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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.3625256545900000000.1	x^16 + 9x^14 + 33x^12 + 66x^10 + 83x^8 + 62x^6 + 2x^4 - 38x^2 - 19	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{5} \)	16T1581	Trivial
16.6.3625256545900000000.1	x^16 - x^15 - 4x^14 - x^13 + 11x^12 + 3x^11 - 21x^10 - 5x^9 + 44x^8 + 39x^7 - 45x^6 - 18x^5 + 60x^4 + 20x^3 - 15x^2 - 8x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{5} \)	16T1581	Trivial
16.0.7798330765786322853.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 17x^12 - 18x^11 - 10x^10 + 23x^9 - 37x^8 + 12x^7 + 28x^6 + 7x^5 + 44x^4 + 19x^3 + 11x^2 + 1	\( 3^{8}\cdot 7^{5}\cdot 13^{4}\cdot 19^{5} \)	16T1581	Trivial
16.2.90631413647500000000.1	x^16 + 7x^14 - 8x^13 + 2x^12 - 48x^11 - 13x^10 + 6x^9 + 103x^8 + 30x^7 - 101x^6 - 166x^5 + 132x^4 + 100x^3 - 105x^2 - 10x - 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{4}\cdot 19^{5} \)	16T1581	Trivial
16.6.90631413647500000000.1	x^16 - 3x^15 + 9x^14 - 7x^13 + 3x^12 + 28x^11 - 59x^10 + 103x^9 - 292x^8 + 256x^7 - 211x^6 + 328x^5 - 121x^4 - 52x^3 + 8x^2 + 7x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{4}\cdot 19^{5} \)	16T1581	Trivial
16.0.382118207523529819797.1	x^16 - 3x^15 + 4x^14 - 6x^13 + 13x^12 - 31x^11 + 24x^10 + 45x^9 - 43x^8 - 11x^7 - 7x^6 - 45x^5 + 26x^4 + 56x^3 + 31x^2 + 8x + 1	\( 3^{8}\cdot 7^{7}\cdot 13^{4}\cdot 19^{5} \)	16T1581	$[2]$
16.0.417825257207682301952.1	x^16 - 5x^14 + 9x^12 - 10x^10 + 7x^8 + x^6 + 5x^4 + 6x^2 + 2	\( 2^{21}\cdot 13^{4}\cdot 17^{8} \)	16T1581	Trivial
16.0.2715864171849934962688.1	x^16 - 3x^15 + 10x^14 - 16x^13 + 27x^12 - 28x^11 + 42x^10 - 49x^9 + 64x^8 - 49x^7 + 42x^6 - 28x^5 + 27x^4 - 16x^3 + 10x^2 - 3x + 1	\( 2^{20}\cdot 13^{5}\cdot 17^{8} \)	16T1581	Trivial
16.0.3711358090754064908288.1	x^16 - 4x^15 + 10x^14 - 14x^13 + 29x^12 - 52x^11 + 97x^10 - 90x^9 + 154x^8 - 116x^7 + 241x^6 - 52x^5 + 260x^4 + 80x^3 + 336x^2 + 128x + 256	\( 2^{26}\cdot 17^{5}\cdot 79^{4} \)	16T1581	Trivial
16.0.22717295368601600000000.1	x^16 - 2x^14 - 26x^13 - 12x^12 + 8x^11 + 264x^10 + 212x^9 + 500x^8 - 134x^7 + 976x^6 - 34x^5 + 963x^4 - 28x^3 + 302x^2 - 20x + 11	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	$[4]$
16.4.22717295368601600000000.1	x^16 - 4x^15 + 8x^14 + 20x^13 - 46x^12 + 22x^11 + 184x^10 + 72x^9 + 90x^8 + 20x^7 - 1200x^6 - 2446x^5 - 1629x^4 + 294x^3 + 716x^2 + 36x + 11	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	Trivial (GRH)
