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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.932482440555078125.1	x^16 - 8x^15 + 35x^14 - 105x^13 + 238x^12 - 427x^11 + 624x^10 - 755x^9 + 763x^8 - 645x^7 + 451x^6 - 254x^5 + 108x^4 - 30x^3 + 5x^2 - x + 1	\( 5^{8}\cdot 19^{6}\cdot 50741 \)	16T1638	Trivial
16.0.1050441646224587049.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 70x^12 - 56x^11 + 25x^10 + 7x^9 - 30x^8 + 34x^7 - 18x^6 - 2x^5 + 8x^4 - 3x^3 + 1	\( 3^{8}\cdot 37^{6}\cdot 62401 \)	16T1638	Trivial
16.2.1204374553600000000.1	x^16 - 4x^14 + 6x^12 - 2x^10 - 7x^8 + 15x^6 - 13x^4 + 6x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 19^{6} \)	16T1638	Trivial
16.2.1204374553600000000.2	x^16 + 4x^14 + 6x^12 + 2x^10 - 7x^8 - 15x^6 - 13x^4 - 6x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 19^{6} \)	16T1638	Trivial
16.0.1475459685741235401.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 266x^12 - 504x^11 + 781x^10 - 1001x^9 + 1061x^8 - 922x^7 + 642x^6 - 344x^5 + 130x^4 - 27x^3 - x^2 + 2x + 1	\( 3^{8}\cdot 37^{6}\cdot 87649 \)	16T1638	Trivial
16.4.5265996154167578125.1	x^16 - x^15 - x^14 - 4x^13 - 5x^12 + 32x^11 - 5x^10 - 23x^9 - 37x^8 + 69x^7 + 5x^6 - 76x^5 + 50x^4 + 7x^3 - 22x^2 + 10x - 1	\( 5^{8}\cdot 19^{6}\cdot 29\cdot 41\cdot 241 \)	16T1638	Trivial
16.0.22883116518400000000.1	x^16 + 8x^14 + 30x^12 + 73x^10 + 128x^8 + 163x^6 + 143x^4 + 76x^2 + 19	\( 2^{16}\cdot 5^{8}\cdot 19^{7} \)	16T1638	Trivial
16.4.22883116518400000000.1	x^16 + 5x^14 + 9x^12 + 3x^10 - 7x^8 - 4x^6 - 6x^4 - 19x^2 + 19	\( 2^{16}\cdot 5^{8}\cdot 19^{7} \)	16T1638	Trivial (GRH)
16.8.593799022336695861248.1	x^16 - 2x^15 - 5x^14 + 16x^13 - 9x^12 - 40x^11 + 93x^10 + 16x^9 - 246x^8 + 241x^6 + 20x^5 - 83x^4 - 38x^3 - 30x^2 - 12x - 1	\( 2^{24}\cdot 17\cdot 113^{6} \)	16T1638	Trivial
16.6.803375147867294400512.1	x^16 - 2x^15 - 5x^14 + 8x^13 + 4x^12 - 6x^11 + 12x^10 + 6x^9 - 13x^8 + 6x^7 + 12x^6 - 6x^5 + 4x^4 + 8x^3 - 5x^2 - 2x + 1	\( -\,2^{24}\cdot 23\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.6.1641679649989688557568.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 238x^12 - 336x^11 + 196x^10 + 384x^9 - 1332x^8 + 2188x^7 - 2370x^6 + 1776x^5 - 865x^4 + 212x^3 + 16x^2 - 24x + 4	\( -\,2^{24}\cdot 47\cdot 113^{6} \)	16T1638	Trivial
