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 109)

Label	Polynomial	Discriminant	Galois group	Class group
16.14.1585557504000000000000.1	x^16 - 4x^15 - 12x^14 + 70x^13 - 25x^12 - 262x^11 + 290x^10 + 326x^9 - 604x^8 - 50x^7 + 490x^6 - 146x^5 - 152x^4 + 76x^3 + 12x^2 - 10x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1379	Trivial (GRH)
16.14.2368558831812663574528.1	x^16 - 4x^15 - 8x^14 + 48x^13 + 4x^12 - 208x^11 + 106x^10 + 400x^9 - 290x^8 - 348x^7 + 202x^6 + 192x^5 + 33x^4 - 152x^3 - 2x^2 + 28x - 1	\( -\,2^{32}\cdot 223^{5} \)	16T1759	Trivial (GRH)
16.14.2855404879681090234375.1	x^16 - x^15 - 13x^14 + 7x^13 + 79x^12 - 24x^11 - 271x^10 + 83x^9 + 503x^8 - 192x^7 - 472x^6 + 211x^5 + 201x^4 - 101x^3 - 27x^2 + 16x - 1	\( -\,5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{5} \)	16T1823	Trivial (GRH)
16.14.4052393769272913671875.1	x^16 - 2x^15 - 17x^14 + 23x^13 + 112x^12 - 86x^11 - 375x^10 + 127x^9 + 675x^8 - 62x^7 - 640x^6 + 3x^5 + 293x^4 - 8x^3 - 50x^2 + 4x + 1	\( -\,5^{8}\cdot 29^{4}\cdot 379\cdot 6221^{2} \)	16T1823	Trivial (GRH)
16.14.4810420224000000000000.1	x^16 - 6x^15 - 2x^14 + 76x^13 - 118x^12 - 194x^11 + 618x^10 - 346x^9 - 266x^8 + 350x^7 - 216x^6 + 62x^5 + 123x^4 - 70x^3 - 20x^2 + 8x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 179 \)	16T1379	Trivial (GRH)
16.14.5222794846127590998016.1	x^16 - 10x^14 + 35x^12 - 40x^10 - 39x^8 + 128x^6 - 93x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.14.5222794846127590998016.2	x^16 - 12x^14 + 56x^12 - 126x^10 + 132x^8 - 36x^6 - 33x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.14.8410853036812500000000.1	x^16 - 7x^14 - 24x^12 + 314x^10 - 951x^8 + 1292x^6 - 856x^4 + 261x^2 - 29	\( -\,2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.14.11034809241396899282944.1	x^16 - 11x^14 + 37x^12 - 38x^10 - 25x^8 + 70x^6 - 46x^4 + 12x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.14.12266856094105600000000.1	x^16 - 10x^14 + 33x^12 - 28x^10 - 63x^8 + 148x^6 - 105x^4 + 26x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.14.12266856094105600000000.2	x^16 - 10x^14 + 35x^12 - 40x^10 - 41x^8 + 140x^6 - 115x^4 + 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.14.12806308171801600000000.1	x^16 - 7x^14 + 5x^12 + 70x^10 - 221x^8 + 264x^6 - 138x^4 + 28x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.14.15310680244851363610624.1	x^16 - 10x^14 + 28x^12 - x^10 - 96x^8 + 133x^6 - 67x^4 + 14x^2 - 1	\( -\,2^{16}\cdot 483345053^{2} \)	16T1948	Trivial (GRH)
16.14.15310680244851363610624.2	x^16 - 11x^14 + 40x^12 - 42x^10 - 56x^8 + 153x^6 - 105x^4 + 20x^2 - 1	\( -\,2^{16}\cdot 483345053^{2} \)	16T1948	Trivial (GRH)
16.14.27205187892436187283456.1	x^16 - 10x^14 + 26x^12 + 26x^10 - 211x^8 + 330x^6 - 208x^4 + 48x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 8461^{4} \)	16T1848	Trivial (GRH)
16.14.28678961869849600000000.1	x^16 - 13x^14 + 62x^12 - 134x^10 + 120x^8 + x^6 - 62x^4 + 25x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial (GRH)
16.14.28678961869849600000000.2	x^16 - 12x^14 + 46x^12 - 54x^10 - 25x^8 + 89x^6 - 56x^4 + 13x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1905	Trivial (GRH)