16.8.22717295368601600000000.1	x^16 - 2x^15 - 18x^14 + 24x^13 + 121x^12 - 58x^11 - 354x^10 - 304x^9 + 234x^8 + 1554x^7 + 1110x^6 - 1334x^5 - 2356x^4 - 2136x^3 + 654x^2 + 2376x + 589	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	Trivial (GRH)
16.0.22717295368601600000000.2	x^16 - 2x^15 + 8x^14 + 14x^13 + 15x^12 + 58x^11 + 206x^10 + 268x^9 + 289x^8 + 68x^7 + 1630x^6 - 274x^5 + 1389x^4 - 1706x^3 + 1438x^2 - 290x + 19	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	Trivial
16.4.22717295368601600000000.2	x^16 - 4x^15 - 6x^14 + 4x^13 + 63x^12 + 126x^11 + 62x^10 - 326x^9 - 1366x^8 - 2656x^7 - 3512x^6 - 3076x^5 - 1704x^4 - 434x^3 + 98x^2 + 80x - 11	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	Trivial (GRH)
16.8.22717295368601600000000.2	x^16 - 12x^14 - 24x^13 + 55x^12 + 176x^11 + 60x^10 - 470x^9 - 619x^8 + 454x^7 + 1370x^6 + 718x^5 - 1103x^4 - 934x^3 + 50x^2 + 110x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{5} \)	16T1581	Trivial (GRH)
16.0.59381729452065038532608.1	x^16 + 2x^14 - 13x^12 + 8x^10 + 315x^8 + 714x^6 + 269x^4 - 340x^2 + 68	\( 2^{30}\cdot 17^{5}\cdot 79^{4} \)	16T1581	$[2]$
16.12.128691545374490900000000.1	x^16 - 2x^15 + 2x^14 + 22x^13 - 74x^12 + 44x^11 + 204x^10 - 746x^9 + 184x^8 + 1736x^7 - 1356x^6 - 1162x^5 + 1481x^4 - 52x^3 - 436x^2 + 172x - 19	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.4.128691545374490900000000.1	x^16 + 9x^14 + 14x^12 - 65x^10 - 191x^8 - 77x^6 + 160x^4 + 145x^2 + 29	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial
16.8.128691545374490900000000.1	x^16 + 4x^14 - 18x^12 - 38x^10 + 82x^8 + 102x^6 - 85x^4 - 58x^2 + 29	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.12.128691545374490900000000.2	x^16 - 13x^14 + 50x^12 - 15x^10 - 231x^8 + 221x^6 + 242x^4 - 203x^2 + 29	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.4.128691545374490900000000.2	x^16 + 7x^14 - 11x^12 - 142x^10 - 133x^8 + 406x^6 + 704x^4 + 290x^2 + 29	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial
16.8.128691545374490900000000.2	x^16 - 3x^15 - 8x^14 + 16x^13 + 34x^12 - 19x^11 - 97x^10 - 16x^9 + 204x^8 + 146x^7 - 249x^6 - 459x^5 - 112x^4 + 336x^3 + 368x^2 + 143x + 19	\( 2^{8}\cdot 5^{8}\cdot 29^{5}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.4.815265536956502009446400.1	x^16 + 4x^14 - 16x^13 - 30x^12 + 96x^11 + 144x^10 + 16x^9 - 241x^8 - 48x^7 + 344x^6 + 24x^5 - 66x^4 - 248x^3 + 308x^2 - 96x + 7	\( 2^{48}\cdot 5^{2}\cdot 41^{5} \)	16T1581	Trivial (GRH)
16.4.815265536956502009446400.2	x^16 - 12x^14 - 16x^13 + 10x^12 - 64x^10 + 160x^9 + 123x^8 - 144x^7 + 464x^6 + 344x^5 - 142x^4 + 312x^3 + 300x^2 + 80x + 7	\( 2^{48}\cdot 5^{2}\cdot 41^{5} \)	16T1581	Trivial (GRH)
