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 41 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.698896000000000000.1	x^16 - 8x^15 + 26x^14 - 36x^13 - 7x^12 + 94x^11 - 112x^10 - 4x^9 + 126x^8 - 104x^7 - 9x^6 + 64x^5 - 35x^4 - 2x^3 + 10x^2 - 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 19^{2} \)	16T1086	Trivial
16.0.4612830062500000000.1	x^16 - 8x^15 + 36x^14 - 108x^13 + 236x^12 - 364x^11 + 344x^10 - 48x^9 - 339x^8 + 308x^7 + 440x^6 - 1502x^5 + 2147x^4 - 1986x^3 + 1255x^2 - 502x + 101	\( 2^{8}\cdot 5^{12}\cdot 11^{4}\cdot 71^{2} \)	16T1086	Trivial
16.0.4612830062500000000.2	x^16 - 8x^15 + 30x^14 - 65x^13 + 79x^12 - 33x^11 - 27x^10 + 51x^8 + 52x^7 - 172x^6 + 31x^5 + 144x^4 - 16x^3 - 81x^2 - 66x + 121	\( 2^{8}\cdot 5^{12}\cdot 11^{4}\cdot 71^{2} \)	16T1086	Trivial
16.0.9759376000000000000.1	x^16 - 6x^15 + 13x^14 - 67x^12 + 166x^11 - 129x^10 - 364x^9 + 1642x^8 - 3738x^7 + 6067x^6 - 7486x^5 + 7059x^4 - 4982x^3 + 2504x^2 - 810x + 131	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 71^{2} \)	16T1086	Trivial (GRH)
16.0.119251860062500000000.1	x^16 + 4x^14 + 24x^12 + 58x^10 + 159x^8 + 226x^6 + 311x^4 + 207x^2 + 121	\( 2^{8}\cdot 5^{12}\cdot 11^{4}\cdot 19^{4} \)	16T1086	$[2]$
16.4.1020407589171097501696.1	x^16 - 16x^13 + 96x^10 - 8x^9 - 68x^8 - 160x^7 - 16x^6 + 192x^5 + 96x^4 - 48x^3 - 56x^2 + 16x + 2	\( 2^{56}\cdot 7^{2}\cdot 17^{2} \)	16T1086	Trivial (GRH)
16.4.1020407589171097501696.2	x^16 - 8x^15 + 32x^14 - 80x^13 + 116x^12 - 56x^11 - 136x^10 + 328x^9 - 346x^8 + 104x^7 + 208x^6 - 224x^5 + 124x^4 + 56x^3 - 64x^2 - 40x + 47	\( 2^{56}\cdot 7^{2}\cdot 17^{2} \)	16T1086	Trivial (GRH)
16.4.2862678016000000000000.1	x^16 - 2x^15 - 8x^14 + 28x^13 - 8x^12 - 98x^11 + 152x^10 + 22x^9 - 141x^8 - 110x^7 + 96x^6 + 806x^5 - 1132x^4 + 60x^3 + 420x^2 - 6x - 79	\( 2^{28}\cdot 5^{12}\cdot 11^{2}\cdot 19^{2} \)	16T1086	Trivial (GRH)
16.4.2862678016000000000000.2	x^16 - 4x^15 + 6x^14 - 14x^13 + 12x^12 + 42x^11 - 72x^10 + 144x^9 - 149x^8 - 162x^7 + 216x^6 - 560x^5 + 146x^4 + 934x^3 + 10x^2 - 10x + 1	\( 2^{28}\cdot 5^{12}\cdot 11^{2}\cdot 19^{2} \)	16T1086	Trivial (GRH)
16.0.3297889042562500000000.2	x^16 - 3x^15 + 7x^14 - 12x^13 + 17x^12 + 5x^11 - 47x^10 - 31x^9 + 260x^8 - 429x^7 + 563x^6 - 810x^5 + 867x^4 - 533x^3 + 167x^2 - 22x + 1	\( 2^{8}\cdot 5^{12}\cdot 29^{2}\cdot 89^{4} \)	16T1086	$[2]$
16.0.4472934400000000000000.1	x^16 + 4x^14 - 10x^13 + 37x^12 - 120x^11 + 272x^10 - 530x^9 + 860x^8 - 1120x^7 + 1338x^6 - 1210x^5 + 1142x^4 - 690x^3 + 606x^2 - 220x + 181	\( 2^{24}\cdot 5^{14}\cdot 11^{2}\cdot 19^{2} \)	16T1086	$[2]$ (GRH)
