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 matches 1-50 of 52)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.66221484488898283.1	x^16 - x^15 - 3x^13 + 10x^12 - 11x^11 + 17x^10 - 30x^9 + 27x^8 - 20x^7 + 47x^6 - 70x^5 + 35x^4 + 13x^3 - 21x^2 + 8x - 1	\( -\,191^{2}\cdot 283^{5} \)	16T1847	Trivial
16.0.445419681762536869.1	x^16 - 3x^15 + 3x^14 + x^13 - 8x^12 + 2x^11 + 21x^10 - 17x^9 - 9x^8 + 32x^7 - 13x^6 - 64x^5 + 16x^4 + 60x^3 + 16x^2 - 10x + 1	\( 29^{4}\cdot 229^{5} \)	16T1847	Trivial
16.2.879414812513300403.1	x^16 - x^15 + x^14 - 2x^13 + 2x^12 - 4x^11 + 4x^10 - 4x^9 + 3x^8 - 4x^7 + 4x^6 - 4x^5 + 2x^4 - 2x^3 + x^2 - x + 1	\( -\,3^{15}\cdot 23^{2}\cdot 41^{5} \)	16T1847	Trivial
16.0.21338928599875794109.1	x^16 - 4x^15 + 7x^14 - 10x^13 + 16x^12 - 2x^11 - 36x^10 + 27x^9 + 10x^8 + 34x^7 + 23x^6 - 125x^5 + 21x^4 + 115x^3 - 44x^2 - 35x + 25	\( 229^{5}\cdot 5821^{2} \)	16T1847	Trivial
16.2.22241012005863051507.1	x^16 - x^15 - x^14 - 5x^13 + 8x^12 - 8x^11 + 6x^10 - 57x^9 + 73x^8 - 57x^7 + 6x^6 - 8x^5 + 8x^4 - 5x^3 - x^2 - x + 1	\( -\,3^{13}\cdot 41^{5}\cdot 347^{2} \)	16T1847	Trivial
16.4.99921317462046419917.1	x^16 - 3x^15 + 2x^14 - 7x^13 + 19x^12 + 5x^11 - 58x^10 + 78x^9 - 97x^8 + 129x^7 - 119x^6 + 135x^5 - 177x^4 + 100x^3 + 17x^2 - 27x + 1	\( 19^{5}\cdot 59^{2}\cdot 103^{5} \)	16T1847	Trivial
16.8.99921317462046419917.1	x^16 - 7x^15 + 15x^14 + 11x^13 - 110x^12 + 192x^11 - 44x^10 - 312x^9 + 440x^8 - 79x^7 - 330x^6 + 282x^5 + 13x^4 - 105x^3 + 25x^2 + 6x + 1	\( 19^{5}\cdot 59^{2}\cdot 103^{5} \)	16T1847	Trivial
16.4.128855729413135989373.1	x^16 - 4x^15 + 4x^14 + 4x^13 - 9x^12 - 6x^11 + 19x^10 - 9x^9 - 15x^7 + 31x^6 - 27x^5 + 27x^4 - 8x^3 - 3x^2 - 3x - 1	\( 19^{5}\cdot 67^{2}\cdot 103^{5} \)	16T1847	Trivial
16.8.128855729413135989373.1	x^16 - 4x^15 + 2x^14 + 11x^13 - 16x^12 + 6x^11 - 20x^10 + 30x^9 + 56x^8 - 146x^7 + 62x^6 + 80x^5 - 69x^4 - 11x^3 + 19x^2 + x - 1	\( 19^{5}\cdot 67^{2}\cdot 103^{5} \)	16T1847	Trivial (GRH)
16.0.360072682058003531008.1	x^16 - 4x^15 + 15x^14 - 45x^13 + 106x^12 - 220x^11 + 390x^10 - 604x^9 + 821x^8 - 990x^7 + 1158x^6 - 846x^5 + 1124x^4 - 538x^3 + 691x^2 + 49x + 343	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{5} \)	16T1847	Trivial (GRH)
16.4.360072682058003531008.1	x^16 - x^15 - x^14 - 3x^13 + 18x^12 + 26x^11 - 20x^10 - 156x^9 - 247x^8 - 94x^7 + 305x^6 + 665x^5 + 681x^4 + 403x^3 + 122x^2 + 3x - 9	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{5} \)	16T1847	Trivial (GRH)
16.0.360072682058003531008.2	x^16 - 6x^15 + 20x^14 - 38x^13 + 25x^12 + 92x^11 - 324x^10 + 500x^9 - 326x^8 - 250x^7 + 950x^6 - 1440x^5 + 1406x^4 - 1064x^3 + 670x^2 - 252x + 63	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{5} \)	16T1847	Trivial (GRH)
