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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.62248030467784704.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 35x^12 + 108x^11 - 48x^10 - 124x^9 + 137x^8 + 56x^7 - 122x^6 - 8x^5 + 55x^4 - 12x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 47^{2} \)	16T1123	Trivial
16.0.102886977600000000.1	x^16 - 3x^15 + 8x^14 - 14x^13 + 23x^12 - 36x^11 + 59x^10 - 90x^9 + 124x^8 - 138x^7 + 127x^6 - 88x^5 + 45x^4 - 13x^3 + x^2 + 2x + 1	\( 2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 11^{2} \)	16T1123	Trivial
16.0.130300992703954944.1	x^16 - 8x^15 + 30x^14 - 68x^13 + 104x^12 - 112x^11 + 80x^10 - 20x^9 - 23x^8 + 4x^7 + 60x^6 - 104x^5 + 102x^4 - 68x^3 + 30x^2 - 8x + 1	\( 2^{36}\cdot 3^{8}\cdot 17^{2} \)	16T1123	Trivial
16.0.1049650016701906944.1	x^16 - 8x^15 + 26x^14 - 36x^13 - 7x^12 + 96x^11 - 120x^10 + 4x^9 + 132x^8 - 120x^7 - 4x^6 + 72x^5 - 40x^4 - 4x^3 + 12x^2 - 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 193^{2} \)	16T1123	Trivial
16.0.1330423833600000000.1	x^16 - x^15 - 3x^14 + 3x^13 + 17x^12 + 6x^11 + 4x^10 + 26x^9 + 74x^8 + 68x^7 + 42x^6 + 36x^5 + 27x^4 + 5x^3 - 3x^2 + x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 89^{2} \)	16T1123	Trivial
16.0.1580350694400000000.1	x^16 - x^15 - 6x^14 + 8x^13 + 14x^12 - 27x^11 - 10x^10 + 27x^9 + 27x^8 - 41x^7 + 6x^6 - 3x^5 + 2x^4 - 12x^3 + 20x^2 - 5x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 97^{2} \)	16T1123	Trivial
16.4.33357054132212465664.1	x^16 - 4x^15 + 8x^14 - 8x^13 - 4x^12 + 28x^11 - 44x^10 + 24x^9 + 28x^8 - 60x^7 + 48x^6 - 16x^5 - 12x^4 + 28x^3 - 28x^2 + 8x + 1	\( 2^{44}\cdot 3^{8}\cdot 17^{2} \)	16T1123	Trivial
16.4.33357054132212465664.2	x^16 - 4x^15 + 20x^13 - 28x^12 - 8x^11 + 52x^10 - 40x^9 - 2x^8 + 40x^6 - 56x^5 + 44x^4 - 48x^3 + 40x^2 - 8x - 2	\( 2^{44}\cdot 3^{8}\cdot 17^{2} \)	16T1123	Trivial
16.8.47917406617600000000.1	x^16 - 4x^14 - 4x^13 - 2x^12 + 24x^11 - 10x^10 - 8x^9 - 14x^8 + 40x^7 + 24x^6 - 68x^5 - 11x^4 + 40x^3 - 8x + 1	\( 2^{32}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial
16.8.47917406617600000000.2	x^16 - 4x^14 - 4x^13 - 2x^12 - 6x^10 + 28x^9 + 108x^8 + 88x^7 - 56x^6 - 120x^5 - 41x^4 + 24x^3 + 16x^2 - 1	\( 2^{32}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial
16.8.54094259814400000000.1	x^16 - 6x^15 + 15x^14 - 22x^13 + 13x^12 + 50x^11 - 156x^10 + 136x^9 + 95x^8 - 246x^7 + 82x^6 + 120x^5 - 88x^4 - 16x^3 + 24x^2 - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 17^{2} \)	16T1123	Trivial
16.0.312101987451565768704.1	x^16 - 8x^15 + 32x^14 - 80x^13 + 140x^12 - 192x^11 + 244x^10 - 304x^9 + 328x^8 - 272x^7 + 216x^6 - 192x^5 + 112x^4 - 32x^3 + 52x^2 + 1	\( 2^{48}\cdot 3^{8}\cdot 13^{2} \)	16T1123	$[2]$
16.8.312101987451565768704.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 44x^12 + 168x^11 - 212x^10 + 80x^9 + 144x^8 - 336x^7 + 424x^6 - 336x^5 + 144x^4 - 40x^3 + 20x^2 - 8x + 1	\( 2^{48}\cdot 3^{8}\cdot 13^{2} \)	16T1123	Trivial
