 + 2383x^10 + 8737x^8 + 17955x^6 + 18924x^4 + 7942x^2 + 361	\( 2^{16}\cdot 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	$[4, 24]$ (GRH)
16.16.33133506085029178470629376.1	x^16 - 30x^14 + 368x^12 - 2383x^10 + 8737x^8 - 17955x^6 + 18924x^4 - 7942x^2 + 361	\( 2^{16}\cdot 3^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1537	Trivial (GRH)
16.0.878599429976165341120303104.1	x^16 + 35x^14 + 431x^12 + 2413x^10 + 6319x^8 + 6993x^6 + 3027x^4 + 459x^2 + 9	\( 2^{12}\cdot 3^{6}\cdot 17^{8}\cdot 59^{6} \)	16T1537	$[72]$ (GRH)
16.0.2548496051647172953576738569.1	x^16 - 7x^15 + 39x^14 - 134x^13 + 455x^12 - 977x^11 + 1703x^10 - 1972x^9 + 1411x^8 - 317x^7 - 285x^6 + 463x^5 + 91x^4 - 366x^3 + 1020x^2 - 432x + 576	\( 3^{6}\cdot 17^{8}\cdot 59^{6}\cdot 109^{2} \)	16T1537	$[2, 66]$ (GRH)