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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.141751072355941015625.1	x^16 - 5x^15 + 13x^14 - 27x^13 + 52x^12 - 93x^11 + 151x^10 - 221x^9 + 285x^8 - 311x^7 + 296x^6 - 277x^5 + 265x^4 - 225x^3 + 141x^2 - 60x + 16	\( 5^{8}\cdot 7^{8}\cdot 29^{4}\cdot 89 \)	16T1806	$[2]$
16.0.141751072355941015625.2	x^16 - x^14 - 4x^13 + 14x^12 + 5x^11 - 13x^10 - 44x^9 + 82x^8 + 9x^7 + 10x^6 - 237x^5 + 386x^4 - 257x^3 + 88x^2 - 15x + 1	\( 5^{8}\cdot 7^{8}\cdot 29^{4}\cdot 89 \)	16T1806	$[2]$
16.0.311682383035759705257.1	x^16 - 4x^15 + 9x^14 - 15x^13 + 9x^12 - 3x^11 + 19x^10 + 23x^9 - 60x^8 - 24x^7 + 6x^6 + 30x^5 + 47x^4 + x^3 - 9x^2 + 2x + 4	\( 3^{21}\cdot 19\cdot 199^{4} \)	16T1806	Trivial
16.0.311682383035759705257.2	x^16 - 7x^15 + 24x^14 - 57x^13 + 114x^12 - 207x^11 + 320x^10 - 425x^9 + 483x^8 - 425x^7 + 320x^6 - 207x^5 + 114x^4 - 57x^3 + 24x^2 - 7x + 1	\( 3^{21}\cdot 19\cdot 199^{4} \)	16T1806	Trivial
16.2.604509857290349609375.1	x^16 - x^15 - 4x^13 + 12x^12 - 44x^11 + 73x^10 - 107x^9 + 121x^8 - 107x^7 + 73x^6 - 44x^5 + 12x^4 - 4x^3 - x + 1	\( -\,5^{9}\cdot 7^{8}\cdot 19\cdot 41^{4} \)	16T1806	Trivial
16.6.604509857290349609375.1	x^16 - 3x^15 - x^14 + 2x^13 + 13x^12 - 11x^11 - 12x^10 + 4x^9 + 28x^8 + 41x^7 + 12x^6 - 60x^5 - 87x^4 - 59x^3 - 23x^2 - x + 1	\( -\,5^{9}\cdot 7^{8}\cdot 19\cdot 41^{4} \)	16T1806	Trivial (GRH)
16.2.916309678419056250000.1	x^16 - 7x^15 + 24x^14 - 53x^13 + 94x^12 - 134x^11 + 158x^10 - 202x^9 + 278x^8 - 215x^7 - 5x^6 + 133x^5 - 140x^4 + 118x^3 - 29x^2 - 36x + 19	\( -\,2^{4}\cdot 3^{2}\cdot 5^{8}\cdot 7^{8}\cdot 41^{4} \)	16T1806	Trivial
16.6.916309678419056250000.1	x^16 - 7x^14 - 3x^12 - 16x^10 - 3x^8 + 77x^6 + 94x^4 + 15x^2 - 9	\( -\,2^{4}\cdot 3^{2}\cdot 5^{8}\cdot 7^{8}\cdot 41^{4} \)	16T1806	Trivial (GRH)
16.8.11522960949248000000000.1	x^16 - 2x^15 + 6x^13 - 39x^12 + 42x^11 + 138x^10 - 284x^9 - 242x^8 + 814x^7 + 326x^6 - 1158x^5 - 205x^4 + 778x^3 + 12x^2 - 244x + 61	\( 2^{24}\cdot 5^{9}\cdot 7^{8}\cdot 61 \)	16T1806	Trivial (GRH)
16.8.11522960949248000000000.2	x^16 - 4x^15 - 10x^14 + 66x^13 - 41x^12 - 312x^11 + 660x^10 + 66x^9 - 1718x^8 + 2040x^7 - 122x^6 - 1586x^5 + 1326x^4 - 350x^3 - 50x^2 + 40x - 5	\( 2^{24}\cdot 5^{9}\cdot 7^{8}\cdot 61 \)	16T1806	Trivial (GRH)
16.4.28750732073369600000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 160x^12 - 232x^11 + 266x^10 - 252x^9 + 211x^8 - 168x^7 + 118x^6 - 56x^5 - 16x^4 + 56x^3 - 52x^2 + 24x - 4	\( 2^{24}\cdot 5^{8}\cdot 7^{8}\cdot 761 \)	16T1806	Trivial (GRH)