16.4.360072682058003531008.2	x^16 - 5x^15 + 14x^14 - 31x^13 + 48x^12 - 52x^11 + 62x^10 - 136x^9 + 251x^8 - 308x^7 + 434x^6 - 622x^5 + 440x^4 + 75x^3 - 278x^2 + 133x - 19	\( 2^{8}\cdot 7^{2}\cdot 19^{5}\cdot 103^{5} \)	16T1847	Trivial (GRH)
16.2.3684999589989814632448.1	x^16 + 18x^14 + 121x^12 + 332x^10 + 122x^8 - 650x^6 - 40x^4 - 283	\( -\,2^{24}\cdot 11^{2}\cdot 283^{5} \)	16T1847	Trivial (GRH)
16.6.3684999589989814632448.1	x^16 - 18x^14 + 121x^12 - 332x^10 + 122x^8 + 650x^6 - 40x^4 - 283	\( -\,2^{24}\cdot 11^{2}\cdot 283^{5} \)	16T1847	Trivial (GRH)
16.8.4885806833123138044688.1	x^16 - 6x^15 + 19x^14 - 43x^13 + 51x^12 - 5x^11 - 129x^10 + 277x^9 - 292x^8 + 120x^7 + 204x^6 - 200x^5 - 5x^4 + 7x^3 + 19x^2 - 2	\( 2^{4}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial
16.8.4885806833123138044688.2	x^16 - x^15 - 12x^14 + 27x^13 + 27x^12 - 116x^11 + 29x^10 + 130x^9 - 87x^8 + 5x^7 + 2x^6 - 15x^5 + 8x^4 + 12x^3 - 15x^2 + 7x - 1	\( 2^{4}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial
16.6.4991994601110295044283.1	x^16 - 7x^15 + 9x^14 + 34x^13 - 91x^12 + 33x^11 + 37x^10 + 149x^9 - 619x^8 + 962x^7 - 697x^6 + 246x^5 - 1356x^4 + 3441x^3 - 2114x^2 - 478x + 503	\( -\,229^{4}\cdot 283^{5} \)	16T1847	Trivial (GRH)
16.4.350231775334226837790993.1	x^16 - 4x^15 - 7x^14 + 27x^13 + 28x^12 + x^11 - 139x^10 - 237x^9 + 335x^8 + 328x^7 + 105x^6 - 783x^5 - 5x^4 + 413x^3 + 31x^2 - 74x - 17	\( 3^{5}\cdot 17^{10}\cdot 59^{5} \)	16T1847	Trivial
16.8.350231775334226837790993.1	x^16 - 4x^15 + 8x^14 - 20x^13 + 8x^12 + 147x^11 - 537x^10 + 939x^9 - 873x^8 + 296x^7 + 432x^6 - 529x^5 + 416x^4 - 198x^3 - 21x^2 + 45x - 9	\( 3^{5}\cdot 17^{10}\cdot 59^{5} \)	16T1847	Trivial (GRH)
16.0.692690614636144888905728.1	x^16 + 26x^14 + 281x^12 + 1632x^10 + 5347x^8 + 9726x^6 + 9490x^4 + 5554x^2 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.692690614636144888905728.1	x^16 - 9x^14 + 5x^12 + 120x^10 - 66x^8 - 864x^6 - 227x^4 + 2777x^2 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.8.692690614636144888905728.1	x^16 - 2x^14 + 14x^12 - 94x^10 - 81x^8 + 464x^6 + 2017x^4 - 5554x^2 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.0.692690614636144888905728.2	x^16 + 2x^14 + 14x^12 + 94x^10 - 81x^8 - 464x^6 + 2017x^4 + 5554x^2 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.692690614636144888905728.2	x^16 + 12x^14 + 39x^12 + 18x^10 + 164x^8 + 627x^6 - 1775x^4 - 2777x^2 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.692690614636144888905728.3	x^16 + 14x^14 + 63x^12 + 85x^10 - 404x^8 - 1479x^6 - 1923x^4 + 2777	\( 2^{22}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.8.2677031113194834203046033.1	x^16 - 4x^15 - 17x^14 + 54x^13 + 192x^12 - 283x^11 - 1347x^10 + 234x^9 + 5066x^8 + 3586x^7 - 7788x^6 - 12227x^5 - 1321x^4 + 7988x^3 + 5967x^2 + 1475x + 71	\( 3^{5}\cdot 17^{8}\cdot 47^{2}\cdot 59^{5} \)	16T1847	Trivial (GRH)
