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 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.315864215936279296875.1	x^16 - 5x^15 + 11x^14 - 15x^13 + 17x^12 - 10x^11 - 32x^10 + 150x^9 - 380x^8 + 690x^7 - 998x^6 + 1195x^5 - 1153x^4 + 915x^3 - 496x^2 + 170x + 1	\( -\,3^{12}\cdot 5^{14}\cdot 97379 \)	16T1604	Trivial
16.6.315864215936279296875.1	x^16 - 2x^15 + 2x^14 - 6x^13 - 9x^12 + 23x^11 - 35x^10 - 23x^9 + 4x^8 - 9x^7 - 15x^6 + 61x^5 + 36x^4 - 18x^3 - 17x^2 + x + 1	\( -\,3^{12}\cdot 5^{14}\cdot 97379 \)	16T1604	Trivial (GRH)
16.4.363435710723876953125.1	x^16 - 2x^15 + 5x^13 - 21x^11 + 7x^10 + 35x^9 - 75x^8 - 50x^7 + 67x^6 - 39x^5 - 195x^4 + 25x^3 + 15x^2 - 133x - 59	\( 3^{12}\cdot 5^{15}\cdot 22409 \)	16T1604	Trivial
16.4.363435710723876953125.2	x^16 - 8x^15 + 25x^14 - 35x^13 + 5x^12 + 61x^11 - 98x^10 + 50x^9 + 40x^8 - 75x^7 + 37x^6 + 9x^5 - 20x^4 + 10x^3 - 5x^2 + 3x + 1	\( 3^{12}\cdot 5^{15}\cdot 22409 \)	16T1604	Trivial
16.2.728457570428466796875.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 180x^12 - 261x^11 + 268x^10 - 163x^9 - 9x^8 + 145x^7 - 170x^6 + 105x^5 - 30x^4 - 5x^3 + 5x - 5	\( -\,3^{12}\cdot 5^{14}\cdot 224579 \)	16T1604	Trivial
16.6.728457570428466796875.1	x^16 - 6x^15 + 16x^14 - 39x^13 + 98x^12 - 186x^11 + 199x^10 - 12x^9 - 122x^8 + 24x^7 + 56x^6 + 153x^5 - 127x^4 - 27x^3 + 44x^2 - 12x + 1	\( -\,3^{12}\cdot 5^{14}\cdot 224579 \)	16T1604	Trivial (GRH)
16.10.2490368000000000000000.1	x^16 - 4x^15 + 30x^12 - 12x^11 + 108x^10 - 200x^9 - 465x^8 + 340x^7 + 628x^6 - 112x^5 - 350x^4 - 40x^3 + 60x^2 + 16x + 1	\( -\,2^{32}\cdot 5^{15}\cdot 19 \)	16T1604	Trivial (GRH)
16.6.2490368000000000000000.1	x^16 - 4x^15 + 20x^13 - 45x^12 + 48x^11 - 12x^10 - 40x^9 + 65x^8 - 40x^7 - 12x^6 + 48x^5 - 45x^4 + 20x^3 - 4x + 1	\( -\,2^{32}\cdot 5^{15}\cdot 19 \)	16T1604	Trivial (GRH)
16.10.5216665600000000000000.1	x^16 - 4x^15 - 8x^14 + 28x^13 + 60x^12 - 48x^11 - 278x^10 - 196x^9 + 481x^8 + 840x^7 + 90x^6 - 700x^5 - 540x^4 - 60x^3 + 90x^2 + 40x + 5	\( -\,2^{32}\cdot 5^{14}\cdot 199 \)	16T1604	Trivial (GRH)
16.6.5216665600000000000000.1	x^16 - 4x^15 + 14x^14 - 24x^13 + 31x^12 - 12x^11 - 34x^10 + 88x^9 - 168x^8 + 172x^7 - 114x^6 + 32x^5 - 14x^4 - 36x^3 + 64x^2 - 16x + 1	\( -\,2^{32}\cdot 5^{14}\cdot 199 \)	16T1604	Trivial (GRH)
16.4.12967160400000000000000.1	x^16 - 2x^14 - 7x^12 - 29x^10 - 20x^8 + 266x^6 + 173x^4 - 172x^2 + 61	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61 \)	16T1604	Trivial (GRH)
16.4.12967160400000000000000.2	x^16 - x^14 - 8x^12 - 13x^10 + 25x^8 + 8x^6 + 22x^4 + 116x^2 + 61	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61 \)	16T1604	Trivial (GRH)
16.8.35677798400000000000000.1	x^16 - 8x^15 + 22x^14 - 4x^13 - 129x^12 + 332x^11 - 170x^10 - 752x^9 + 1484x^8 - 416x^7 - 1440x^6 + 1444x^5 - 129x^4 - 332x^3 + 108x^2 - 16x + 1	\( 2^{32}\cdot 5^{14}\cdot 1361 \)	16T1604	Trivial (GRH)