16.0.43558190527945433806128.1	x^16 - 10x^14 + 51x^12 - 178x^10 + 404x^8 - 495x^6 + 212x^4 + 55x^2 + 3	\( 2^{4}\cdot 3\cdot 13^{12}\cdot 79^{4} \)	16T1806	$[2]$
16.0.43558190527945433806128.2	x^16 - 4x^15 + 11x^14 - 33x^13 + 74x^12 - 146x^11 + 246x^10 - 315x^9 + 368x^8 - 315x^7 + 246x^6 - 146x^5 + 74x^4 - 33x^3 + 11x^2 - 4x + 1	\( 2^{4}\cdot 3\cdot 13^{12}\cdot 79^{4} \)	16T1806	$[2]$ (GRH)
16.10.98317748803358910546875.1	x^16 - 4x^15 - 3x^14 + 23x^13 - 19x^12 + 4x^11 + 55x^10 - 36x^9 - 26x^8 - 344x^7 - 450x^6 + 371x^5 + 984x^4 + 734x^3 + 273x^2 + 52x + 4	\( -\,5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.6.98317748803358910546875.1	x^16 - 5x^15 + x^14 + 28x^13 - 42x^12 + 31x^11 - 116x^10 + 187x^9 + 12x^8 - 212x^7 + 134x^6 - x^5 - 27x^4 - 8x^3 + 21x^2 - 10x + 1	\( -\,5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.6.98317748803358910546875.2	x^16 - 2x^15 - 12x^14 + 22x^13 + 62x^12 - 91x^11 - 180x^10 + 207x^9 + 304x^8 - 311x^7 - 273x^6 + 332x^5 + 44x^4 - 161x^3 + 64x^2 - 6x - 1	\( -\,5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.10.169821566114892663671875.1	x^16 - 3x^15 - 8x^14 + 19x^13 + 39x^12 - 67x^11 - 143x^10 + 400x^9 + 459x^8 - 1404x^7 - 950x^6 + 2043x^5 + 722x^4 - 1015x^3 + 88x^2 + 27x + 1	\( -\,5^{8}\cdot 7^{8}\cdot 19\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.12.545216607000444867578125.1	x^16 - 5x^15 - 9x^14 + 106x^13 - 179x^12 - 382x^11 + 1762x^10 - 1815x^9 - 1420x^8 + 3778x^7 - 422x^6 - 3017x^5 + 589x^4 + 1879x^3 - 648x^2 - 234x + 11	\( 5^{8}\cdot 7^{8}\cdot 61\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.8.545216607000444867578125.1	x^16 - 10x^14 - 19x^12 + 208x^10 + 462x^8 - 231x^6 - 850x^4 - 313x^2 + 61	\( 5^{8}\cdot 7^{8}\cdot 61\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.2.572030538492270025000000.1	x^16 + 22x^14 + 185x^12 + 765x^10 + 1672x^8 + 1899x^6 + 953x^4 + 56x^2 - 64	\( -\,2^{6}\cdot 5^{8}\cdot 7^{8}\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.6.572030538492270025000000.1	x^16 - x^15 - 4x^14 - 14x^13 + 29x^12 + 90x^11 + 20x^10 - 385x^9 - 627x^8 + 1200x^7 + 1408x^6 - 161x^5 - 4766x^4 + 1855x^3 + 2474x^2 - 584x - 359	\( -\,2^{6}\cdot 5^{8}\cdot 7^{8}\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.10.715038173115337531250000.1	x^16 - 9x^14 + 4x^12 + 174x^10 - 548x^8 + 340x^6 + 449x^4 - 320x^2 - 80	\( -\,2^{4}\cdot 5^{9}\cdot 7^{8}\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.14.715038173115337531250000.1	x^16 - x^15 - 21x^14 + 14x^13 + 153x^12 - 3x^11 - 561x^10 - 265x^9 + 964x^8 + 660x^7 - 753x^6 - 561x^5 + 227x^4 + 168x^3 - 12x^2 - 14x - 1	\( -\,2^{4}\cdot 5^{9}\cdot 7^{8}\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.4.940420076832457667578125.