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 70)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.316940672000000000.1	x^16 - 4x^15 + 6x^14 - 2x^13 - 7x^12 + 37x^10 - 64x^9 + 32x^8 + 14x^7 + 8x^6 - 82x^5 + 119x^4 - 90x^3 + 40x^2 - 10x + 1	\( -\,2^{16}\cdot 5^{9}\cdot 19^{5} \)	16T1782	Trivial
16.0.1792376890861328125.1	x^16 - 3x^15 + 4x^14 - 5x^12 + 13x^11 - 25x^9 + x^8 + 25x^7 - 13x^5 - 5x^4 + 4x^2 + 3x + 1	\( 5^{9}\cdot 41^{5}\cdot 89^{2} \)	16T1782	Trivial
16.2.7923516800000000000.2	x^16 - 4x^15 + 3x^14 + 6x^13 - 21x^12 + 16x^11 + 6x^10 - 48x^9 + 57x^8 - 48x^7 + 6x^6 + 16x^5 - 21x^4 + 6x^3 + 3x^2 - 4x + 1	\( -\,2^{16}\cdot 5^{11}\cdot 19^{5} \)	16T1782	Trivial
16.0.20912044280500000000.1	x^16 - 2x^15 + 10x^13 - 5x^12 - 8x^11 + 43x^10 - 4x^9 - 41x^8 + 72x^7 + 28x^6 - 52x^5 + 53x^4 + 56x^3 - 22x^2 - 12x + 4	\( 2^{8}\cdot 5^{9}\cdot 19^{2}\cdot 41^{5} \)	16T1782	Trivial
16.6.114415582592000000000.1	x^16 - 6x^15 + 3x^14 + 46x^13 - 85x^12 - 56x^11 + 195x^10 + 42x^9 - 222x^8 - 78x^7 + 201x^6 + 52x^5 - 119x^4 + 20x^3 + 20x^2 - 20x + 5	\( -\,2^{16}\cdot 5^{9}\cdot 19^{7} \)	16T1782	Trivial (GRH)
16.2.114415582592000000000.4	x^16 - 8x^15 + 34x^14 - 92x^13 + 173x^12 - 222x^11 + 181x^10 - 52x^9 - 78x^8 + 140x^7 - 70x^6 - 32x^5 + 53x^4 + 10x^3 - 8x^2 - 4x - 1	\( -\,2^{16}\cdot 5^{9}\cdot 19^{7} \)	16T1782	$[2]$
16.2.114415582592000000000.5	x^16 - 2x^15 - 6x^14 + 8x^13 + 32x^12 - 82x^11 + 44x^10 + 70x^9 - 135x^8 + 70x^7 + 44x^6 - 82x^5 + 32x^4 + 8x^3 - 6x^2 - 2x + 1	\( -\,2^{16}\cdot 5^{9}\cdot 19^{7} \)	16T1782	Trivial
16.6.2860389564800000000000.1	x^16 - 4x^15 - 4x^14 + 34x^13 - 6x^12 - 92x^11 + 14x^10 + 172x^9 - 3x^8 - 330x^7 + 200x^6 + 134x^5 - 139x^4 + 38x^3 - 79x^2 + 98x - 29	\( -\,2^{16}\cdot 5^{11}\cdot 19^{7} \)	16T1782	Trivial (GRH)
16.0.31347719877728869140625.1	x^16 - x^15 + 6x^14 - 5x^13 - 10x^12 - 34x^11 + 45x^10 + 70x^9 + 131x^8 + 70x^7 + 45x^6 - 34x^5 - 10x^4 - 5x^3 + 6x^2 - x + 1	\( 5^{9}\cdot 11^{5}\cdot 31^{5}\cdot 59^{2} \)	16T1782	$[2]$ (GRH)
16.4.31347719877728869140625.1	x^16 - 2x^15 - 7x^14 + 13x^13 + 30x^12 - 46x^11 - 91x^10 + 83x^9 + 129x^8 - 221x^7 - 293x^6 + 173x^5 + 268x^4 - 93x^3 - 139x^2 + 15x + 25	\( 5^{9}\cdot 11^{5}\cdot 31^{5}\cdot 59^{2} \)	16T1782	$[2]$ (GRH)
16.0.31347719877728869140625.2	x^16 - 5x^15 + 14x^14 - 32x^13 + 88x^12 - 221x^11 + 458x^10 - 708x^9 + 821x^8 - 708x^7 + 458x^6 - 221x^5 + 88x^4 - 32x^3 + 14x^2 - 5x + 1	\( 5^{9}\cdot 11^{5}\cdot 31^{5}\cdot 59^{2} \)	16T1782	$[2]$ (GRH)
16.4.31347719877728869140625.2	x^16 - 6x^15 + 8x^14 + 26x^13 - 61x^12 - 58x^11 + 170x^10 + 97x^9 - 424x^8 - 44x^7 + 556x^6 + 125x^5 - 645x^4 - 90x^3 + 495x^2 - 200x + 25	\( 5^{9}\cdot 11^{5}\cdot 31^{5}\cdot 59^{2} \)	16T1782	$[2]$ (GRH)