16.10.2479984152112082714624.1	x^16 - 8x^15 + 26x^14 - 42x^13 + x^12 + 176x^11 - 369x^10 + 184x^9 + 335x^8 - 508x^7 + 137x^6 + 222x^5 - 173x^4 - 28x^3 + 46x^2 - 4	\( -\,2^{24}\cdot 71\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.4.2549842860622282227712.1	x^16 - 8x^15 + 38x^14 - 126x^13 + 313x^12 - 604x^11 + 907x^10 - 1048x^9 + 883x^8 - 456x^7 + 13x^6 + 214x^5 - 185x^4 + 64x^3 + 10x^2 - 16x + 4	\( 2^{24}\cdot 73\cdot 113^{6} \)	16T1638	Trivial
16.6.2759418986152880766976.1	x^16 - 2x^15 - 3x^14 - 6x^13 + 38x^12 + 10x^11 - 119x^10 + 38x^9 + 106x^8 + 102x^7 - 327x^6 + 6x^5 + 329x^4 - 244x^3 + 36x^2 + 16x - 4	\( -\,2^{24}\cdot 79\cdot 113^{6} \)	16T1638	Trivial
16.8.3108712528703878332416.1	x^16 - 2x^15 - 9x^14 + 12x^13 + 23x^12 - 14x^11 + 3x^10 + 10x^9 - 2x^8 - 50x^7 - 182x^6 - 48x^5 + 149x^4 + 164x^3 + 86x^2 + 24x + 4	\( 2^{24}\cdot 89\cdot 113^{6} \)	16T1638	Trivial
16.6.3597723488275274924032.1	x^16 - 2x^15 - 5x^14 + 16x^13 - 18x^12 + 6x^11 + 18x^10 - 46x^9 + 59x^8 - 46x^7 + 18x^6 + 6x^5 - 18x^4 + 16x^3 - 5x^2 - 2x + 1	\( -\,2^{24}\cdot 103\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.8.4785321532948666646528.1	x^16 - 16x^14 - 2x^13 + 73x^12 - 22x^11 - 139x^10 + 136x^9 + 131x^8 - 230x^7 - 74x^6 + 140x^5 + 18x^4 - 40x^3 + 5x^2 + 14x + 1	\( 2^{24}\cdot 113^{6}\cdot 137 \)	16T1638	Trivial
16.2.5274332492520063238144.1	x^16 - 6x^15 + 21x^14 - 54x^13 + 109x^12 - 184x^11 + 270x^10 - 368x^9 + 508x^8 - 736x^7 + 1080x^6 - 1472x^5 + 1744x^4 - 1728x^3 + 1344x^2 - 768x + 256	\( -\,2^{24}\cdot 113^{6}\cdot 151 \)	16T1638	Trivial
16.10.5833202160601659342848.1	x^16 - 16x^14 - 2x^13 + 101x^12 + 6x^11 - 329x^10 + 20x^9 + 587x^8 - 86x^7 - 566x^6 + 76x^5 + 286x^4 + 4x^3 - 67x^2 - 18x - 1	\( -\,2^{24}\cdot 113^{6}\cdot 167 \)	16T1638	Trivial (GRH)
16.12.6741365371234253012992.1	x^16 - 2x^15 - 11x^14 + 18x^13 + 49x^12 - 42x^11 - 154x^10 + 395x^8 + 2x^7 - 536x^6 + 184x^5 + 200x^4 - 96x^3 - 18x^2 + 12x - 1	\( 2^{24}\cdot 113^{6}\cdot 193 \)	16T1638	Trivial (GRH)
16.10.6950941496764851552256.1	x^16 - 2x^15 - 9x^14 + 12x^13 + 22x^12 - 22x^11 - 50x^10 + 74x^9 + 129x^8 - 186x^7 - 190x^6 + 166x^5 + 110x^4 - 56x^3 - 23x^2 + 6x + 1	\( -\,2^{24}\cdot 113^{6}\cdot 199 \)	16T1638	Trivial (GRH)
16.10.8941914689305537675264.1	x^16 - 2x^14 - 13x^12 + 30x^10 + 32x^8 - 102x^6 + 29x^4 + 30x^2 - 1	\( -\,2^{32}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.10.8941914689305537675264.2	x^16 + 2x^14 - 17x^12 - 14x^10 + 91x^8 - 4x^6 - 156x^4 + 112x^2 - 16	\( -\,2^{32}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.10.8941914689305537675264.3	x^16 - 6x^14 - 9x^12 + 82x^10 - 27x^8 - 252x^6 + 156x^4 + 144x^2 - 16	