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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.30476530300390625.1	x^16 - 2x^15 + 6x^14 - 6x^13 + 11x^12 - 5x^11 + 10x^10 - 2x^9 + 8x^8 - 5x^7 + 8x^6 - 6x^5 + 9x^4 - 3x^3 + 5x^2 - x + 1	\( 5^{8}\cdot 11\cdot 19\cdot 139^{4} \)	16T1862	Trivial
16.0.83791245579190272.1	x^16 - 2x^15 + 6x^14 - 8x^13 + 18x^12 - 24x^11 + 42x^10 - 50x^9 + 66x^8 - 66x^7 + 68x^6 - 52x^5 + 39x^4 - 20x^3 + 10x^2 - 2x + 1	\( 2^{16}\cdot 3^{9}\cdot 19\cdot 43^{4} \)	16T1862	Trivial
16.0.324305279368750000.1	x^16 - x^15 + 7x^14 - x^13 + 18x^12 + 11x^11 + 30x^10 + 39x^9 + 48x^8 + 54x^7 + 47x^6 + 34x^5 + 15x^4 + 7x^3 + x^2 + 1	\( 2^{4}\cdot 5^{8}\cdot 139^{5} \)	16T1862	Trivial
16.0.1659654671208873984.1	x^16 - 4x^15 + 4x^14 + 10x^13 - 29x^12 + 20x^11 + 28x^10 - 72x^9 + 64x^8 + 6x^7 - 76x^6 + 72x^5 - 12x^4 - 28x^3 + 24x^2 - 8x + 1	\( 2^{16}\cdot 3^{8}\cdot 43^{4}\cdot 1129 \)	16T1862	Trivial
16.4.38669960766845703125.1	x^16 - 2x^15 + 5x^14 - 5x^13 - x^12 + 8x^11 - 22x^10 + 15x^9 + x^8 - 7x^7 + 23x^6 + 4x^5 - 26x^4 - 9x^3 + 9x^2 + 6x + 1	\( 5^{12}\cdot 101\cdot 199^{4} \)	16T1862	Trivial
16.4.38669960766845703125.2	x^16 - 7x^15 + 22x^14 - 49x^13 + 83x^12 - 101x^11 + 89x^10 - 82x^9 + 123x^8 - 204x^7 + 276x^6 - 283x^5 + 218x^4 - 123x^3 + 48x^2 - 11x + 1	\( 5^{12}\cdot 101\cdot 199^{4} \)	16T1862	Trivial
16.2.76191308837646484375.1	x^16 - 3x^15 + 4x^14 - 6x^13 + 6x^12 - 14x^11 + 25x^10 - 50x^9 + 67x^8 - 80x^7 + 70x^6 - 48x^5 + 31x^4 - 23x^3 + 16x^2 - 6x + 1	\( -\,5^{12}\cdot 199^{5} \)	16T1862	Trivial
16.6.76191308837646484375.1	x^16 - 4x^15 + 9x^14 - 4x^13 - 27x^12 + 72x^11 - 86x^10 + 18x^9 + 66x^8 - 72x^7 + 94x^6 - 115x^5 + 40x^4 + 14x^3 - 12x^2 + x + 1	\( -\,5^{12}\cdot 199^{5} \)	16T1862	Trivial
16.2.106592794630031250000.1	x^16 + 6x^14 - 4x^12 - 5x^10 + 18x^8 - 26x^6 + 9x^4 - 5x^2 - 5	\( -\,2^{4}\cdot 3^{8}\cdot 5^{9}\cdot 151^{4} \)	16T1862	Trivial
16.6.106592794630031250000.1	x^16 - x^15 + x^14 + 10x^13 - 21x^12 + 19x^11 + 6x^10 - 92x^9 + 100x^8 - 65x^7 - 44x^6 + 136x^5 - 7x^4 - 37x^3 + 3x^2 + 6x + 1	\( -\,2^{4}\cdot 3^{8}\cdot 5^{9}\cdot 151^{4} \)	16T1862	Trivial
16.8.299022171870361328125.1	x^16 - 3x^15 - x^14 + 8x^13 + 7x^12 - x^11 - 118x^10 + 197x^9 + x^8 - 229x^7 + 84x^6 + 105x^5 - 19x^4 - 32x^3 - 5x^2 + 5x + 1	\( 5^{12}\cdot 11\cdot 71\cdot 199^{4} \)	16T1862	Trivial
16.6.9409213886215506250000.1	x^16 + 5x^14 - 15x^12 - 36x^10 + 54x^8 + 95x^6 - 51x^4 - 92x^2 - 16	\( -\,2^{4}\cdot 5^{8}\cdot 6229^{4} \)	16T1862	Trivial
