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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.5415791883780096.1	x^16 - 4x^15 + 11x^14 - 24x^13 + 46x^12 - 84x^11 + 143x^10 - 208x^9 + 259x^8 - 284x^7 + 278x^6 - 234x^5 + 160x^4 - 84x^3 + 32x^2 - 8x + 1	\( 2^{16}\cdot 3^{10}\cdot 7^{2}\cdot 13^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.0.14132332667142144.1	x^16 - 4x^15 + 7x^14 - 6x^13 + 9x^12 - 28x^11 + 51x^10 - 54x^9 + 55x^8 - 82x^7 + 112x^6 - 104x^5 + 66x^4 - 30x^3 + 11x^2 - 4x + 1	\( 2^{16}\cdot 3^{12}\cdot 7^{4}\cdot 13^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.8.51969104281600000000.1	x^16 - 4x^15 - 4x^14 + 48x^13 - 76x^12 - 80x^11 + 412x^10 - 508x^9 - 11x^8 + 792x^7 - 1056x^6 + 708x^5 - 314x^4 + 132x^3 - 52x^2 + 12x - 1	\( 2^{40}\cdot 5^{8}\cdot 11^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.51969104281600000000.2	x^16 - 4x^15 + 12x^14 - 36x^13 + 86x^12 - 184x^11 + 368x^10 - 600x^9 + 914x^8 - 1328x^7 + 1568x^6 - 1600x^5 + 1408x^4 - 672x^3 + 184x^2 - 32x + 4	\( 2^{40}\cdot 5^{8}\cdot 11^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.98751019467096981504.1	x^16 - 4x^15 + 8x^14 - 12x^13 + 30x^12 - 68x^11 + 136x^10 - 256x^9 + 400x^8 - 420x^7 + 372x^6 - 268x^5 + 18x^4 + 60x^3 + 40x^2 + 8x + 1	\( 2^{40}\cdot 3^{12}\cdot 13^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	$[2]$
16.8.98751019467096981504.1	x^16 - 4x^15 + 4x^14 + 8x^13 - 34x^12 + 56x^11 - 20x^10 - 92x^9 + 136x^8 - 116x^6 + 48x^5 + 28x^4 - 16x^3 + 4x^2 - 2	\( 2^{40}\cdot 3^{12}\cdot 13^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.0.184703321113600000000.1	x^16 - 6x^15 + 12x^14 - 32x^12 + 50x^11 + 16x^10 - 100x^9 + 137x^8 - 20x^7 - 153x^6 + 82x^5 + 14x^4 - 100x^3 + 85x^2 + 50x + 25	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 101^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.0.727403732765419503616.1	x^16 + 4x^14 - 16x^13 + 6x^12 - 88x^11 + 48x^10 - 340x^9 + 155x^8 - 464x^7 + 1712x^6 + 4132x^5 + 9858x^4 + 18096x^3 + 19528x^2 + 20808x + 12434	\( 2^{40}\cdot 17^{4}\cdot 89^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	$[2]$
16.12.1854324698882154430464.1	x^16 - 12x^14 - 28x^13 + 2x^12 + 148x^11 + 292x^10 + 28x^9 - 680x^8 - 896x^7 - 48x^6 + 760x^5 + 624x^4 + 160x^3 - 20x^2 - 16x - 2	\( 2^{40}\cdot 3^{10}\cdot 13^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.4.1854324698882154430464.1	x^16 - 4x^15 + 4x^14 + 12x^13 - 42x^12 + 36x^11 - 12x^10 + 88x^9 - 216x^8 + 236x^7 - 144x^6 + 12x^5 + 66x^4 - 60x^3 + 28x^2 - 8x + 1	\( 2^{40}\cdot 3^{10}\cdot 13^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.4.2517630976000000000000.1	x^16 - 2x^15 - 3x^14 + 23x^12 + 32x^11 - 121x^10 - 32x^9 + 202x^8 + 104x^7 - 317x^6 - 268x^5 - 41x^4 - 14x^3 - 14x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 7^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.4.4525017128717153992704.1	x^16 - 4x^15 + 4x^14 + 8x^13 + 14x^12 + 8x^11 - 68x^10 - 128x^9 - 296x^8 - 408x^7 - 548x^6 - 552x^5 - 428x^4 - 256x^3 - 104x^2 - 24x - 2	\( 2^{46}\cdot 3^{12}\cdot 11^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial
16.12.6288261618073600000000.1	x^16 - 4x^14 - 4x^13 - 18x^12 + 32x^11 + 16x^10 - 124x^9 + 376x^8 + 240x^7 - 852x^6 - 52x^5 + 542x^4 - 112x^3 - 64x^2 + 20x - 1	\( 2^{40}\cdot 5^{8}\cdot 11^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.4.6288261618073600000000.1	x^16 - 4x^14 - 4x^13 - 18x^12 - 8x^11 - 64x^10 - 64x^9 + 16x^8 - 80x^7 - 32x^6 - 152x^5 + 212x^4 + 48x^3 - 144x^2 + 80x + 164	\( 2^{40}\cdot 5^{8}\cdot 11^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.1318435990955622400000000.1	x^16 - 4x^15 + 14x^14 - 62x^12 + 336x^11 - 506x^10 + 464x^9 + 1797x^8 - 5824x^7 + 14078x^6 - 20632x^5 + 25740x^4 - 23124x^3 + 15444x^2 - 7600x + 2399	\( 2^{32}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.1318435990955622400000000.2	x^16 - 4x^15 + 4x^14 + 44x^13 - 207x^12 + 392x^11 + 110x^10 - 2400x^9 + 6827x^8 - 10824x^7 + 11648x^6 - 9140x^5 + 6782x^4 - 5384x^3 + 4228x^2 - 2184x + 676	\( 2^{32}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.8.1793717610161784125128704.1	x^16 - 4x^15 - 2x^14 + 48x^13 - 132x^12 + 44x^11 + 594x^10 - 1368x^9 + 232x^8 + 3500x^7 - 4352x^6 - 6164x^5 + 22311x^4 - 19596x^3 + 440x^2 + 4352x + 337	\( 2^{32}\cdot 3^{12}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.8.1793717610161784125128704.2	x^16 - 8x^15 + 18x^14 + 12x^13 - 118x^12 + 96x^11 + 284x^10 - 140x^9 - 702x^8 - 328x^7 + 1298x^6 + 444x^5 - 235x^4 + 324x^3 - 858x^2 + 80x + 73	\( 2^{32}\cdot 3^{12}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.8.76293902388586086400000000.1	x^16 + 4x^14 - 6x^12 - 8x^11 - 40x^10 + 48x^9 - 51x^8 + 48x^7 - 456x^6 + 1294x^4 + 224x^3 - 676x^2 - 192x + 9	\( 2^{48}\cdot 5^{8}\cdot 7^{4}\cdot 17^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.459191708201416736032948224.1	x^16 + 56x^14 - 48x^13 + 1228x^12 - 1824x^11 + 14432x^10 - 27216x^9 + 100960x^8 - 202176x^7 + 444176x^6 - 766464x^5 + 1141096x^4 - 1454976x^3 + 1316480x^2 - 683808x + 153796	\( 2^{40}\cdot 3^{12}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	$[2, 2, 2, 50]$ (GRH)
16.16.459191708201416736032948224.1	x^16 - 4x^15 - 56x^14 + 196x^13 + 1292x^12 - 3592x^11 - 16228x^10 + 30016x^9 + 120247x^8 - 102368x^7 - 498028x^6 - 16192x^5 + 888188x^4 + 640876x^3 - 24896x^2 - 80284x - 11831	\( 2^{40}\cdot 3^{12}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.8.459191708201416736032948224.1	x^16 + 20x^14 - 24x^13 - 170x^12 + 456x^11 - 1888x^10 + 1044x^9 + 3145x^8 + 2592x^7 + 7580x^6 - 29244x^5 + 15796x^4 + 25776x^3 - 44728x^2 + 9636x - 503	\( 2^{40}\cdot 3^{12}\cdot 17^{4}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)
16.0.1638350662595178231031136256.1	x^16 + 56x^14 - 48x^13 + 1112x^12 - 1456x^11 + 10632x^10 - 14592x^9 + 50410x^8 - 67552x^7 + 150072x^6 - 181520x^5 + 258952x^4 - 260368x^3 + 292616x^2 - 209824x + 97081	\( 2^{40}\cdot 3^{8}\cdot 17^{6}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	$[2, 2, 2, 116]$ (GRH)
16.16.1638350662595178231031136256.1	x^16 - 64x^14 - 48x^13 + 1412x^12 + 1744x^11 - 13032x^10 - 19392x^9 + 53464x^8 + 91072x^7 - 83472x^6 - 179488x^5 + 6952x^4 + 105760x^3 + 29264x^2 - 7040x - 1724	\( 2^{40}\cdot 3^{8}\cdot 17^{6}\cdot 97^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T595)	Trivial (GRH)