16.8.4472934400000000000000.1	x^16 - 16x^14 - 10x^13 + 97x^12 + 90x^11 - 298x^10 - 290x^9 + 540x^8 + 440x^7 - 772x^6 - 130x^5 + 637x^4 - 210x^3 - 154x^2 + 110x - 19	\( 2^{24}\cdot 5^{14}\cdot 11^{2}\cdot 19^{2} \)	16T1086	Trivial (GRH)
16.0.7471219580228520116224.1	x^16 + 8x^14 - 16x^13 + 56x^12 - 88x^11 + 144x^10 - 264x^9 + 842x^8 - 1376x^7 + 1896x^6 - 1920x^5 + 1744x^4 - 904x^3 + 528x^2 - 168x + 31	\( 2^{58}\cdot 7^{2}\cdot 23^{2} \)	16T1086	Trivial
16.8.12874930290062500000000.1	x^16 - 4x^15 + 6x^14 - x^13 - 44x^12 + 132x^11 - 117x^10 - 18x^9 + 122x^8 - 121x^7 - 228x^6 + 431x^5 + 211x^4 - 607x^3 + 224x^2 + 33x - 19	\( 2^{8}\cdot 5^{12}\cdot 11^{8}\cdot 31^{2} \)	16T1086	Trivial (GRH)
16.8.35093559222562500000000.1	x^16 - x^15 - 15x^14 + 10x^13 + 64x^12 + 29x^11 - 133x^10 - 170x^9 - 49x^8 + 159x^7 + 247x^6 + 398x^5 - 66x^4 - 302x^3 - 154x^2 - 18x + 31	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	16T1086	Trivial (GRH)
16.12.350539780096000000000000.1	x^16 - 4x^15 - 14x^14 + 84x^13 - 49x^12 - 418x^11 + 1098x^10 - 678x^9 - 1893x^8 + 4714x^7 - 4208x^6 + 546x^5 + 2111x^4 - 1622x^3 + 144x^2 + 268x - 79	\( 2^{24}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	16T1086	Trivial (GRH)
16.4.350539780096000000000000.1	x^16 - 4x^15 + 14x^14 - 4x^13 - 61x^12 + 334x^11 - 662x^10 + 698x^9 + 811x^8 - 4230x^7 + 8348x^6 - 9162x^5 + 5699x^4 + 930x^3 - 1300x^2 + 288x - 19	\( 2^{24}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	16T1086	Trivial (GRH)
16.0.799999549910140441329664.2	x^16 + 12x^12 - 16x^10 + 450x^8 - 928x^6 + 1332x^4 - 816x^2 + 289	\( 2^{60}\cdot 7^{4}\cdot 17^{2} \)	16T1086	$[2]$ (GRH)
16.0.799999549910140441329664.3	x^16 + 12x^12 + 16x^10 + 450x^8 + 928x^6 + 1332x^4 + 816x^2 + 289	\( 2^{60}\cdot 7^{4}\cdot 17^{2} \)	16T1086	$[2]$ (GRH)
16.12.806950076416000000000000.1	x^16 - 2x^15 - 16x^14 + 24x^13 + 34x^12 + 70x^11 + 142x^10 - 802x^9 - 157x^8 + 1698x^7 - 618x^6 - 1130x^5 + 864x^4 + 44x^3 - 186x^2 + 38x + 1	\( 2^{28}\cdot 5^{12}\cdot 11^{4}\cdot 29^{2} \)	16T1086	Trivial (GRH)
16.4.806950076416000000000000.1	x^16 - 4x^15 + 2x^14 + 20x^13 - 56x^12 + 32x^11 - 64x^10 + 436x^9 - 514x^8 + 644x^7 - 1624x^6 + 352x^5 + 956x^4 - 480x^3 + 2000x^2 - 1480x - 820	\( 2^{28}\cdot 5^{12}\cdot 11^{4}\cdot 29^{2} \)	16T1086	$[2]$ (GRH)