16.8.590176434905728000000000.1	x^16 - 6x^14 - 14x^13 + 15x^12 + 138x^11 - 206x^10 - 108x^9 + 622x^8 - 1084x^7 + 622x^6 + 642x^5 - 686x^4 - 48x^2 + 124x - 11	\( 2^{16}\cdot 5^{9}\cdot 11^{5}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.8.590176434905728000000000.2	x^16 - 8x^15 + 26x^14 - 42x^13 - 11x^12 + 248x^11 - 579x^10 + 574x^9 + 131x^8 - 1240x^7 + 2053x^6 - 2118x^5 + 394x^4 + 1500x^3 - 1841x^2 + 912x - 149	\( 2^{16}\cdot 5^{9}\cdot 11^{5}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.0.590176434905728000000000.3	x^16 - 8x^15 + 41x^14 - 140x^13 + 364x^12 - 726x^11 + 1103x^10 - 1204x^9 + 673x^8 + 36x^7 + 171x^6 - 684x^5 + 108x^4 + 202x^3 + 215x^2 + 64x + 59	\( 2^{16}\cdot 5^{9}\cdot 11^{5}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.8.590176434905728000000000.3	x^16 - 7x^14 - 12x^13 - 25x^12 + 58x^11 + 247x^10 + 262x^9 - 307x^8 - 1470x^7 + 42x^6 + 2354x^5 - 124x^4 - 1290x^3 - 239x^2 + 40x - 5	\( 2^{16}\cdot 5^{9}\cdot 11^{5}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.4.3544928919759039306640625.1	x^16 - 3x^15 + 8x^14 - 41x^13 + 90x^12 - 206x^11 + 538x^10 - 718x^9 + 1246x^8 - 1560x^7 - 1520x^6 + 5230x^5 - 11770x^4 + 21665x^3 - 17560x^2 + 5220x - 495	\( 5^{14}\cdot 41^{5}\cdot 2239^{2} \)	16T1782	Trivial (GRH)
16.8.3544928919759039306640625.1	x^16 - 4x^15 + 3x^14 + 2x^13 + 16x^12 - 69x^11 + 60x^10 + 51x^9 + 119x^8 - 418x^7 + 90x^6 + 53x^5 + 421x^4 - 351x^3 + 12x^2 + 18x + 1	\( 5^{14}\cdot 41^{5}\cdot 2239^{2} \)	16T1782	Trivial (GRH)
16.0.14754410872643200000000000.1	x^16 + 3x^14 - 6x^13 + 35x^12 + 116x^11 + 105x^10 + 58x^9 - 101x^8 + 3250x^6 - 5000x^5 + 7375x^4 - 17000x^3 + 23750x^2 - 15500x + 3875	\( 2^{16}\cdot 5^{11}\cdot 11^{5}\cdot 31^{5} \)	16T1782	$[2, 2]$ (GRH)
16.4.14754410872643200000000000.1	x^16 - 4x^15 - 7x^14 + 56x^13 + 27x^12 - 396x^11 - 198x^10 + 994x^9 - 73x^8 - 4538x^7 + 8258x^6 - 7156x^5 + 3760x^4 - 1188x^3 + 208x^2 - 20x + 1	\( 2^{16}\cdot 5^{11}\cdot 11^{5}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.4.14754410872643200000000000.2	x^16 - 8x^15 + 42x^14 - 154x^13 + 382x^12 - 554x^11 - 137x^10 + 2288x^9 - 4195x^8 + 5754x^7 - 11486x^6 + 18476x^5 - 17552x^4 + 14776x^3 - 18480x^2 + 14992x - 3184	\( 2^{16}\cdot 5^{11}\cdot 11^{5}\cdot 31^{5} \)	16T1782	$[2, 2]$ (GRH)
16.4.14754410872643200000000000.3	x^16 - 4x^15 + 8x^14 - 32x^13 + 60x^12 - 60x^11 + 286x^10 - 500x^9 + 423x^8 - 1228x^7 - 74x^6 + 5924x^5 - 11258x^4 + 20720x^3 - 32698x^2 + 26132x - 6301	\( 2^{16}\cdot 5^{11}\cdot 11^{5}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.4.30383373909389970532990976.1	x^16 + 16x^14 + 80x^12 + 96x^10 - 136x^8 + 56x^6 - 168x^2 + 14	\( 2^{65}\cdot 7^{7} \)	16T1782	$[2]$ (GRH)
16.8.30383373909389970532990976.1	x^16 - 16x^14 + 80x^12 - 96x^10 - 136x^8 - 56x^6 + 168x^2 + 14	\( 2^{65}\cdot 7^{7} \)	16T1782	Trivial (GRH)
16.4.30383373909389970532990976.2	x^16 + 16x^14 + 96x^12 + 272x^10 + 400x^8 + 336x^6 - 224x^2 + 56	\( 2^{65}\cdot 7^{7} \)	16T1782	$[2]$ (GRH)
16.8.30383373909389970532990976.2	x^16 - 16x^12 - 24x^10 + 64x^8 + 112x^6 - 112x^4 - 56x^2 + 14	\( 2^{65}\cdot 7^{7} \)	16T1782	Trivial (GRH)
