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 66)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.25405371337890625.3	x^16 - x^15 + 3x^14 - 2x^13 + x^12 + 9x^11 - 20x^10 + 9x^9 + 14x^8 - 27x^7 + 10x^6 + 7x^5 + 6x^4 - 9x^3 - 3x^2 + 2x + 1	\( 5^{12}\cdot 101^{4} \)	16T1263	Trivial
16.0.635134283447265625.1	x^16 - x^14 - 10x^13 + 7x^12 + 15x^11 + 17x^10 - 55x^9 + 5x^8 + 5x^7 + 83x^6 - 85x^5 - 8x^4 + 30x^3 + x^2 - 5x + 1	\( 5^{14}\cdot 101^{4} \)	16T1263	Trivial
16.0.259160193017822265625.11	x^16 - 7x^15 + 37x^14 - 116x^13 + 292x^12 - 456x^11 + 478x^10 + 202x^9 - 1185x^8 + 2156x^7 - 196x^6 - 4451x^5 + 12348x^4 - 16596x^3 + 16675x^2 - 9802x + 4111	\( 5^{12}\cdot 101^{6} \)	16T1263	$[2]$ (GRH)
16.0.259160193017822265625.12	x^16 - 2x^15 + 15x^14 - 35x^13 + 104x^12 - 237x^11 + 493x^10 - 860x^9 + 1891x^8 - 2087x^7 + 5648x^6 - 3986x^5 + 11209x^4 - 5424x^3 + 12119x^2 - 3479x + 5041	\( 5^{12}\cdot 101^{6} \)	16T1263	$[2]$ (GRH)
16.0.322581582210337451521.2	x^16 - 5x^15 + 17x^14 - 39x^13 + 71x^12 - 120x^11 + 188x^10 - 277x^9 + 337x^8 - 323x^7 + 309x^6 - 292x^5 + 231x^4 - 169x^3 + 108x^2 - 63x + 27	\( 13^{12}\cdot 61^{4} \)	16T1263	Trivial
16.0.6479004825445556640625.6	x^16 - 24x^14 - 15x^13 + 287x^12 + 245x^11 - 2007x^10 - 2005x^9 + 9205x^8 + 9110x^7 - 27618x^6 - 25420x^5 + 54852x^4 + 39985x^3 - 66171x^2 - 30745x + 42191	\( 5^{14}\cdot 101^{6} \)	16T1263	$[2, 2]$ (GRH)
16.0.6479004825445556640625.7	x^16 + 26x^14 - 10x^13 + 332x^12 - 215x^11 + 2623x^10 - 1875x^9 + 13365x^8 - 8500x^7 + 43177x^6 - 20250x^5 + 85157x^4 - 26025x^3 + 98444x^2 - 22120x + 52081	\( 5^{14}\cdot 101^{6} \)	16T1263	$[2]$ (GRH)
16.0.54516287393547029307049.1	x^16 - x^15 + 2x^13 - 6x^12 - 28x^11 - 24x^10 - 38x^9 + 104x^8 + 348x^7 + 31x^6 - 37x^5 + 437x^4 + 86x^3 - 169x^2 - 62x + 139	\( 13^{14}\cdot 61^{4} \)	16T1263	Trivial (GRH)
16.12.226902568837089461272576.1	x^16 - 4x^15 - 10x^14 + 64x^13 - 31x^12 - 280x^11 + 514x^10 + 68x^9 - 1189x^8 + 1448x^7 - 244x^6 - 1304x^5 + 1780x^4 - 1136x^3 + 384x^2 - 64x + 4	\( 2^{44}\cdot 337^{4} \)	16T1263	Trivial
16.4.226902568837089461272576.1	x^16 - 4x^15 + 10x^14 - 16x^13 + 35x^12 - 64x^11 + 66x^10 + 36x^9 + 20x^8 - 732x^7 + 1714x^6 - 2288x^5 + 1283x^4 - 224x^3 + 370x^2 + 60x - 79	\( 2^{44}\cdot 337^{4} \)	16T1263	$[2]$
16.0.1200326067404665657109641.9	x^16 - 2x^15 - 10x^13 + 9x^12 - 7x^11 - 43x^10 + 342x^9 + 17x^8 + 849x^7 - 1526x^6 - 3083x^5 + 591x^4 - 2808x^3 + 11718x^2 - 3078x + 2187	\( 13^{12}\cdot 61^{6} \)	16T1263	$[2]$ (GRH)