16.6.9409213886215506250000.2	x^16 - x^15 + 3x^14 - 8x^13 + 30x^12 - 4x^11 + 7x^10 - 194x^9 + 65x^8 + 372x^7 - 244x^6 - 234x^5 + 267x^4 - 21x^3 - 59x^2 + 20x - 1	\( -\,2^{4}\cdot 5^{8}\cdot 6229^{4} \)	16T1862	Trivial
16.12.47009627709670400000000.1	x^16 - 2x^15 - 14x^14 + 30x^13 + 36x^12 - 126x^11 + 50x^10 + 176x^9 - 290x^8 + 28x^7 + 340x^6 - 232x^5 - 99x^4 + 130x^3 - 26x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 89\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.4.47009627709670400000000.1	x^16 - 8x^14 - 4x^13 + 2x^12 - 32x^11 - 32x^10 - 20x^9 - 75x^8 - 40x^7 - 128x^6 - 256x^5 + 32x^4 - 128x^3 - 512x^2 + 256	\( 2^{16}\cdot 5^{8}\cdot 89\cdot 379^{4} \)	16T1862	$[2]$
16.8.47009627709670400000000.1	x^16 - 6x^15 + 6x^14 + 46x^13 - 154x^12 + 66x^11 + 530x^10 - 1096x^9 + 305x^8 + 1686x^7 - 2510x^6 + 1132x^5 + 404x^4 - 560x^3 + 144x^2 + 6x - 1	\( 2^{16}\cdot 5^{8}\cdot 89\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.8.47009627709670400000000.2	x^16 - 14x^14 - 12x^13 + 50x^12 + 40x^11 - 98x^10 + 2x^9 + 171x^8 - 100x^7 - 190x^6 + 30x^5 + 78x^4 + 32x^3 - 4x^2 + 30x + 9	\( 2^{16}\cdot 5^{8}\cdot 89\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.10.47046069431077531250000.1	x^16 - 2x^15 - 7x^14 + 26x^13 - 22x^12 - 84x^11 + 219x^10 - 147x^9 - 246x^8 + 753x^7 - 658x^6 - 118x^5 + 583x^4 - 409x^3 + 130x^2 - 19x + 1	\( -\,2^{4}\cdot 5^{9}\cdot 6229^{4} \)	16T1862	Trivial (GRH)
16.10.79757907687193600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 40x^12 + 124x^11 - 404x^10 + 502x^9 - 78x^8 - 764x^7 + 966x^6 - 62x^5 - 573x^4 + 328x^3 + 40x^2 - 84x + 19	\( -\,2^{16}\cdot 5^{8}\cdot 151\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.2.79757907687193600000000.1	x^16 - 4x^15 + 12x^14 - 22x^13 + 9x^12 + 8x^11 - 74x^10 + 54x^9 + 193x^8 + 210x^7 + 730x^6 + 1902x^5 + 2034x^4 + 2460x^3 + 3860x^2 + 2672x + 596	\( -\,2^{16}\cdot 5^{8}\cdot 151\cdot 379^{4} \)	16T1862	$[2]$
16.10.92962859291033600000000.1	x^16 - 2x^15 - 16x^14 + 32x^13 + 70x^12 - 128x^11 - 154x^10 + 162x^9 + 285x^8 + 42x^7 - 430x^6 - 234x^5 + 298x^4 + 190x^3 - 38x^2 - 68x - 11	\( -\,2^{20}\cdot 5^{8}\cdot 11\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.2.92962859291033600000000.1	x^16 - 2x^15 - 4x^14 - 4x^13 - 4x^12 + 22x^11 + 20x^10 + 38x^9 - 17x^8 - 148x^7 - 40x^6 - 82x^5 + 6x^4 - 36x^3 - 4x^2 - 8x + 1	\( -\,2^{20}\cdot 5^{8}\cdot 11\cdot 379^{4} \)	16T1862	$[2]$