\( -\,2^{32}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.10.143070635028888602804224.1	x^16 - 10x^14 + 25x^12 + 18x^10 - 94x^8 - 6x^6 + 53x^4 - 2x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.14.143070635028888602804224.1	x^16 - 12x^14 + 50x^12 - 72x^10 - 55x^8 + 276x^6 - 284x^4 + 96x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.2.143070635028888602804224.1	x^16 + 14x^14 + 71x^12 + 154x^10 + 112x^8 - 54x^6 - 87x^4 - 22x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	$[2]$ (GRH)
16.6.143070635028888602804224.1	x^16 + 14x^14 + 47x^12 - 50x^10 - 299x^8 + 84x^6 + 284x^4 - 48x^2 - 16	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.10.143070635028888602804224.2	x^16 - 14x^14 + 47x^12 + 50x^10 - 299x^8 - 84x^6 + 284x^4 + 48x^2 - 16	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.14.143070635028888602804224.2	x^16 - 14x^14 + 71x^12 - 154x^10 + 112x^8 + 54x^6 - 87x^4 + 22x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.6.143070635028888602804224.2	x^16 + 12x^14 + 28x^12 - 20x^10 - 89x^8 - 32x^6 + 38x^4 + 16x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.6.143070635028888602804224.3	x^16 + 4x^14 - 24x^12 - 80x^10 + 3x^8 + 140x^6 + 106x^4 + 20x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.6.143070635028888602804224.4	x^16 - 2x^14 - 21x^12 + 14x^10 + 104x^8 + 42x^6 - 51x^4 - 18x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.12.13588112604256141991477248.1	x^16 - 2x^15 - 27x^14 + 52x^13 + 184x^12 - 188x^11 - 556x^10 - 262x^9 + 261x^8 + 1340x^7 + 1583x^6 - 14x^5 - 1003x^4 - 482x^3 + 70x^2 + 108x + 23	\( 2^{24}\cdot 73^{3}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.4.13588112604256141991477248.1	x^16 - 14x^13 - 63x^12 + 38x^11 + 193x^10 + 800x^9 + 535x^8 - 1926x^7 - 3970x^6 - 2708x^5 - 730x^4 + 10848x^3 - 6321x^2 - 958x + 1751	\( 2^{24}\cdot 73^{3}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.0.38915212727857699962748928.1	x^16 + 18x^14 + 131x^12 + 498x^10 + 1062x^8 + 1262x^6 + 773x^4 + 202x^2 + 17	\( 2^{40}\cdot 17\cdot 113^{6} \)	16T1638	$[2, 28]$ (GRH)
16.16.38915212727857699962748928.1	x^16 - 18x^14 + 131x^12 - 498x^10 + 1062x^8 - 1262x^6 + 773x^4 - 202x^2 + 17	\( 2^{40}\cdot 17\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.8.61103770654221524409516032.1	x^16 - 2x^15 - 9x^14 + 60x^13 - 99x^12 - 116x^11 + 509x^10 - 582x^9 - 402x^8 + 482x^7 + 967x^6 + 872x^5 - 3365x^4 + 1884x^3 + 1621x^2 - 2502x + 617	\( 2^{24}\cdot 113^{8}\cdot 137 \)	16T1638	$[2]$ (GRH)