16.14.28825732500500357840896.1	x^16 - 15x^14 + 74x^12 - 154x^10 + 118x^8 + 26x^6 - 77x^4 + 32x^2 - 4	\( -\,2^{18}\cdot 43^{2}\cdot 2777^{4} \)	16T1879	Trivial (GRH)
16.14.32694615909228402695152.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 104x^12 + 78x^11 + 166x^10 - 258x^9 - 37x^8 + 266x^7 - 119x^6 - 95x^5 + 93x^4 + 3x^3 - 19x^2 + x + 1	\( -\,2^{4}\cdot 43^{2}\cdot 2777^{4}\cdot 18583 \)	16T1879	Trivial (GRH)
16.14.50641820249485101608827.1	x^16 - 2x^15 - 14x^14 + 15x^13 + 104x^12 - 35x^11 - 420x^10 - 45x^9 + 899x^8 + 376x^7 - 925x^6 - 658x^5 + 280x^4 + 377x^3 + 109x^2 + 6x - 1	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.14.109744110351674560546875.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 117x^12 + 65x^11 + 226x^10 - 272x^9 - 137x^8 + 321x^7 - 36x^6 - 152x^5 + 63x^4 + 27x^3 - 17x^2 - 2x + 1	\( -\,3^{12}\cdot 5^{12}\cdot 31\cdot 149^{2}\cdot 1229 \)	16T1771	Trivial (GRH)
16.14.110940987391802500000000.1	x^16 - x^15 - 21x^14 + 30x^13 + 161x^12 - 296x^11 - 504x^10 + 1221x^9 + 409x^8 - 2037x^7 + 487x^6 + 1223x^5 - 639x^4 - 177x^3 + 167x^2 - 24x - 1	\( -\,2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 89^{4} \)	16T1719	Trivial (GRH)
16.14.112467297327629238009856.1	x^16 - 5x^14 - 14x^12 + 128x^10 - 277x^8 + 256x^6 - 108x^4 + 19x^2 - 1	\( -\,2^{20}\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.14.130936142356695004217344.1	x^16 - 12x^14 + 50x^12 - 80x^10 + 13x^8 + 88x^6 - 78x^4 + 20x^2 - 1	\( -\,2^{60}\cdot 337^{2} \)	16T1771	Trivial (GRH)
16.14.143070635028888602804224.1	x^16 - 12x^14 + 50x^12 - 72x^10 - 55x^8 + 276x^6 - 284x^4 + 96x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.14.143070635028888602804224.2	x^16 - 14x^14 + 71x^12 - 154x^10 + 112x^8 + 54x^6 - 87x^4 + 22x^2 - 1	\( -\,2^{36}\cdot 113^{6} \)	16T1638	Trivial (GRH)
16.14.170690133797345543359375.1	x^16 - 2x^15 - 19x^14 + 26x^13 + 130x^12 - 67x^11 - 463x^10 - 207x^9 + 1033x^8 + 924x^7 - 1394x^6 - 803x^5 + 937x^4 + 5x^3 - 100x^2 + 19x - 1	\( -\,5^{8}\cdot 19^{4}\cdot 31^{3}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.14.204900930748825600000000.1	x^16 - 16x^14 + 97x^12 - 268x^10 + 277x^8 + 152x^6 - 500x^4 + 272x^2 - 16	\( -\,2^{20}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.14.210271325920312500000000.1	x^16 - x^15 - 24x^14 + 46x^13 + 173x^12 - 506x^11 - 236x^10 + 1853x^9 - 1192x^8 - 1736x^7 + 2296x^6 - 177x^5 - 847x^4 + 373x^3 - 6x^2 - 17x + 1	\( -\,2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 29^{5} \)	16T1616	Trivial (GRH)
16.14.248730575542681600000000.1	x^16 - 14x^14 + 73x^12 - 180x^10 + 217x^8 - 112x^6 + 9x^4 + 6x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.14.248730575542681600000000.2	x^16 - 14x^14 + 55x^12 - 56x^10 - 87x^8 + 196x^6 - 103x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.14.303774876408217600000000.1	x^16 - 12x^14 + 40x^12 - 10x^10 - 126x^8 + 184x^6 - 93x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.14.303774876408217600000000.2	x^16 - 10x^14 + 11x^12 + 104x^10 - 287x^8 + 272x^6 - 109x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.14.394949915114816900000000.1	x^16 - 4x^15 - 6x^14 + 51x^13 - 73x^12 - 120x^11 + 632x^10 - 657x^9 - 978x^8 + 2624x^7 - 1454x^6 - 1075x^5 + 1804x^4 - 959x^3 + 238x^2 - 26x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 89^{5} \)	16T1719	Trivial (GRH)