16.8.922091585536000000000000.1	x^16 - 4x^15 + 2x^14 + 10x^13 + 4x^12 - 18x^11 - 144x^10 + 196x^9 - 229x^8 + 814x^7 - 424x^6 - 1208x^5 + 1626x^4 - 890x^3 + 390x^2 - 150x + 25	\( 2^{28}\cdot 5^{12}\cdot 11^{4}\cdot 31^{2} \)	16T1086	Trivial (GRH)
16.8.922091585536000000000000.2	x^16 - 16x^14 - 32x^13 + 36x^12 + 184x^11 + 88x^10 - 236x^9 - 146x^8 + 320x^7 + 144x^6 - 608x^5 - 324x^4 + 360x^3 + 200x^2 + 20x + 5	\( 2^{28}\cdot 5^{12}\cdot 11^{4}\cdot 31^{2} \)	16T1086	Trivial (GRH)
16.12.1033426763776000000000000.1	x^16 - 2x^15 - 22x^14 + 48x^13 + 158x^12 - 428x^11 - 268x^10 + 1728x^9 - 1546x^8 - 2800x^7 + 6680x^6 - 184x^5 - 6728x^4 + 3600x^3 - 800x^2 + 88x - 4	\( 2^{28}\cdot 5^{12}\cdot 11^{2}\cdot 19^{4} \)	16T1086	Trivial (GRH)
16.4.1033426763776000000000000.1	x^16 - 2x^15 + 2x^14 - 10x^13 + 8x^12 - 48x^11 + 234x^10 - 242x^9 - 213x^8 + 1264x^7 - 2042x^6 - 1238x^5 + 5324x^4 - 1494x^3 - 2864x^2 + 660x + 521	\( 2^{28}\cdot 5^{12}\cdot 11^{2}\cdot 19^{4} \)	16T1086	$[2]$ (GRH)
16.8.1179591173081788711960576.1	x^16 - 60x^12 + 96x^10 + 246x^8 - 448x^6 - 92x^4 + 224x^2 + 49	\( 2^{58}\cdot 7^{2}\cdot 17^{4} \)	16T1086	Trivial (GRH)
16.12.3295982154256000000000000.1	x^16 - 4x^15 - 15x^14 + 66x^13 + 103x^12 - 524x^11 - 225x^10 + 2200x^9 - 1068x^8 - 3038x^7 + 3306x^6 - 792x^5 - 709x^4 + 3000x^3 - 2465x^2 - 1080x + 1255	\( 2^{16}\cdot 5^{12}\cdot 11^{8}\cdot 31^{2} \)	16T1086	Trivial (GRH)
16.4.3295982154256000000000000.1	x^16 - 4x^15 + 11x^14 - 10x^13 - 20x^12 + 114x^11 - 315x^10 + 720x^9 - 964x^8 + 1050x^7 - 935x^6 + 34x^5 + 930x^4 - 600x^3 - 74x^2 + 146x - 29	\( 2^{16}\cdot 5^{12}\cdot 11^{8}\cdot 31^{2} \)	16T1086	$[2]$ (GRH)
16.0.278516178950416000000000000.1	x^16 + 8x^14 - 500x^12 - 5272x^10 + 93094x^8 + 1493272x^6 + 3095180x^4 - 22264968x^2 + 24611521	\( 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4}\cdot 41^{2} \)	16T1086	$[2, 2]$ (GRH)
16.0.278516178950416000000000000.2	x^16 - 2x^14 - 495x^12 + 5498x^10 + 56739x^8 - 1365298x^6 + 4983385x^4 + 16480442x^2 + 24611521	\( 2^{16}\cdot 5^{12}\cdot 11^{4}\cdot 29^{4}\cdot 41^{2} \)	16T1086	$[2, 2]$ (GRH)
16.0.3649130316009439966523293696.1	x^16 + 7x^14 - 34x^13 + 81x^12 - 204x^11 + 542x^10 - 1564x^9 + 276x^8 + 3264x^7 + 3748x^6 - 19448x^5 + 15372x^4 + 41072x^3 - 21800x^2 - 48688x + 30992	\( 2^{24}\cdot 13^{2}\cdot 17^{12}\cdot 47^{2} \)	16T1086	$[2, 2, 2]$ (GRH)
16.0.3649130316009439966523293696.2	x^16 + 43x^14 - 14x^13 + 759x^12 - 86x^11 + 5942x^10 + 2238x^9 + 22556x^8 + 18358x^7 + 59154x^6 + 65770x^5 + 148973x^4 + 142466x^3 + 220377x^2 + 144520x + 109651	\( 2^{24}\cdot 13^{2}\cdot 17^{12}\cdot 47^{2} \)	16T1086	$[2, 2, 2]$ (GRH)