16.0.388916940619465549414400000000.1	x^16 + 58x^14 + 1367x^12 + 16960x^10 + 120229x^8 + 495332x^6 + 1151727x^4 + 1374078x^2 + 643829	\( 2^{24}\cdot 5^{8}\cdot 19^{4}\cdot 29^{5}\cdot 149^{2} \)	16T1581	$[2, 2, 522]$ (GRH)
16.16.388916940619465549414400000000.1	x^16 - 58x^14 + 1367x^12 - 16960x^10 + 120229x^8 - 495332x^6 + 1151727x^4 - 1374078x^2 + 643829	\( 2^{24}\cdot 5^{8}\cdot 19^{4}\cdot 29^{5}\cdot 149^{2} \)	16T1581	Trivial (GRH)
16.4.598754691200949156441938198528.1	x^16 + 50x^14 + 724x^12 + 1964x^10 - 25019x^8 - 120366x^6 + 13038x^4 + 8960x^2 + 392	\( 2^{29}\cdot 7^{2}\cdot 17^{8}\cdot 239^{4} \)	16T1581	$[2]$ (GRH)
16.4.598754691200949156441938198528.2	x^16 + 6x^14 - 88x^13 - 205x^12 - 1008x^11 - 1384x^10 + 432x^9 + 14995x^8 + 62128x^7 + 159022x^6 + 342440x^5 + 495345x^4 + 713632x^3 + 517820x^2 + 285408x + 18512	\( 2^{29}\cdot 7^{2}\cdot 17^{8}\cdot 239^{4} \)	16T1581	$[2, 2]$ (GRH)
16.4.782771961926717643161600000000.1	x^16 + 20x^14 + 88x^12 - 304x^10 - 1856x^8 + 304x^6 + 4056x^4 + 2464x^2 + 176	\( 2^{44}\cdot 5^{8}\cdot 11^{5}\cdot 29^{4} \)	16T1581	$[2]$ (GRH)
16.4.782771961926717643161600000000.2	x^16 + 40x^14 + 352x^12 - 2432x^10 - 29696x^8 + 9728x^6 + 259584x^4 + 315392x^2 + 45056	\( 2^{44}\cdot 5^{8}\cdot 11^{5}\cdot 29^{4} \)	16T1581	$[2]$ (GRH)
16.0.922577448288361543921511328125.1	x^16 + 12x^14 - 53x^13 + 33x^12 - 167x^11 + 1082x^10 - 2396x^9 + 3804x^8 + 16906x^7 - 15648x^6 + 39596x^5 - 22955x^4 - 62084x^3 + 94930x^2 - 112901x + 136081	\( 5^{8}\cdot 13^{8}\cdot 29^{5}\cdot 109^{4} \)	16T1581	$[2, 52]$ (GRH)
16.0.922577448288361543921511328125.2	x^16 - 6x^15 + 3x^14 + 51x^13 - 152x^12 + 14x^11 + 1414x^10 - 3139x^9 - 2526x^8 - 2335x^7 + 52321x^6 - 35827x^5 - 43181x^4 - 76748x^3 + 325013x^2 - 292433x + 128909	\( 5^{8}\cdot 13^{8}\cdot 29^{5}\cdot 109^{4} \)	16T1581	$[2, 52]$ (GRH)
16.8.2163000964871588780441600000000.1	x^16 - 40x^14 + 434x^12 + 140x^10 - 15923x^8 + 14380x^6 + 80736x^4 + 42720x^2 + 5696	\( 2^{30}\cdot 5^{8}\cdot 31^{4}\cdot 89^{5} \)	16T1581	$[2]$ (GRH)
16.0.3692367450289578023321600000000.1	x^16 + 42x^14 + 751x^12 + 7446x^10 + 44613x^8 + 164642x^6 + 363229x^4 + 434236x^2 + 212531	\( 2^{32}\cdot 5^{8}\cdot 11^{5}\cdot 29^{4}\cdot 139^{2} \)	16T1581	$[2, 2, 2822]$ (GRH)
16.16.3692367450289578023321600000000.1	x^16 - 42x^14 + 751x^12 - 7446x^10 + 44613x^8 - 164642x^6 + 363229x^4 - 434236x^2 + 212531	\( 2^{32}\cdot 5^{8}\cdot 11^{5}\cdot 29^{4}\cdot 139^{2} \)	16T1581	Trivial (GRH)