16.8.35677798400000000000000.2	x^16 - 4x^15 - 12x^14 + 52x^13 + 26x^12 - 244x^11 + 130x^10 + 436x^9 - 576x^8 - 68x^7 + 570x^6 - 432x^5 + 91x^4 + 144x^3 - 178x^2 + 88x - 19	\( 2^{32}\cdot 5^{14}\cdot 1361 \)	16T1604	Trivial (GRH)
16.0.57608204400000000000000.1	x^16 + 8x^14 + 13x^12 - 34x^10 - 95x^8 + 41x^6 + 343x^4 + 473x^2 + 271	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 271 \)	16T1604	$[2]$ (GRH)
16.8.57608204400000000000000.1	x^16 - 8x^14 + 13x^12 + 34x^10 - 95x^8 - 41x^6 + 343x^4 - 473x^2 + 271	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 271 \)	16T1604	Trivial (GRH)
16.0.57608204400000000000000.2	x^16 + 19x^14 + 152x^12 + 667x^10 + 1750x^8 + 2798x^6 + 2642x^4 + 1331x^2 + 271	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 271 \)	16T1604	$[2]$ (GRH)
16.8.57608204400000000000000.2	x^16 - 19x^14 + 152x^12 - 667x^10 + 1750x^8 - 2798x^6 + 2642x^4 - 1331x^2 + 271	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 271 \)	16T1604	Trivial (GRH)
16.14.637534208000000000000000.1	x^16 - 20x^14 + 120x^12 - 180x^10 - 610x^8 + 2260x^6 - 2280x^4 + 820x^2 - 95	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	Trivial (GRH)
16.2.637534208000000000000000.1	x^16 + 20x^14 + 120x^12 + 180x^10 - 610x^8 - 2260x^6 - 2280x^4 - 820x^2 - 95	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	$[2]$ (GRH)
16.14.637534208000000000000000.2	x^16 - 20x^14 - 20x^13 + 140x^12 + 280x^11 - 280x^10 - 1220x^9 - 570x^8 + 1600x^7 + 1820x^6 - 340x^5 - 1220x^4 - 360x^3 + 120x^2 + 60x + 5	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	Trivial (GRH)
16.2.637534208000000000000000.2	x^16 - 20x^13 + 30x^12 + 40x^10 - 180x^9 + 145x^8 + 160x^7 - 80x^6 - 140x^5 - 420x^4 + 320x^3 + 880x^2 - 480x - 695	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	$[4]$ (GRH)
16.12.3388997632000000000000000.1	x^16 - 20x^14 + 130x^12 - 240x^10 - 445x^8 + 1440x^6 - 70x^4 - 1300x^2 + 505	\( 2^{40}\cdot 5^{15}\cdot 101 \)	16T1604	Trivial (GRH)
16.4.3388997632000000000000000.1	x^16 - 4x^15 + 20x^14 - 100x^13 + 330x^12 - 1012x^11 + 2808x^10 - 6420x^9 + 12825x^8 - 21140x^7 + 23628x^6 - 13532x^5 + 140x^4 + 5160x^3 - 3700x^2 + 1296x - 199	\( 2^{40}\cdot 5^{15}\cdot 101 \)	16T1604	Trivial (GRH)
16.12.3388997632000000000000000.2	x^16 - 4x^15 - 20x^14 + 140x^13 - 140x^12 - 952x^11 + 3648x^10 - 4680x^9 - 2700x^8 + 19960x^7 - 35912x^6 + 36248x^5 - 21680x^4 + 6720x^3 - 320x^2 - 384x + 76	\( 2^{40}\cdot 5^{15}\cdot 101 \)	16T1604	Trivial (GRH)
16.4.3388997632000000000000000.2	x^16 + 20x^14 + 130x^12 + 240x^10 - 445x^8 - 1440x^6 - 70x^4 + 1300x^2 + 505	\( 2^{40}\cdot 5^{15}\cdot 101 \)	16T1604	Trivial (GRH)
16.0.10909410918400000000000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 80x^12 - 116x^11 + 178x^10 - 208x^9 + 176x^8 - 160x^7 + 160x^6 - 100x^5 + 45x^4 - 40x^3 + 20x^2 + 5	\( 2^{32}\cdot 5^{14}\cdot 281\cdot 1481 \)	16T1604	$[2]$ (GRH)
16.10.15561655362000000000000000.1	x^16 + 5x^14 - 35x^12 - 100x^10 + 325x^8 + 365x^6 - 965x^4 + 410x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.6.15561655362000000000000000.1	x^16 + 5x^14 - 25x^12 - 100x^10 + 40x^8 + 310x^6 + 110x^4 - 125x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	$[2]$ (GRH)