16.6.105111414766566400000000.1	x^16 + 2x^14 - 6x^13 - 21x^12 + 22x^11 - 166x^10 - 150x^9 - 94x^8 - 498x^7 - 12x^6 - 304x^5 - 1007x^4 - 556x^3 - 304x^2 - 44x + 1	\( -\,2^{16}\cdot 5^{8}\cdot 199\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.8.519087175531000000000000.1	x^16 - 17x^14 + 125x^12 - 522x^10 + 1359x^8 - 2263x^6 + 2350x^4 - 1373x^2 + 331	\( 2^{12}\cdot 5^{12}\cdot 199^{4}\cdot 331 \)	16T1862	Trivial (GRH)
16.0.824090213843697600000000.1	x^16 + 18x^14 + 93x^12 + 214x^10 + 382x^8 + 1059x^6 + 1636x^4 + 971x^2 + 151	\( 2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 151^{5} \)	16T1862	$[2]$
16.0.824090213843697600000000.2	x^16 + 19x^14 + 160x^12 + 763x^10 + 2104x^8 + 3064x^6 + 1963x^4 + 604x^2 + 151	\( 2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 151^{5} \)	16T1862	$[2]$
16.14.1700293663096832000000000.1	x^16 - 6x^15 + 2x^14 + 38x^13 - 36x^12 - 34x^11 - 38x^10 - 174x^9 + 526x^8 + 374x^7 - 746x^6 - 278x^5 + 276x^4 + 50x^3 - 34x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{9}\cdot 139^{5} \)	16T1862	Trivial (GRH)
16.6.1700293663096832000000000.1	x^16 - 6x^14 - 12x^13 - 18x^12 + 2x^11 + 52x^10 + 144x^9 - 338x^8 - 316x^7 + 1858x^6 - 322x^5 - 3487x^4 - 934x^3 - 200x^2 + 880x - 29	\( -\,2^{24}\cdot 5^{9}\cdot 139^{5} \)	16T1862	Trivial (GRH)
16.10.2163499270773145600000000.1	x^16 - 6x^14 - 42x^12 + 170x^10 + 289x^8 - 594x^6 - 612x^4 + 56x^2 - 1	\( -\,2^{28}\cdot 5^{8}\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.14.2163499270773145600000000.1	x^16 - 20x^14 + 144x^12 - 442x^10 + 503x^8 - 34x^6 - 146x^4 + 26x^2 - 1	\( -\,2^{28}\cdot 5^{8}\cdot 379^{4} \)	16T1862	Trivial (GRH)
16.12.4703591978355965636328125.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 97x^12 + 127x^11 + 53x^10 - 309x^9 + 285x^8 + 109x^7 - 393x^6 + 223x^5 + 77x^4 - 155x^3 + 55x^2 + 6x - 4	\( 5^{8}\cdot 1229\cdot 9949^{4} \)	16T1862	Trivial (GRH)
16.16.10860280397062169600000000.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 180x^12 - 194x^11 + 862x^10 + 90x^9 - 1913x^8 + 402x^7 + 2166x^6 - 570x^5 - 1230x^4 + 194x^3 + 284x^2 + 16x - 1	\( 2^{16}\cdot 5^{8}\cdot 29\cdot 379^{4}\cdot 709 \)	16T1862	Trivial (GRH)
16.0.58609993297236388431250000.1	x^16 - 4x^15 + 23x^14 - 68x^13 + 190x^12 - 364x^11 + 524x^10 - 648x^9 + 1053x^8 - 3056x^7 + 12244x^6 - 23337x^5 + 23765x^4 - 13814x^3 + 7189x^2 + 4667x + 7171	\( 2^{4}\cdot 5^{8}\cdot 6229^{5} \)	16T1862	$[28]$ (GRH)
16.16.58609993297236388431250000.1	x^16 - 3x^15 - 36x^14 + 127x^13 + 410x^12 - 1899x^11 - 1232x^10 + 12698x^9 - 7383x^8 - 35629x^7 + 53331x^6 + 15244x^5 - 84521x^4 + 62713x^3 - 9387x^2 - 6151x + 1721	\( 2^{4}\cdot 5^{8}\cdot 6229^{5} \)	16T1862	Trivial (GRH)