16.8.2677031113194834203046033.2	x^16 - 2x^14 - 3x^13 - 45x^12 + 98x^11 - 123x^10 + 165x^9 + 241x^8 - 1612x^7 + 3150x^6 - 1467x^5 - 1953x^4 + 1305x^3 + 371x^2 - 138x + 21	\( 3^{5}\cdot 17^{8}\cdot 47^{2}\cdot 59^{5} \)	16T1847	Trivial (GRH)
16.0.3152085978008041540118937.1	x^16 - 8x^15 + 25x^14 - 31x^13 - 21x^12 + 128x^11 - 175x^10 + 36x^9 + 253x^8 - 501x^7 + 560x^6 - 438x^5 + 255x^4 - 112x^3 + 36x^2 - 8x + 1	\( 3^{7}\cdot 17^{10}\cdot 59^{5} \)	16T1847	$[12]$ (GRH)
16.0.14398282777667643805518297.1	x^16 - 6x^15 + 20x^14 - 79x^13 + 364x^12 - 1203x^11 + 3126x^10 - 6435x^9 + 10587x^8 - 14212x^7 + 15425x^6 - 13654x^5 + 9823x^4 - 5581x^3 + 2625x^2 - 794x + 224	\( 3^{5}\cdot 17^{8}\cdot 59^{5}\cdot 109^{2} \)	16T1847	$[11]$ (GRH)
16.0.14398282777667643805518297.2	x^16 - 4x^15 + x^14 + 29x^13 - 73x^12 + 67x^11 + 270x^10 - 1151x^9 + 1165x^8 + 2263x^7 - 6761x^6 + 4085x^5 + 5564x^4 - 10479x^3 + 7164x^2 - 2535x + 462	\( 3^{5}\cdot 17^{8}\cdot 59^{5}\cdot 109^{2} \)	16T1847	$[11]$ (GRH)
16.12.20012264788472373431042048.1	x^16 - 31x^14 + 357x^12 - 1814x^10 + 3279x^8 + 2759x^6 - 11352x^4 + 1460x^2 + 2777	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.20012264788472373431042048.1	x^16 - 2x^15 + 9x^14 - 26x^13 + 74x^12 - 126x^11 + 213x^10 - 362x^9 + 169x^8 + 244x^7 - 580x^6 + 1668x^5 - 5031x^4 + 13006x^3 - 16417x^2 + 3698x + 2623	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.8.20012264788472373431042048.1	x^16 - 3x^14 - 126x^12 + 351x^10 + 3851x^8 - 9347x^6 - 6685x^4 + 16925x^2 + 2777	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.12.20012264788472373431042048.2	x^16 - 2x^15 - 18x^14 + 12x^13 + 39x^12 - 22x^11 + 418x^10 + 700x^9 - 608x^8 - 2790x^7 - 5870x^6 - 2596x^5 + 7931x^4 + 5024x^3 - 4307x^2 - 1640x + 976	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.20012264788472373431042048.2	x^16 + 12x^14 - 39x^12 - 546x^10 - 447x^8 + 5438x^6 + 15110x^4 + 13150x^2 + 2777	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.8.20012264788472373431042048.2	x^16 - 3x^14 - 65x^12 + 213x^10 + 835x^8 - 2109x^6 - 2802x^4 + 2769x^2 + 2777	\( 2^{16}\cdot 43^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.50433375648128664641902992.1	x^16 + 2x^14 - 32x^12 - 70x^10 + 133x^8 + 249x^6 - 219x^4 - 177x^2 + 177	\( 2^{4}\cdot 3^{7}\cdot 17^{10}\cdot 59^{5} \)	16T1847	$[2]$ (GRH)
16.4.50433375648128664641902992.2	x^16 - 10x^14 - 11x^13 + 72x^12 + 118x^11 - 383x^10 - 292x^9 + 1103x^8 - 678x^7 - 297x^6 + 3429x^5 - 1920x^4 - 6765x^3 - 5781x^2 - 2016x + 291	\( 2^{4}\cdot 3^{7}\cdot 17^{10}\cdot 59^{5} \)	16T1847	$[2]$ (GRH)
