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
16.0.184832000000000000000.1	x^16 + 5x^12 + 10x^10 + 10x^6 + 25x^4 + 20x^2 + 5	\( 2^{24}\cdot 5^{15}\cdot 19^{2} \)	16T1584	$[2]$
16.4.184832000000000000000.1	x^16 + 5x^12 - 10x^10 - 10x^6 + 25x^4 - 20x^2 + 5	\( 2^{24}\cdot 5^{15}\cdot 19^{2} \)	16T1584	Trivial
16.0.811028480000000000000.1	x^16 - 2x^15 + 4x^14 - 12x^13 + 32x^12 - 58x^11 + 74x^10 - 126x^9 + 229x^8 - 254x^7 + 102x^6 + 130x^5 - 184x^4 + 40x^3 + 50x^2 - 30x + 5	\( 2^{24}\cdot 5^{13}\cdot 199^{2} \)	16T1584	$[2]$
16.4.811028480000000000000.1	x^16 + 2x^14 - x^12 - 22x^10 + 61x^8 - 60x^4 - 80x^2 + 80	\( 2^{24}\cdot 5^{13}\cdot 199^{2} \)	16T1584	Trivial
16.4.30233088000000000000000.1	x^16 - 2x^15 - 10x^14 + 10x^13 + 75x^12 - 56x^11 - 258x^10 + 100x^9 + 760x^8 - 490x^7 - 798x^6 + 416x^5 + 690x^4 + 80x^3 - 310x^2 - 88x + 1	\( 2^{24}\cdot 3^{10}\cdot 5^{15} \)	16T1584	Trivial
16.8.30233088000000000000000.1	x^16 - 4x^15 + 10x^13 + 15x^12 - 72x^11 + 88x^10 - 50x^9 - 135x^8 + 710x^7 - 1262x^6 + 1038x^5 - 345x^4 - 40x^3 + 60x^2 - 14x + 1	\( 2^{24}\cdot 3^{10}\cdot 5^{15} \)	16T1584	Trivial (GRH)
16.4.30233088000000000000000.2	x^16 + 10x^14 + 35x^12 + 80x^10 - 35x^8 - 1020x^6 - 465x^4 + 90x^2 + 45	\( 2^{24}\cdot 3^{10}\cdot 5^{15} \)	16T1584	Trivial
16.8.30233088000000000000000.2	x^16 - 2x^15 - 10x^14 + 30x^13 + 40x^12 - 166x^11 - 158x^10 + 410x^9 + 590x^8 - 310x^7 - 758x^6 - 54x^5 + 360x^4 + 110x^3 - 50x^2 - 18x + 1	\( 2^{24}\cdot 3^{10}\cdot 5^{15} \)	16T1584	Trivial (GRH)
16.0.37935534080000000000000.1	x^16 - 2x^15 + 14x^14 - 26x^13 + 64x^12 - 130x^11 + 257x^10 - 292x^9 + 398x^8 - 462x^7 + 212x^6 + 70x^5 + 24x^4 - 206x^3 + 29x^2 + 88x + 41	\( 2^{24}\cdot 5^{13}\cdot 1361^{2} \)	16T1584	$[4]$
16.0.37935534080000000000000.2	x^16 - 4x^15 - 2x^14 + 4x^13 + 53x^12 + 16x^11 - 10x^10 + 40x^9 - 4x^8 - 40x^7 - 10x^6 - 16x^5 + 53x^4 - 4x^3 - 2x^2 + 4x + 1	\( 2^{24}\cdot 5^{13}\cdot 1361^{2} \)	16T1584	$[4]$
16.0.47316992000000000000000.1	x^16 + 10x^14 + 20x^12 - 10x^10 + 130x^8 + 270x^6 + 180x^4 + 50x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 19^{2} \)	16T1584	$[4]$
16.12.47316992000000000000000.1	x^16 - 10x^14 + 20x^12 + 10x^10 + 130x^8 - 270x^6 + 180x^4 - 50x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 19^{2} \)	16T1584	Trivial (GRH)
16.0.47316992000000000000000.2	x^16 + 10x^14 + 40x^12 + 90x^10 + 140x^8 + 160x^6 + 115x^4 + 40x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 19^{2} \)	16T1584	$[2]$
16.12.47316992000000000000000.2	x^16 - 10x^14 + 40x^12 - 90x^10 + 140x^8 - 160x^6 + 115x^4 - 40x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 19^{2} \)	16T1584	Trivial (GRH)
16.4.904914537956817626953125.1	x^16 + 5x^14 - 15x^12 - 40x^10 - 20x^8 - 990x^6 - 480x^4 - 405x^2 + 45	\( 3^{10}\cdot 5^{15}\cdot 22409^{2} \)	16T1584	Trivial (GRH)