16.0.533712866115399450624.1	x^16 - 4x^12 - 8x^11 - 20x^10 - 8x^9 + 104x^8 - 32x^7 + 8x^6 - 72x^5 + 112x^4 - 56x^3 + 12x^2 + 8x + 1	\( 2^{48}\cdot 3^{8}\cdot 17^{2} \)	16T1123	$[2]$
16.8.533712866115399450624.1	x^16 - 8x^14 + 16x^12 - 8x^11 - 28x^10 + 32x^9 + 14x^8 - 48x^7 + 72x^6 - 56x^5 - 8x^4 + 80x^3 - 80x^2 + 24x - 2	\( 2^{48}\cdot 3^{8}\cdot 17^{2} \)	16T1123	Trivial
16.8.2193989347201600000000.1	x^16 - 3x^15 - 9x^14 + 39x^13 - 5x^12 - 124x^11 + 143x^10 + 40x^9 - 181x^8 + 249x^7 - 270x^6 - 46x^5 + 447x^4 - 332x^3 - 44x^2 + 112x - 16	\( 2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 41^{2} \)	16T1123	Trivial
16.4.10338244865665600000000.1	x^16 + 8x^14 - 21x^13 + 37x^12 - 106x^11 + 219x^10 - 424x^9 + 425x^8 - 571x^7 + 647x^6 - 423x^5 + 385x^4 - 250x^3 + 4x^2 + 56x - 16	\( 2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 89^{2} \)	16T1123	Trivial
16.12.12266856094105600000000.1	x^16 - 12x^14 + 48x^12 - 66x^10 - 2x^8 + 48x^6 - 13x^4 - 6x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial (GRH)
16.4.12266856094105600000000.1	x^16 + 6x^14 + x^12 - 60x^10 - 149x^8 - 132x^6 - 33x^4 + 6x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial
16.12.12266856094105600000000.2	x^16 - 6x^14 + x^12 + 60x^10 - 149x^8 + 132x^6 - 33x^4 - 6x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial (GRH)
16.4.12266856094105600000000.2	x^16 + 6x^14 + x^12 - 40x^10 - 44x^8 + 38x^6 + 62x^4 + 16x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1123	Trivial
16.12.14378528585820405760000.1	x^16 - 6x^15 + 7x^14 + 14x^13 - 13x^12 - 46x^11 + 12x^10 + 136x^9 - 153x^8 + 14x^7 + 150x^6 - 188x^5 + 38x^4 + 72x^3 - 50x^2 + 12x - 1	\( 2^{24}\cdot 5^{4}\cdot 13^{8}\cdot 41^{2} \)	16T1123	Trivial
16.8.67752721551626076160000.1	x^16 - 6x^15 + 5x^14 + 50x^13 - 160x^12 + 60x^11 + 573x^10 - 1240x^9 + 599x^8 + 1728x^7 - 3735x^6 + 2936x^5 + 126x^4 - 2222x^3 + 1769x^2 - 502x + 17	\( 2^{24}\cdot 5^{4}\cdot 13^{8}\cdot 89^{2} \)	16T1123	Trivial
16.8.755850865401985600000000.1	x^16 - 3x^15 - 5x^14 + 19x^13 - 26x^12 + 77x^11 + 22x^10 - 479x^9 + 726x^8 - 647x^7 + 69x^6 + 2390x^5 - 4813x^4 + 3964x^3 - 1644x^2 + 304x - 16	\( 2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 761^{2} \)	16T1123	Trivial (GRH)
16.8.1544986154559078400000000.1	x^16 - 2x^14 - 18x^13 - 40x^12 + 12x^11 - 115x^10 - 582x^9 + 951x^8 + 5488x^7 + 3832x^6 - 8592x^5 - 13376x^4 - 1536x^3 + 6080x^2 + 2304x - 256	\( 2^{24}\cdot 5^{8}\cdot 13^{8}\cdot 17^{2} \)	16T1123	$[2]$ (GRH)
16.0.3333974497696153600000000.1	x^16 - 2x^15 - 3x^14 + 20x^13 + 3x^12 - 108x^11 + 115x^10 + 286x^9 - 285x^8 - 280x^7 + 762x^6 - 424x^5 + 68x^4 - 176x^3 + 344x^2 - 96x + 16	\( 2^{24}\cdot 5^{8}\cdot 37^{4}\cdot 521^{2} \)	16T1123	Trivial
16.0.3333974497696153600000000.2	x^16 - 2x^15 + 9x^14 + 8x^13 + 7x^12 - 52x^11 + 3x^10 - 140x^9 - 44x^8 + 124x^7 + 401x^6 + 196x^5 + 473x^4 + 330x^3 + 52x^2 + 56x + 49	\( 2^{24}\cdot 5^{8}\cdot 37^{4}\cdot 521^{2} \)	16T1123	Trivial