16.4.38974026016400000000000000.1	x^16 + 22x^14 + 153x^12 + 484x^10 + 2010x^8 + 4334x^6 - 3532x^4 + 492x^2 + 41	\( 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{5} \)	16T1782	Trivial (GRH)
16.8.38974026016400000000000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 40x^12 + 124x^11 - 442x^10 + 692x^9 - 449x^8 - 420x^7 + 1550x^6 - 2220x^5 + 760x^4 + 1280x^3 - 880x^2 + 80	\( 2^{16}\cdot 5^{14}\cdot 29^{2}\cdot 41^{5} \)	16T1782	Trivial (GRH)
16.0.71411348623593088000000000.1	x^16 - 6x^15 + 9x^14 + 12x^13 - 11x^12 - 304x^11 + 1853x^10 - 7002x^9 + 19375x^8 - 42224x^7 + 77587x^6 - 119942x^5 + 150974x^4 - 154396x^3 + 122166x^2 - 68728x + 29161	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.12.71411348623593088000000000.1	x^16 - 2x^15 - 24x^14 + 24x^13 + 76x^12 - 354x^11 + 280x^10 + 1366x^9 - 2482x^8 - 250x^7 + 4120x^6 - 4686x^5 + 2095x^4 + 330x^3 - 660x^2 + 176x - 11	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.4.71411348623593088000000000.1	x^16 - 4x^15 - 5x^14 + 40x^13 + 7x^12 - 272x^11 + 166x^10 + 1980x^9 - 6409x^8 + 8478x^7 - 1708x^6 - 12920x^5 + 24790x^4 - 24494x^3 + 14786x^2 - 5400x + 905	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.8.71411348623593088000000000.1	x^16 - 2x^15 - 16x^14 + 48x^13 - 60x^12 + 118x^11 - 692x^10 + 2280x^9 - 2671x^8 + 1120x^7 - 1702x^6 + 3322x^5 - 2375x^4 + 662x^3 - 61x^2 + 2x + 1	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.0.71411348623593088000000000.2	x^16 - 4x^15 + 13x^14 - 64x^13 + 247x^12 - 864x^11 + 2618x^10 - 5542x^9 + 8379x^8 - 11438x^7 + 17213x^6 - 27738x^5 + 39409x^4 - 38290x^3 + 24066x^2 - 14520x + 7139	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2, 2]$ (GRH)
16.12.71411348623593088000000000.2	x^16 - 4x^15 - 6x^14 + 8x^13 - 94x^12 + 54x^11 + 1066x^10 + 594x^9 - 3913x^8 - 4508x^7 + 6949x^6 + 9662x^5 - 6944x^4 - 8236x^3 + 4071x^2 + 2410x - 1055	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.4.71411348623593088000000000.2	x^16 + 11x^14 - 24x^13 - 29x^12 - 296x^11 - 778x^10 - 98x^9 - 3662x^8 + 7176x^7 - 10421x^6 + 5808x^5 - 7387x^4 - 29168x^3 - 20571x^2 - 6098x - 709	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.8.71411348623593088000000000.2	x^16 - 4x^15 - 5x^14 + 66x^13 - 188x^12 + 474x^11 - 1268x^10 + 1906x^9 - 716x^8 - 2196x^7 + 4270x^6 - 2898x^5 - 111x^4 + 740x^3 + 9x^2 - 50x - 5	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.0.71411348623593088000000000.3	x^16 - 8x^15 + 37x^14 - 100x^13 + 207x^12 - 286x^11 + 358x^10 + 72x^9 - 673x^8 + 2526x^7 - 3172x^6 + 3186x^5 + 746x^4 - 4012x^3 + 6552x^2 - 4378x + 1969	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.4.71411348623593088000000000.3	x^16 - 8x^15 + 43x^14 - 136x^13 + 208x^12 + 222x^11 - 2238x^10 + 5472x^9 - 6273x^8 + 4002x^7 - 3274x^6 + 3660x^5 - 1796x^4 - 152x^3 + 344x^2 - 80	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.8.71411348623593088000000000.3	x^16 - 8x^15 + 14x^14 + 34x^13 - 88x^12 - 168x^11 + 476x^10 - 336x^9 - 315x^8 + 1526x^7 - 832x^6 - 778x^5 + 551x^4 + 104x^3 - 85x^2 - 2x + 1	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.4.71411348623593088000000000.4	x^16 - 122x^12 + 448x^10 + 3031x^8 - 9328x^6 - 34034x^4 - 17160x^2 + 1705	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.8.71411348623593088000000000.4	x^16 - 4x^15 - 9x^14 + 22x^13 - 4x^12 - 14x^11 - 22x^10 + 470x^9 + 683x^8 - 2346x^7 + 3189x^6 + 2570x^5 - 9555x^4 + 9230x^3 - 1405x^2 - 5500x + 3025	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.4.71411348623593088000000000.5	x^16 - 4x^15 + 10x^13 - 11x^12 + 26x^11 + 48x^10 + 70x^9 + 89x^8 - 140x^7 - 292x^6 + 24x^5 - 336x^4 + 680x^3 - 40x^2 - 416x + 16	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.8.71411348623593088000000000.5	x^16 - 4x^15 - 6x^14 + 78x^13 - 221x^12 + 134x^11 + 1029x^10 - 4162x^9 + 8136x^8 - 7496x^7 - 4106x^6 + 25022x^5 - 43771x^4 + 47240x^3 - 32420x^2 + 12550x - 2005	\( 2^{16}\cdot 5^{9}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2]$ (GRH)
16.12.838551590929703359619140625.1	x^16 - 4x^15 - 7x^14 + 31x^13 + 32x^12 - 80x^11 - 123x^10 + 63x^9 + 215x^8 + 63x^7 - 123x^6 - 80x^5 + 32x^4 + 31x^3 - 7x^2 - 4x + 1	\( 5^{12}\cdot 41^{5}\cdot 172181^{2} \)	16T1782	Trivial (GRH)
16.4.838551590929703359619140625.1	x^16 - 2x^15 - 9x^14 + 12x^13 + 81x^12 + 74x^11 - 411x^10 - 999x^9 + 997x^8 + 3961x^7 + 809x^6 - 6076x^5 - 8494x^4 + 4032x^3 + 5946x^2 - 2162x - 739	\( 5^{12}\cdot 41^{5}\cdot 172181^{2} \)	16T1782	$[2]$ (GRH)
16.0.1785283715589827200000000000.1	x^16 - 6x^15 + 4x^14 + 46x^13 - 102x^12 + 12x^11 - 476x^10 + 3828x^9 - 8581x^8 - 5690x^7 + 90585x^6 - 303000x^5 + 620865x^4 - 882920x^3 + 889190x^2 - 596950x + 206555	\( 2^{16}\cdot 5^{11}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2, 6]$ (GRH)
16.8.1785283715589827200000000000.1	x^16 - 2x^15 - 9x^14 + 14x^13 + 168x^12 - 192x^11 - 1517x^10 + 2262x^9 + 3872x^8 - 8540x^7 + 2443x^6 + 5658x^5 - 16938x^4 + 20974x^3 + 6092x^2 - 26932x + 12641	\( 2^{16}\cdot 5^{11}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.0.1785283715589827200000000000.2	x^16 - 2x^15 + 4x^14 - 18x^13 + 369x^12 - 810x^11 - 928x^10 + 2726x^9 + 2444x^8 - 6078x^7 - 2775x^6 + 3100x^5 + 12731x^4 - 13470x^3 + 1008x^2 + 328x + 1681	\( 2^{16}\cdot 5^{11}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2, 18]$ (GRH)
16.8.1785283715589827200000000000.2	x^16 - 4x^15 + 20x^14 - 30x^13 - 184x^12 + 460x^11 - 1056x^10 + 2530x^9 - 366x^8 - 3046x^7 + 6544x^6 - 3026x^5 + 1615x^4 - 5166x^3 - 1732x^2 + 1430x + 181	\( 2^{16}\cdot 5^{11}\cdot 11^{7}\cdot 31^{5} \)	16T1782	Trivial (GRH)
16.0.1785283715589827200000000000.3	x^16 - 6x^15 + 11x^14 - 6x^13 + 50x^12 - 252x^11 + 484x^10 - 540x^9 + 1339x^8 - 4710x^7 + 8820x^6 - 9210x^5 + 13210x^4 - 25680x^3 + 40465x^2 - 27750x + 11105	\( 2^{16}\cdot 5^{11}\cdot 11^{7}\cdot 31^{5} \)	16T1782	$[2, 6]$ (GRH)