16.8.58609993297236388431250000.1	x^16 - 5x^15 + 2x^14 + 27x^13 - 225x^12 + 72x^11 + 902x^10 + 1524x^9 + 1292x^8 + 312x^7 - 465x^6 - 784x^5 - 682x^4 - 365x^3 - 129x^2 - 25x - 1	\( 2^{4}\cdot 5^{8}\cdot 6229^{5} \)	16T1862	$[2]$ (GRH)
16.8.58609993297236388431250000.2	x^16 - 4x^15 - 3x^14 + 44x^13 - 65x^12 - 148x^11 + 346x^10 + 558x^9 - 1225x^8 - 1132x^7 + 693x^6 + 1606x^5 + 16004x^4 - 33290x^3 + 14871x^2 - 1412x + 31	\( 2^{4}\cdot 5^{8}\cdot 6229^{5} \)	16T1862	Trivial (GRH)
16.12.90939332507261158400000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 110x^12 + 114x^11 + 118x^10 - 348x^9 + 213x^8 + 202x^7 - 388x^6 + 162x^5 + 92x^4 - 120x^3 + 20x^2 + 20x - 4	\( 2^{16}\cdot 5^{8}\cdot 379^{4}\cdot 172169 \)	16T1862	Trivial (GRH)
16.12.293049966486181942156250000.1	x^16 - 5x^15 - 15x^14 + 120x^13 - 102x^12 - 633x^11 + 1820x^10 - 1358x^9 - 3155x^8 + 10733x^7 - 13704x^6 + 6103x^5 + 3418x^4 - 4641x^3 + 1521x^2 - 91x - 11	\( 2^{4}\cdot 5^{9}\cdot 6229^{5} \)	16T1862	Trivial (GRH)
16.4.293049966486181942156250000.1	x^16 - 6x^15 + x^14 - 8x^13 - 18x^12 + 14x^11 + 23x^10 + 260x^9 + 23x^8 + 1146x^7 + 821x^6 + 1284x^5 - 3123x^4 - 6852x^3 - 9591x^2 - 8918x - 3061	\( 2^{4}\cdot 5^{9}\cdot 6229^{5} \)	16T1862	$[2]$ (GRH)
16.8.293049966486181942156250000.1	x^16 - 5x^15 + 9x^14 - 56x^13 + 19x^12 + 503x^11 - 736x^10 + 710x^9 - 42x^8 - 3555x^7 + 6616x^6 - 744x^5 - 2895x^4 - 16230x^3 - 11950x^2 + 3060x + 2556	\( 2^{4}\cdot 5^{9}\cdot 6229^{5} \)	16T1862	Trivial (GRH)
16.8.293049966486181942156250000.2	x^16 - 7x^15 + 12x^14 + 42x^13 - 232x^12 + 225x^11 + 600x^10 - 2311x^9 + 3605x^8 + 2764x^7 - 15725x^6 + 12720x^5 + 4603x^4 - 9928x^3 + 2327x^2 + 1923x - 639	\( 2^{4}\cdot 5^{9}\cdot 6229^{5} \)	16T1862	$[2]$ (GRH)
16.4.372363261088299238400000000.1	x^16 - 2x^15 + 18x^14 - 22x^13 + 123x^12 + 76x^11 + 218x^10 + 1830x^9 - 1475x^8 + 7618x^7 - 7324x^6 + 5362x^5 - 4906x^4 - 30404x^3 + 30716x^2 - 54512x + 56044	\( 2^{16}\cdot 5^{8}\cdot 89^{3}\cdot 379^{4} \)	16T1862	$[2]$ (GRH)
16.4.819966223623022182400000000.1	x^16 + 4x^14 - 120x^12 - 884x^10 - 612x^8 + 8544x^6 + 23072x^4 + 20752x^2 + 6064	\( 2^{28}\cdot 5^{8}\cdot 379^{5} \)	16T1862	Trivial (GRH)
16.0.6647800525757166617600000000.1	x^16 + 20x^14 + 159x^12 + 652x^10 + 1497x^8 + 1944x^6 + 1357x^4 + 438x^2 + 41	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 41\cdot 811^{4} \)	16T1862	$[2, 100]$ (GRH)