16.8.4953544231498452828160000.1	x^16 - 2x^15 - 11x^14 + 14x^13 + 11x^12 + 34x^11 + 140x^10 - 108x^9 + 73x^8 - 786x^7 - 974x^6 - 552x^5 - 1676x^4 + 1452x^3 - 236x^2 + 1788x + 569	\( 2^{24}\cdot 5^{4}\cdot 13^{8}\cdot 761^{2} \)	16T1123	Trivial
16.12.7760997646539675402240000.1	x^16 - 16x^14 + 32x^12 - 160x^11 + 24x^10 + 576x^9 - 410x^8 - 352x^7 + 1392x^6 - 224x^5 - 1520x^4 - 160x^3 + 200x^2 + 32x + 1	\( 2^{50}\cdot 3^{8}\cdot 5^{4}\cdot 41^{2} \)	16T1123	Trivial (GRH)
16.4.42345450969766297600000000.1	x^16 - 8x^15 + 36x^14 - 82x^13 - 47x^12 + 1140x^11 - 5559x^10 + 17048x^9 - 41895x^8 + 81372x^7 - 120353x^6 + 122178x^5 - 44765x^4 - 160x^3 + 81666x^2 + 22288x - 4684	\( 2^{24}\cdot 5^{8}\cdot 13^{8}\cdot 89^{2} \)	16T1123	$[2]$ (GRH)
16.16.45644971526166937600000000.1	x^16 - 34x^14 + 441x^12 - 2860x^10 + 10235x^8 - 21020x^6 + 24521x^4 - 15006x^2 + 3721	\( 2^{40}\cdot 5^{8}\cdot 13^{4}\cdot 61^{2} \)	16T1123	Trivial (GRH)
16.0.1173621921239636377600000000.1	x^16 + 36x^14 - 28x^13 + 551x^12 - 812x^11 + 5292x^10 - 7616x^9 + 41399x^8 - 21780x^7 + 237130x^6 + 39612x^5 + 871247x^4 + 452756x^3 + 1745324x^2 + 996728x + 1038209	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 13^{4}\cdot 101^{2} \)	16T1123	$[2, 614]$ (GRH)
16.16.1173621921239636377600000000.1	x^16 - 58x^14 - 12x^13 + 1318x^12 + 552x^11 - 14920x^10 - 9424x^9 + 88401x^8 + 73696x^7 - 260876x^6 - 265584x^5 + 323136x^4 + 394888x^3 - 96914x^2 - 199276x - 45649	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 13^{4}\cdot 101^{2} \)	16T1123	Trivial (GRH)
16.0.17772472233483803830517760000.1	x^16 + 24x^14 + 300x^12 + 2664x^10 + 17982x^8 + 90504x^6 + 327996x^4 + 776952x^2 + 962361	\( 2^{52}\cdot 3^{12}\cdot 5^{4}\cdot 109^{2} \)	16T1123	$[2, 2]$ (GRH)
16.0.24407831947565316121600000000.1	x^16 - 27x^14 + 311x^12 - 1953x^10 + 7240x^8 - 20277x^6 + 72591x^4 - 220383x^2 + 271441	\( 2^{16}\cdot 5^{8}\cdot 37^{8}\cdot 521^{2} \)	16T1123	$[2]$ (GRH)
16.0.86417794464669065070143078400.1	x^16 + 24x^14 + 212x^12 + 880x^10 + 1836x^8 + 1984x^6 + 1092x^4 + 280x^2 + 25	\( 2^{64}\cdot 3^{8}\cdot 5^{2}\cdot 13^{4} \)	16T1123	$[3, 162]$ (GRH)
16.8.23630709513618089564484100000000.1	x^16 - 16x^14 - 291x^12 + 2492x^10 + 25077x^8 + 30716x^6 - 95104x^4 - 105792x^2 + 92416	\( 2^{8}\cdot 5^{8}\cdot 17^{4}\cdot 19^{2}\cdot 97^{8} \)	16T1123	Trivial (GRH)
16.8.23630709513618089564484100000000.2	x^16 - 7x^15 - 9x^14 + 217x^13 - 581x^12 - 1302x^11 + 9399x^10 - 9371x^9 - 32065x^8 + 62047x^7 + 39775x^6 - 99694x^5 - 78458x^4 + 20384x^3 + 41772x^2 + 4200x - 1424	\( 2^{8}\cdot 5^{8}\cdot 17^{4}\cdot 19^{2}\cdot 97^{8} \)	16T1123	Trivial (GRH)
16.8.789464195714758583406110606440000.1	x^16 - 14x^14 - 323x^12 + 2243x^10 + 22890x^8 + 18367x^6 - 113900x^4 - 109744x^2 + 92416	\( 2^{6}\cdot 5^{4}\cdot 17^{8}\cdot 19^{2}\cdot 97^{8} \)	16T1123	Trivial (GRH)
16.8.789464195714758583406110606440000.2	x^16 - 8x^15 + 22x^14 + 69x^13 - 1083x^12 + 1666x^11 + 2984x^10 + 50655x^9 - 100815x^8 - 823340x^7 + 2232798x^6 + 1240595x^5 - 9310725x^4 + 10100722x^3 - 2301660x^2 + 217481x + 99662	\( 2^{6}\cdot 5^{4}\cdot 17^{8}\cdot 19^{2}\cdot 97^{8} \)	16T1123	Trivial (GRH)