16.10.15561655362000000000000000.2	x^16 - 80x^12 + 45x^10 + 660x^8 - 585x^6 - 80x^4 + 75x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.6.15561655362000000000000000.2	x^16 - 80x^12 - 45x^10 + 660x^8 + 585x^6 - 80x^4 - 75x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.10.15561655362000000000000000.3	x^16 - 5x^14 - 25x^12 + 100x^10 + 40x^8 - 310x^6 + 110x^4 + 125x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.6.15561655362000000000000000.3	x^16 - 5x^14 - 35x^12 + 100x^10 + 325x^8 - 365x^6 - 965x^4 - 410x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	$[2]$ (GRH)
16.10.15561655362000000000000000.4	x^16 - 5x^14 - 25x^12 + 145x^10 - 95x^8 - 160x^6 + 140x^4 + 5x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.6.15561655362000000000000000.4	x^16 + 5x^14 - 25x^12 - 145x^10 - 95x^8 + 160x^6 + 140x^4 - 5x^2 - 5	\( -\,2^{16}\cdot 3^{12}\cdot 5^{15}\cdot 11^{4} \)	16T1604	Trivial (GRH)
16.0.44736472678400000000000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 276x^12 - 564x^11 + 994x^10 - 1516x^9 + 2032x^8 - 2376x^7 + 2444x^6 - 2164x^5 + 1661x^4 - 1052x^3 + 556x^2 - 208x + 61	\( 2^{32}\cdot 5^{14}\cdot 19\cdot 89819 \)	16T1604	$[2]$ (GRH)
16.16.5576192976486400000000000000.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 192x^12 - 668x^11 + 1486x^10 + 2316x^9 - 5512x^8 - 5488x^7 + 11144x^6 + 9476x^5 - 11587x^4 - 10676x^3 + 4096x^2 + 5496x + 1121	\( 2^{32}\cdot 5^{14}\cdot 199\cdot 421\cdot 2539 \)	16T1604	Trivial (GRH)
16.16.24481709943872400000000000000.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 197x^12 - 638x^11 + 1501x^10 + 1966x^9 - 5312x^8 - 3858x^7 + 9939x^6 + 5586x^5 - 9402x^4 - 5796x^3 + 3186x^2 + 2916x + 531	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 115166641 \)	16T1604	Trivial (GRH)
16.8.34571164844032000000000000000.1	x^16 - 20x^14 - 60x^13 - 280x^12 - 440x^11 + 2840x^10 + 16220x^9 + 41485x^8 + 53840x^7 + 24200x^6 - 14580x^5 - 23030x^4 + 18240x^3 + 28920x^2 - 40480x - 9595	\( 2^{40}\cdot 5^{15}\cdot 101^{3} \)	16T1604	Trivial (GRH)
16.8.34571164844032000000000000000.2	x^16 - 4x^15 + 20x^14 - 120x^13 + 110x^12 - 752x^11 + 3748x^10 - 3060x^9 + 56705x^8 - 202360x^7 + 95728x^6 + 20428x^5 + 209820x^4 + 106260x^3 - 26360x^2 - 1244x + 281	\( 2^{40}\cdot 5^{15}\cdot 101^{3} \)	16T1604	Trivial (GRH)
16.0.22659849813268057575626593255030784.1	x^16 + 128x^14 - 80x^13 + 6332x^12 - 5824x^11 + 160000x^10 - 148464x^9 + 2242654x^8 - 1881184x^7 + 17993888x^6 - 14153040x^5 + 80597868x^4 - 64732256x^3 + 177167392x^2 - 145993456x + 155307329	\( 2^{68}\cdot 449^{4}\cdot 1889 \)	16T1604	$[2, 2, 1782]$ (GRH)
16.0.411636046819158392832000000000000000.1	x^16 + 180x^14 + 13050x^12 + 498960x^10 + 11122875x^8 + 149415840x^6 + 1189252530x^4 + 5153811300x^2 + 9348963705	\( 2^{40}\cdot 3^{12}\cdot 5^{15}\cdot 41\cdot 563021 \)	16T1604	$[2, 2, 4, 109256]$ (GRH)