16.14.434911971099673600000000.1	x^16 - 7x^14 - x^12 + 117x^10 - 343x^8 + 384x^6 - 181x^4 + 30x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.14.434911971099673600000000.2	x^16 - 15x^14 + 84x^12 - 218x^10 + 258x^8 - 101x^6 - 26x^4 + 19x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.14.585531072079462400000000.1	x^16 - 4x^15 - 16x^14 + 74x^13 + 51x^12 - 454x^11 + 240x^10 + 1142x^9 - 1240x^8 - 868x^7 + 1356x^6 + 106x^5 - 513x^4 + 78x^3 + 60x^2 - 18x + 1	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.14.585531072079462400000000.2	x^16 - 18x^14 + 112x^12 - 244x^10 - 169x^8 + 1472x^6 - 2014x^4 + 890x^2 - 89	\( -\,2^{28}\cdot 5^{8}\cdot 89^{5} \)	16T1778	Trivial (GRH)
16.14.637534208000000000000000.1	x^16 - 20x^14 + 120x^12 - 180x^10 - 610x^8 + 2260x^6 - 2280x^4 + 820x^2 - 95	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	Trivial (GRH)
16.14.637534208000000000000000.2	x^16 - 20x^14 - 20x^13 + 140x^12 + 280x^11 - 280x^10 - 1220x^9 - 570x^8 + 1600x^7 + 1820x^6 - 340x^5 - 1220x^4 - 360x^3 + 120x^2 + 60x + 5	\( -\,2^{40}\cdot 5^{15}\cdot 19 \)	16T1604	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)
16.14.734874894868691892043776.1	x^16 - 6x^15 + 6x^14 + 38x^13 - 133x^12 + 54x^11 + 524x^10 - 688x^9 - 796x^8 + 1336x^7 + 514x^6 - 984x^5 - 146x^4 + 306x^3 + 12x^2 - 34x + 1	\( -\,2^{24}\cdot 3\cdot 37\cdot 4457^{4} \)	16T1916	Trivial (GRH)
16.14.734874894868691892043776.2	x^16 - 22x^14 - 2x^13 + 190x^12 + 30x^11 - 834x^10 - 148x^9 + 2015x^8 + 278x^7 - 2670x^6 - 92x^5 + 1742x^4 - 194x^3 - 388x^2 + 94x + 1	\( -\,2^{24}\cdot 3\cdot 37\cdot 4457^{4} \)	16T1916	Trivial (GRH)
16.14.907610275348357845090304.1	x^16 - 18x^14 + 115x^12 - 342x^10 + 505x^8 - 352x^6 + 88x^4 + 8x^2 - 4	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.14.1010567048425312500000000.1	x^16 - 2x^15 - 21x^14 + 27x^13 + 176x^12 - 130x^11 - 725x^10 + 325x^9 + 1615x^8 - 565x^7 - 2175x^6 + 485x^5 + 1620x^4 - 75x^3 - 425x^2 + 25x + 25	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.14.1010567048425312500000000.2	x^16 - 23x^14 + 174x^12 - 477x^10 + 51x^8 + 1825x^6 - 2800x^4 + 1375x^2 - 125	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.14.1019726702995046400000000.1	x^16 - 8x^15 + 20x^14 - 82x^12 + 128x^11 + 4x^10 - 240x^9 + 258x^8 + 100x^7 - 334x^6 + 56x^5 + 163x^4 - 40x^3 - 30x^2 + 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 92639 \)	16T1378	Trivial (GRH)
16.14.1426559715404800186341167.1	x^16 - 4x^15 - 8x^14 + 46x^13 + 13x^12 - 207x^11 + 52x^10 + 458x^9 - 222x^8 - 508x^7 + 303x^6 + 248x^5 - 162x^4 - 32x^3 + 24x^2 - 1	\( -\,26683\cdot 327203\cdot 163394721598783 \)	$S_{16}$ (as 16T1954)	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)
16.14.1700293663096832000000000.1	x^16 - 6x^15 + 2x^14 + 38x^13 - 36x^12 - 34x^11 - 38x^10 - 174x^9 + 526x^8 + 374x^7 - 746x^6 - 278x^5 + 276x^4 + 50x^3 - 34x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{9}\cdot 139^{5} \)	16T1862	Trivial (GRH)