16.4.89815699851913524288684032.1	x^16 - 4x^14 - 26x^13 - 134x^12 + 106x^11 - 147x^10 + 1682x^9 - 793x^8 + 1600x^7 - 5811x^6 - 1202x^5 - 3915x^4 + 14240x^3 + 4142x^2 - 776x - 10876	\( 2^{24}\cdot 113^{6}\cdot 137^{3} \)	16T1638	Trivial (GRH)
16.4.89815699851913524288684032.2	x^16 - 4x^15 + 14x^13 - 33x^12 + 410x^11 - 2015x^10 + 3312x^9 + 4165x^8 - 30050x^7 + 67424x^6 - 91756x^5 + 89074x^4 - 69276x^3 + 43559x^2 - 17302x + 1681	\( 2^{24}\cdot 113^{6}\cdot 137^{3} \)	16T1638	Trivial (GRH)
16.16.320934015608385267004604416.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 177x^12 - 212x^11 + 865x^10 + 240x^9 - 2078x^8 - 36x^7 + 2751x^6 + 36x^5 - 1951x^4 - 284x^3 + 571x^2 + 202x + 17	\( 2^{24}\cdot 113^{6}\cdot 1409\cdot 6521 \)	16T1638	Trivial (GRH)
16.0.11246496478350875289234440192.1	x^16 + 48x^14 + 910x^12 + 8876x^10 + 48315x^8 + 146964x^6 + 231234x^4 + 146812x^2 + 4913	\( 2^{40}\cdot 17^{3}\cdot 113^{6} \)	16T1638	$[2, 2, 344]$ (GRH)
16.8.21507630806109425391040987136.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 54x^12 + 40x^11 - 212x^10 + 312x^9 - 159x^8 - 224x^7 + 464x^6 - 320x^5 - 48x^4 + 256x^3 - 128x^2 + 8	\( 2^{62}\cdot 7^{8}\cdot 809 \)	16T1638	Trivial (GRH)
16.8.86030523224437701564163948544.1	x^16 - 40x^14 - 64x^13 + 404x^12 + 912x^11 - 1688x^10 - 5248x^9 + 2104x^8 + 12992x^7 + 1384x^6 - 9440x^5 + 15604x^4 + 24336x^3 - 6200x^2 - 10144x + 3025	\( 2^{64}\cdot 7^{8}\cdot 809 \)	16T1638	$[2]$ (GRH)
16.8.552818012943116902826353691133.1	x^16 - 8x^15 + 25x^14 - 35x^13 - 7x^12 + 133x^11 - 266x^10 + 230x^9 + 29x^8 - 319x^7 + 343x^6 - 91x^5 - 119x^4 + 126x^3 - 24x^2 - 18x + 9	\( 3^{9}\cdot 7^{14}\cdot 43^{6}\cdot 6551 \)	16T1638	Trivial (GRH)
16.12.18769827417290930495444346043497.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 173x^12 - 54x^11 + 643x^10 - 432x^9 - 843x^8 + 1366x^7 - 65x^6 - 1584x^5 + 934x^4 + 798x^3 - 543x^2 - 108x + 81	\( 3^{8}\cdot 13^{6}\cdot 79^{8}\cdot 390673 \)	16T1638	Trivial (GRH)
16.8.1022160505931823153325927974904917.1	x^16 - 6x^15 - 19x^14 + 140x^13 - 602x^12 + 1855x^11 + 5089x^10 - 15091x^9 + 30122x^8 - 102555x^7 - 56966x^6 - 200613x^5 - 2441943x^4 + 188181x^3 - 4217589x^2 - 820314x + 87777	\( 3^{9}\cdot 7^{14}\cdot 43^{8}\cdot 6551 \)	16T1638	$[2]$ (GRH)
16.12.3171985166605736283336492032000000.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 171x^12 - 66x^11 + 649x^10 - 352x^9 - 945x^8 + 1162x^7 + 241x^6 - 1320x^5 + 580x^4 + 602x^3 - 405x^2 - 36x + 81	\( 2^{16}\cdot 5^{6}\cdot 181^{8}\cdot 2689073 \)	16T1638	Trivial (GRH)