16.4.904914537956817626953125.2	x^16 - 4x^15 + 5x^14 - 35x^12 + 3x^11 - 7x^10 + 50x^9 + 25x^8 - 50x^7 + 233x^6 - 12x^5 - 20x^4 - 75x^3 + 5x^2 + x + 1	\( 3^{10}\cdot 5^{15}\cdot 22409^{2} \)	16T1584	Trivial
16.0.1337065472000000000000000.1	x^16 - 10x^12 - 10x^8 + 50x^6 + 395x^4 + 390x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 101^{2} \)	16T1584	$[2]$
16.8.1337065472000000000000000.1	x^16 - 10x^12 - 10x^8 - 50x^6 + 395x^4 - 390x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 101^{2} \)	16T1584	Trivial (GRH)
16.0.1337065472000000000000000.2	x^16 + 10x^14 + 45x^12 + 120x^10 + 205x^8 + 230x^6 + 155x^4 + 50x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 101^{2} \)	16T1584	$[2]$
16.8.1337065472000000000000000.2	x^16 - 10x^14 + 45x^12 - 120x^10 + 205x^8 - 230x^6 + 155x^4 - 50x^2 + 5	\( 2^{32}\cdot 5^{15}\cdot 101^{2} \)	16T1584	Trivial (GRH)
16.4.3658203648000000000000000.1	x^16 - 10x^14 - 25x^12 + 460x^10 - 1295x^8 - 4620x^6 + 17835x^4 + 26730x^2 + 5445	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	$[2]$
16.8.3658203648000000000000000.1	x^16 - 2x^15 - 10x^14 + 30x^13 - 65x^12 + 164x^11 - 98x^10 + 80x^9 - 10x^8 - 2650x^7 + 2872x^6 + 1236x^5 + 5610x^4 - 7120x^3 - 7700x^2 + 4992x + 3001	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.4.3658203648000000000000000.2	x^16 - 2x^15 - 20x^12 + 204x^11 - 318x^10 - 120x^9 - 260x^8 + 90x^7 + 6062x^6 - 3244x^5 - 11705x^4 + 90x^3 + 2980x^2 + 9362x + 7741	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.8.3658203648000000000000000.2	x^16 + 10x^14 - 25x^12 - 460x^10 - 1295x^8 + 4620x^6 + 17835x^4 - 26730x^2 + 5445	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.4.3658203648000000000000000.3	x^16 - 2x^15 - 10x^14 + 35x^12 + 114x^11 - 178x^10 + 580x^9 + 115x^8 - 420x^7 - 2868x^6 - 9414x^5 - 13995x^4 - 16740x^3 - 18090x^2 - 3078x + 4941	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	$[2]$ (GRH)
16.8.3658203648000000000000000.3	x^16 - 2x^15 - 10x^14 + 60x^13 + 10x^12 - 406x^11 + 382x^10 + 1610x^9 - 1495x^8 - 4570x^7 + 82x^6 + 5826x^5 + 4200x^4 - 220x^3 - 1760x^2 - 1398x - 449	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.4.3658203648000000000000000.4	x^16 - 2x^15 - 40x^13 - 30x^12 - 36x^11 + 92x^10 + 240x^9 - 520x^8 - 1480x^7 - 2968x^6 - 3824x^5 - 3440x^4 - 4720x^3 - 2240x^2 + 832x + 496	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.8.3658203648000000000000000.4	x^16 - 6x^15 + 50x^13 + 30x^12 - 668x^11 + 1328x^10 - 430x^9 - 1365x^8 + 4000x^7 - 11592x^6 + 15502x^5 + 1250x^4 - 22930x^3 + 21800x^2 - 7936x + 961	\( 2^{24}\cdot 3^{10}\cdot 5^{15}\cdot 11^{2} \)	16T1584	Trivial (GRH)
16.8.4499892817920000000000000.1	x^16 - 8x^15 + 22x^14 + 10x^13 - 219x^12 + 610x^11 - 732x^10 + 96x^9 + 1051x^8 - 2260x^7 + 3730x^6 - 3980x^5 + 1625x^4 + 530x^3 - 600x^2 + 130x - 5	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 61^{2} \)	16T1584	Trivial (GRH)