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 181x^12 - 267x^11 + 289x^10 - 213x^9 + 70x^8 + 63x^7 - 122x^6 + 104x^5 - 58x^4 + 24x^3 + 4x^2 - 10x + 5	\( 3^{2}\cdot 5^{8}\cdot 7^{8}\cdot 41^{4}\cdot 16421 \)	16T1806	Trivial (GRH)
16.4.974239510869647386328125.1	x^16 - 3x^15 + x^14 - 21x^13 + 36x^12 + 33x^11 + 135x^10 + 56x^9 - 618x^8 - 522x^7 - 502x^6 + 91x^5 + 2353x^4 + 2426x^3 + 811x^2 - 1518x - 1179	\( 5^{8}\cdot 7^{8}\cdot 109\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.8.974239510869647386328125.1	x^16 + 6x^14 - 59x^12 - 116x^10 + 626x^8 + 621x^6 - 1638x^4 - 1341x^2 + 109	\( 5^{8}\cdot 7^{8}\cdot 109\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.2.1170875008476365207421875.1	x^16 - 8x^15 + 47x^14 - 189x^13 + 598x^12 - 1495x^11 + 3042x^10 - 5057x^9 + 6868x^8 - 7569x^7 + 6620x^6 - 4451x^5 + 2134x^4 - 615x^3 + 31x^2 + 43x - 11	\( -\,5^{8}\cdot 7^{8}\cdot 131\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.6.1170875008476365207421875.1	x^16 - 5x^15 + 20x^13 + 40x^12 - 90x^11 - 457x^10 + 1004x^9 + 724x^8 - 3465x^7 + 2425x^6 + 1840x^5 - 4664x^4 + 4831x^3 - 3165x^2 + 1038x - 76	\( -\,5^{8}\cdot 7^{8}\cdot 131\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.4.1573083980853742568750000.1	x^16 + 12x^14 + 19x^12 - 234x^10 - 883x^8 - 75x^6 + 3048x^4 + 3832x^2 + 1331	\( 2^{4}\cdot 5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.8.1573083980853742568750000.1	x^16 - 7x^15 + 14x^14 - 9x^13 + 11x^12 + 6x^11 - 31x^10 + 24x^9 - 62x^8 + 24x^7 - 31x^6 + 6x^5 + 11x^4 - 9x^3 + 14x^2 - 7x + 1	\( 2^{4}\cdot 5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.8.1573083980853742568750000.2	x^16 - 5x^15 - 6x^14 + 53x^13 - 58x^12 + 29x^11 + 51x^10 - 147x^9 + 208x^8 - 147x^7 + 51x^6 + 29x^5 - 58x^4 + 53x^3 - 6x^2 - 5x + 1	\( 2^{4}\cdot 5^{8}\cdot 7^{8}\cdot 11\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.14.1599897912345567726171875.1	x^16 - 7x^15 + x^14 + 88x^13 - 137x^12 - 345x^11 + 808x^10 + 495x^9 - 1894x^8 - 77x^7 + 2094x^6 - 356x^5 - 1111x^4 + 247x^3 + 247x^2 - 36x - 19	\( -\,5^{8}\cdot 7^{8}\cdot 179\cdot 251^{4} \)	16T1806	Trivial (GRH)
16.10.2109611104584685031250000.1	x^16 - 16x^14 + 74x^12 - 53x^10 - 226x^8 + 110x^6 + 161x^4 - 35x^2 - 5	\( -\,2^{4}\cdot 3^{16}\cdot 5^{9}\cdot 199^{4} \)	16T1806	Trivial (GRH)