16.8.262699715898099216000000000000.1	x^16 + 36x^14 - 360x^12 - 16686x^10 - 63711x^8 + 712314x^6 + 1580175x^4 - 7634979x^2 + 3538161	\( 2^{16}\cdot 3^{12}\cdot 5^{12}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4} \)	16T1086	$[2]$ (GRH)
16.0.835586729888343128721772773376.1	x^16 - 8x^15 + 96x^14 - 400x^13 + 2668x^12 - 6304x^11 + 33752x^10 - 44128x^9 + 246024x^8 - 180656x^7 + 1196888x^6 - 721360x^5 + 3884800x^4 - 2790640x^3 + 7393712x^2 - 5546400x + 6575522	\( 2^{62}\cdot 7^{6}\cdot 17^{2}\cdot 73^{2} \)	16T1086	$[2, 2, 2, 1876]$ (GRH)
16.0.835586729888343128721772773376.2	x^16 + 64x^14 + 2224x^12 - 592x^11 + 41104x^10 - 36672x^9 + 458360x^8 - 600224x^7 + 3274368x^6 - 4535584x^5 + 13795312x^4 - 14357632x^3 + 26002080x^2 - 13908224x + 16366712	\( 2^{62}\cdot 7^{6}\cdot 17^{2}\cdot 73^{2} \)	16T1086	$[2, 2, 2, 1446]$ (GRH)
16.8.2015232217016213221512488943616.1	x^16 + x^14 - 159x^12 - 256x^10 + 6291x^8 + 3349x^6 - 83249x^4 + 37570x^2 + 195364	\( 2^{22}\cdot 13^{2}\cdot 17^{12}\cdot 47^{4} \)	16T1086	$[2, 2]$ (GRH)
16.8.2015232217016213221512488943616.2	x^16 - 6x^14 - 301x^12 + 114x^10 + 21373x^8 + 16524x^6 - 496060x^4 - 360672x^2 + 3125824	\( 2^{22}\cdot 13^{2}\cdot 17^{12}\cdot 47^{4} \)	16T1086	$[2, 2]$ (GRH)
16.8.68188413910586864400000000000000.1	x^16 - 20x^14 - 3570x^12 + 57700x^10 + 2444730x^8 - 12589250x^6 - 227795875x^4 - 78186900x^2 + 918393025	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 11^{2}\cdot 19^{2}\cdot 29^{6} \)	16T1086	$[2, 2]$ (GRH)
16.16.323391267567114489856000000000000.1	x^16 - 8x^15 - 180x^14 + 1300x^13 + 11182x^12 - 63596x^11 - 361460x^10 + 1315740x^9 + 6387559x^8 - 12019788x^7 - 57282828x^6 + 46017268x^5 + 234002138x^4 - 74291988x^3 - 364246632x^2 + 70705872x + 84272481	\( 2^{24}\cdot 5^{12}\cdot 29^{6}\cdot 41^{2}\cdot 281^{2} \)	16T1086	Trivial (GRH)
16.16.717316692595573067776000000000000.1	x^16 - 4x^15 - 172x^14 + 700x^13 + 11388x^12 - 47976x^11 - 364924x^10 + 1634904x^9 + 5800142x^8 - 29221492x^7 - 40497068x^6 + 268291916x^5 + 45483164x^4 - 1137376128x^3 + 565699204x^2 + 1697235840x - 1439480519	\( 2^{24}\cdot 5^{12}\cdot 29^{4}\cdot 89^{2}\cdot 5591^{2} \)	16T1086	Trivial (GRH)
16.8.1807769551224448500316223474054987776.1	x^16 - 8x^15 - 40x^14 + 96x^13 + 532x^12 + 2008x^11 - 33864x^10 - 108104x^9 + 308810x^8 + 324776x^7 - 1325160x^6 - 603568x^5 + 6613892x^4 + 435432x^3 - 16868624x^2 + 10924760x - 1804313	\( 2^{56}\cdot 7^{8}\cdot 17^{2}\cdot 41^{4}\cdot 73^{2} \)	16T1086	$[4]$ (GRH)