16.0.189300033486712326031511552.1	x^16 - 5x^15 + 42x^14 - 134x^13 + 542x^12 - 1111x^11 + 3053x^10 - 4356x^9 + 14437x^8 - 33767x^7 + 64198x^6 - 97940x^5 + 1019x^4 + 24420x^3 + 541550x^2 - 827633x + 1593481	\( 2^{12}\cdot 23^{4}\cdot 2777^{5} \)	16T1847	$[2]$ (GRH)
16.12.189300033486712326031511552.1	x^16 - 5x^15 - 7x^14 + 49x^13 - 170x^12 + 1077x^11 - 13x^10 - 13481x^9 + 23377x^8 + 25178x^7 - 132886x^6 + 147502x^5 + 172031x^4 - 506979x^3 + 172437x^2 + 282407x - 164249	\( 2^{12}\cdot 23^{4}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.12.189300033486712326031511552.2	x^16 - 2x^15 - 50x^14 + 161x^13 + 800x^12 - 4052x^11 - 2018x^10 + 39729x^9 - 53813x^8 - 118888x^7 + 380348x^6 - 139384x^5 - 680481x^4 + 887718x^3 + 73908x^2 - 776145x + 402469	\( 2^{12}\cdot 23^{4}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.16.543610144983731863601610752.1	x^16 - x^15 - 50x^14 - 8x^13 + 851x^12 + 814x^11 - 5542x^10 - 7699x^9 + 14106x^8 + 25239x^7 - 9932x^6 - 30358x^5 - 5363x^4 + 10996x^3 + 5988x^2 + 985x + 37	\( 2^{16}\cdot 24197^{5} \)	16T1847	Trivial (GRH)
16.0.1740395992564167723139530752.1	x^16 + 43x^14 + 713x^12 + 5842x^10 + 25032x^8 + 54431x^6 + 54622x^4 + 22216x^2 + 2777	\( 2^{16}\cdot 401^{2}\cdot 2777^{5} \)	16T1847	$[6, 96]$ (GRH)
16.16.1740395992564167723139530752.1	x^16 - 43x^14 + 713x^12 - 5842x^10 + 25032x^8 - 54431x^6 + 54622x^4 - 22216x^2 + 2777	\( 2^{16}\cdot 401^{2}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.0.34791049278958839270503088128.1	x^16 + 44x^14 + 823x^12 + 8547x^10 + 53931x^8 + 211945x^6 + 507347x^4 + 677516x^2 + 387152	\( 2^{22}\cdot 24197^{5} \)	16T1847	$[2, 2, 548]$ (GRH)
16.12.66814405147552869881269516352.1	x^16 - 3x^15 - 39x^14 + 85x^13 + 146x^12 + 676x^11 + 7986x^10 - 30713x^9 - 64431x^8 + 96157x^7 - 253495x^6 + 1354110x^5 + 3223597x^4 - 4349716x^3 - 9123536x^2 - 2980192x - 161632	\( 2^{6}\cdot 43^{6}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.4.66814405147552869881269516352.1	x^16 - 7x^15 + 45x^14 - 140x^13 + 228x^12 + 712x^11 - 5230x^10 + 19654x^9 - 54463x^8 + 117065x^7 - 236177x^6 + 186494x^5 - 201775x^4 - 1012458x^3 + 3355324x^2 - 853320x + 8859211	\( 2^{6}\cdot 43^{6}\cdot 2777^{5} \)	16T1847	$[8]$ (GRH)
16.8.66814405147552869881269516352.1	x^16 - 8x^15 + 58x^14 - 184x^13 + 213x^12 + 50x^11 - 1926x^10 + 4497x^9 - 6310x^8 + 25938x^7 - 226076x^6 + 535769x^5 + 1230405x^4 - 3972392x^3 + 137642x^2 + 3400920x - 96931	\( 2^{6}\cdot 43^{6}\cdot 2777^{5} \)	16T1847	Trivial (GRH)
16.8.66814405147552869881269516352.2	x^16 - x^15 - 33x^14 + 60x^13 + 88x^12 - 115x^11 + 2504x^10 - 7350x^9 - 4482x^8 + 24867x^7 - 81962x^6 + 167546x^5 + 196404x^4 - 625613x^3 - 281403x^2 + 21230x + 2597393	\( 2^{6}\cdot 43^{6}\cdot 2777^{5} \)	16T1847	Trivial (GRH)