16.8.4499892817920000000000000.2	x^16 - 2x^14 - 111x^12 - 8x^10 + 1486x^8 + 570x^6 - 2940x^4 + 360x^2 + 45	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 61^{2} \)	16T1584	Trivial (GRH)
16.12.88813928632320000000000000.1	x^16 - 16x^14 - 24x^12 + 1154x^10 - 3134x^8 - 1380x^6 + 2805x^4 - 810x^2 + 45	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 271^{2} \)	16T1584	Trivial (GRH)
16.4.88813928632320000000000000.1	x^16 + 16x^14 - 24x^12 - 1154x^10 - 3134x^8 + 1380x^6 + 2805x^4 + 810x^2 + 45	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 271^{2} \)	16T1584	$[2]$ (GRH)
16.12.88813928632320000000000000.2	x^16 - 6x^15 - 6x^14 + 60x^13 + 123x^12 - 442x^11 - 1652x^10 + 4972x^9 + 2992x^8 - 19506x^7 + 13432x^6 + 13990x^5 - 22450x^4 + 6156x^3 + 7260x^2 - 5704x + 1051	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 271^{2} \)	16T1584	Trivial (GRH)
16.4.88813928632320000000000000.2	x^16 - 6x^15 + 10x^14 + 44x^13 - 340x^12 + 1190x^11 - 3228x^10 + 7786x^9 - 16478x^8 + 32338x^7 - 57642x^6 + 84982x^5 - 96837x^4 + 78850x^3 - 37316x^2 + 5296x + 1171	\( 2^{24}\cdot 3^{10}\cdot 5^{13}\cdot 271^{2} \)	16T1584	$[2]$ (GRH)
16.8.1278525864673280000000000000.1	x^16 + 16x^14 + 56x^12 - 104x^10 - 299x^8 + 520x^6 - 130x^4 - 60x^2 + 5	\( 2^{48}\cdot 5^{13}\cdot 61^{2} \)	16T1584	Trivial (GRH)
16.8.1278525864673280000000000000.2	x^16 + 8x^14 + 14x^12 - 28x^10 - 79x^8 + 20x^6 + 80x^4 - 40x^2 + 5	\( 2^{48}\cdot 5^{13}\cdot 61^{2} \)	16T1584	Trivial (GRH)
16.4.13639404879872000000000000000.1	x^16 - 10x^14 - 75x^12 - 320x^10 + 1080x^8 - 29080x^6 + 20880x^4 + 191900x^2 + 51005	\( 2^{32}\cdot 5^{15}\cdot 101^{4} \)	16T1584	$[2]$ (GRH)
16.4.13639404879872000000000000000.2	x^16 + 30x^14 + 215x^12 - 110x^10 - 9215x^8 - 3640x^6 + 22785x^4 - 65650x^2 + 51005	\( 2^{32}\cdot 5^{15}\cdot 101^{4} \)	16T1584	$[2]$ (GRH)
16.0.414692653834021167975731560448.1	x^16 + 88x^14 + 2928x^12 + 47936x^10 + 418966x^8 + 1996208x^6 + 4988280x^4 + 5617888x^2 + 1612808	\( 2^{59}\cdot 449^{2}\cdot 1889^{2} \)	16T1584	$[2, 2, 1782]$ (GRH)
16.16.414692653834021167975731560448.1	x^16 - 88x^14 + 2928x^12 - 47936x^10 + 418966x^8 - 1996208x^6 + 4988280x^4 - 5617888x^2 + 1612808	\( 2^{59}\cdot 449^{2}\cdot 1889^{2} \)	16T1584	Trivial (GRH)
16.16.244746206612159968802812500000000.1	x^16 - 52x^14 + 1074x^12 - 11128x^10 + 60181x^8 - 163020x^6 + 211440x^4 - 112320x^2 + 11520	\( 2^{8}\cdot 3^{10}\cdot 5^{13}\cdot 115166641^{2} \)	16T1584	Trivial (GRH)
16.0.20900613426398125371268864579469312.1	x^16 + 224x^14 - 192x^13 + 20314x^12 - 35512x^11 + 970632x^10 - 2489256x^9 + 27814397x^8 - 82717776x^7 + 504053312x^6 - 1361814944x^5 + 5267824628x^4 - 9998030224x^3 + 21102481608x^2 - 15119234336x + 13719758722	\( 2^{57}\cdot 449^{4}\cdot 1889^{2} \)	16T1584	$[2, 2, 2, 2, 85042]$ (GRH)