16.8.21165357964667333064935497269248.1	x^16 + 6x^14 - 253x^12 - 646x^10 + 1339x^8 + 526x^6 - 711x^4 - 14x^2 + 8	\( 2^{23}\cdot 7^{8}\cdot 17^{8}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.8.21165357964667333064935497269248.2	x^16 - 2x^14 - 81x^12 + 170x^10 + 1480x^8 - 1472x^6 - 6640x^4 - 2592x^2 + 128	\( 2^{23}\cdot 7^{8}\cdot 17^{8}\cdot 89^{4} \)	16T1581	Trivial (GRH)
16.8.34608015437945420487065600000000.1	x^16 - 26x^14 - 234x^12 + 5216x^10 - 7172x^8 - 18512x^6 + 5264x^4 + 17088x^2 + 5696	\( 2^{34}\cdot 5^{8}\cdot 31^{4}\cdot 89^{5} \)	16T1581	$[2]$ (GRH)
16.12.5108593025111245010631694481358848.1	x^16 + 4x^14 - 24x^13 - 510x^12 + 200x^11 + 1214x^10 - 3156x^9 + 39427x^8 + 31120x^7 - 195162x^6 - 58012x^5 + 191042x^4 + 77680x^3 - 13424x^2 - 1552x + 208	\( 2^{29}\cdot 7^{2}\cdot 17^{8}\cdot 2297^{4} \)	16T1581	$[2]$ (GRH)
16.12.7416612542850992781854363445362688.1	x^16 - 40x^14 + 254x^12 + 7576x^10 - 125103x^8 + 616848x^6 - 628416x^4 - 1479168x^2 + 559872	\( 2^{36}\cdot 3^{5}\cdot 13^{8}\cdot 859^{4} \)	16T1581	Trivial (GRH)
16.12.7416612542850992781854363445362688.2	x^16 - 34x^14 + 235x^12 + 1598x^10 - 13814x^8 + 7118x^6 + 36735x^4 - 6018x^2 + 243	\( 2^{36}\cdot 3^{5}\cdot 13^{8}\cdot 859^{4} \)	16T1581	Trivial (GRH)
16.12.20434372100444980042526777925435392.1	x^16 - 26x^14 - 8x^13 - 45x^12 - 184x^11 + 3026x^10 + 5228x^9 - 3491x^8 - 19536x^7 - 68646x^6 - 16032x^5 + 189433x^4 + 80328x^3 - 117522x^2 - 15876x + 9558	\( 2^{31}\cdot 7^{2}\cdot 17^{8}\cdot 2297^{4} \)	16T1581	$[2]$ (GRH)
16.8.3330410051873424453724414210438886064128.1	x^16 + 42x^14 - 7553x^12 - 165620x^10 + 16173822x^8 - 1388464x^6 - 5161727424x^4 - 6558072192x^2 + 3260442752	\( 2^{39}\cdot 7^{12}\cdot 17^{8}\cdot 89^{4} \)	16T1581	$[2, 4]$ (GRH)
16.8.3330410051873424453724414210438886064128.2	x^16 - 56x^14 - 4242x^12 + 173264x^10 + 5439392x^8 - 88510464x^6 - 155595776x^4 + 1730871296x^2 + 314703872	\( 2^{39}\cdot 7^{12}\cdot 17^{8}\cdot 89^{4} \)	16T1581	$[2, 4]$ (GRH)
16.8.88114204274383121870561308973465600000000.1	x^16 - 4x^15 - 30x^14 + 360x^13 - 1751x^12 + 146x^11 - 12508x^10 + 124450x^9 - 1113909x^8 + 3591426x^7 - 3705988x^6 - 7160878x^5 + 126060809x^4 - 403444758x^3 + 338879286x^2 + 76456848x - 129643679	\( 2^{24}\cdot 5^{8}\cdot 13^{8}\cdot 101^{5}\cdot 199^{4} \)	16T1581	$[2, 4]$ (GRH)
16.8.88114204274383121870561308973465600000000.2	x^16 - 4x^15 - 118x^14 + 1064x^13 - 4490x^12 - 11968x^11 + 247268x^10 + 52168x^9 - 6108960x^8 + 1905944x^7 + 102497032x^6 - 241115296x^5 - 104734960x^4 - 159744048x^3 - 5593072x^2 + 27381472x + 1068656	\( 2^{24}\cdot 5^{8}\cdot 13^{8}\cdot 101^{5}\cdot 199^{4} \)	16T1581	$[2, 2]$ (GRH)