16.0.5397412047087660274024448.1	x^16 + 12x^14 + 65x^12 + 199x^10 + 370x^8 + 438x^6 + 338x^4 + 158x^2 + 32	\( 2^{27}\cdot 7^{8}\cdot 17^{8} \)	16T1806	Trivial (GRH)
16.0.9404760383647261258678272.1	x^16 + 15x^14 + 90x^12 + 269x^10 + 396x^8 + 228x^6 + 64x^4 + 228x^2 + 192	\( 2^{22}\cdot 3^{21}\cdot 11^{8} \)	16T1806	$[2]$ (GRH)
16.4.9404760383647261258678272.1	x^16 - 19x^14 + 133x^12 - 402x^10 + 387x^8 + 492x^6 - 1140x^4 + 528x^2 + 12	\( 2^{22}\cdot 3^{21}\cdot 11^{8} \)	16T1806	Trivial (GRH)
16.4.9404760383647261258678272.2	x^16 + 9x^14 + 27x^12 + 28x^10 + 6x^8 - 3x^6 - 17x^4 - 6x^2 + 3	\( 2^{22}\cdot 3^{21}\cdot 11^{8} \)	16T1806	Trivial (GRH)
16.12.241155561860311524133203125.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 99x^12 + 139x^11 + 41x^10 - 359x^9 + 385x^8 + 141x^7 - 599x^6 + 387x^5 + 193x^4 - 457x^3 + 79x^2 + 130x - 44	\( 5^{8}\cdot 7^{8}\cdot 251^{4}\cdot 26981 \)	16T1806	Trivial (GRH)
16.8.1188132974102094609600000000.1	x^16 + 5x^14 - 4x^12 - 41x^10 - 4x^8 + 92x^6 - 5x^4 - 46x^2 + 11	\( 2^{12}\cdot 3^{16}\cdot 5^{8}\cdot 11\cdot 199^{4} \)	16T1806	$[2]$ (GRH)
16.8.19010127585633513753600000000.1	x^16 - 5x^14 - 4x^12 + 41x^10 - 4x^8 - 92x^6 - 5x^4 + 46x^2 + 11	\( 2^{16}\cdot 3^{16}\cdot 5^{8}\cdot 11\cdot 199^{4} \)	16T1806	Trivial (GRH)
16.16.40257909401173618791773828125.1	x^16 - 8x^15 + 3x^14 + 119x^13 - 197x^12 - 729x^11 + 1607x^10 + 2437x^9 - 6037x^8 - 5071x^7 + 11931x^6 + 7135x^5 - 11817x^4 - 6557x^3 + 4285x^2 + 2898x + 404	\( 5^{8}\cdot 7^{8}\cdot 251^{4}\cdot 509\cdot 8849 \)	16T1806	Trivial (GRH)
16.12.117629536214429777277659119616.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 111x^12 + 120x^11 + 119x^10 - 408x^9 + 282x^8 + 352x^7 - 645x^6 + 90x^5 + 367x^4 - 222x^3 - 49x^2 + 80x + 8	\( 2^{24}\cdot 13^{8}\cdot 41\cdot 47^{4}\cdot 42961 \)	16T1806	Trivial (GRH)
16.16.1757620767940782764845109870592.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 182x^12 - 182x^11 + 854x^10 + 20x^9 - 1819x^8 + 578x^7 + 1910x^6 - 844x^5 - 908x^4 + 418x^3 + 136x^2 - 54x - 3	\( 2^{28}\cdot 3^{20}\cdot 71^{4}\cdot 73897 \)	16T1806	Trivial (GRH)
16.12.364949574671621174049498480790687937724416.1	x^16 - 8x^15 - 194x^14 + 1498x^13 - 33949x^12 + 183856x^11 + 5923877x^10 - 31268076x^9 - 191000463x^8 + 953569804x^7 - 6328543931x^6 + 15514855228x^5 + 502985664539x^4 - 1030653409038x^3 - 10805487081588x^2 + 11323231138444x + 80523074268737	\( 2^{24}\cdot 13^{8}\cdot 41^{3}\cdot 47^{4}\cdot 42961^{3} \)	16T1806	Trivial (GRH)