16.0.1200326067404665657109641.10	x^16 - 6x^15 + 6x^14 + 31x^13 - 51x^12 - 126x^11 + 203x^10 + 618x^9 - 1148x^8 - 1361x^7 + 3664x^6 + 623x^5 - 4565x^4 + 176x^3 + 396x^2 + 1539x + 3537	\( 13^{12}\cdot 61^{6} \)	16T1263	$[2]$ (GRH)
16.0.2643693128974804931640625.24	x^16 - x^15 - 43x^14 + 72x^13 + 1035x^12 - 2082x^11 - 16213x^10 + 30231x^9 + 164376x^8 - 257335x^7 - 1035255x^6 + 1467105x^5 + 4084295x^4 - 5525450x^3 - 10235150x^2 + 9449200x + 15073775	\( 5^{12}\cdot 101^{8} \)	16T1263	$[2, 2]$ (GRH)
16.12.3630441101393431380361216.1	x^16 - 8x^15 + 8x^14 + 80x^13 - 210x^12 - 56x^11 + 640x^10 - 344x^9 - 606x^8 + 80x^7 + 768x^6 + 720x^5 - 1468x^4 - 240x^3 + 872x^2 - 240x + 4	\( 2^{48}\cdot 337^{4} \)	16T1263	Trivial (GRH)
16.4.3630441101393431380361216.1	x^16 + 12x^14 - 16x^13 + 22x^12 - 240x^11 - 296x^10 - 1688x^9 - 3082x^8 - 8544x^7 - 15776x^6 - 28512x^5 - 39380x^4 - 39824x^3 - 26072x^2 - 8400x - 956	\( 2^{48}\cdot 337^{4} \)	16T1263	$[2]$
16.0.14030845564476355702701601.2	x^16 - 5x^15 + 15x^14 - 31x^13 + 46x^12 + 15x^11 - 192x^10 + 136x^9 + 267x^8 - 93x^7 - 264x^6 + 417x^5 - 1621x^4 + 650x^3 + 2949x^2 - 2220x + 1321	\( 13^{4}\cdot 53^{12} \)	16T1263	Trivial (GRH)
16.0.66092328224370123291015625.11	x^16 - 5x^15 - 56x^14 + 250x^13 + 1757x^12 - 5950x^11 - 36793x^10 + 75280x^9 + 566450x^8 - 462345x^7 - 6343597x^6 - 149590x^5 + 49799537x^4 + 16695220x^3 - 238936324x^2 - 59152745x + 510242801	\( 5^{14}\cdot 101^{8} \)	16T1263	$[2, 2, 2]$ (GRH)
16.0.202855105391388496051529329.4	x^16 - 6x^15 + 11x^14 - 45x^13 + 180x^12 - 43x^11 + 636x^10 + 117x^9 - 1380x^8 + 5447x^7 + 4926x^6 - 5313x^5 + 8201x^4 + 11576x^3 + 6901x^2 + 18453x + 15237	\( 13^{14}\cdot 61^{6} \)	16T1263	$[2, 2]$ (GRH)
16.0.202855105391388496051529329.6	x^16 - 5x^15 - 5x^14 - 19x^13 - 6x^12 + 510x^11 + 1715x^10 + 4966x^9 + 12683x^8 + 22321x^7 + 32757x^6 + 32406x^5 + 12309x^4 + 95620x^3 + 252936x^2 + 118683x + 27459	\( 13^{14}\cdot 61^{6} \)	16T1263	$[2]$ (GRH)
16.0.1372437234816400000000000000.1	x^16 - 6x^15 + 18x^14 - 22x^13 + 56x^12 + 44x^11 + 140x^10 - 2526x^9 + 13029x^8 - 38012x^7 + 83260x^6 - 157598x^5 + 277076x^4 - 394094x^3 + 419722x^2 - 278608x + 91181	\( 2^{16}\cdot 5^{14}\cdot 1361^{4} \)	16T1263	$[4, 8]$ (GRH)
16.0.1372437234816400000000000000.2	x^16 - 6x^15 + 18x^14 - 72x^13 + 366x^12 - 706x^11 - 1615x^10 + 10204x^9 - 15146x^8 - 10002x^7 + 68420x^6 - 109908x^5 + 104386x^4 - 59694x^3 + 27777x^2 - 7768x + 1121	\( 2^{16}\cdot 5^{14}\cdot 1361^{4} \)	16T1263	$[2, 8]$ (GRH)
16.0.2371212900396504113756570569.9	x^16 - 4x^15 + 21x^14 - 47x^13 + 150x^12 - 252x^11 + 716x^10 - 1224x^9 + 3145x^8 - 4977x^7 + 9431x^6 - 10964x^5 + 13848x^4 - 9722x^3 + 7618x^2 - 2116x + 937	\( 13^{6}\cdot 53^{12} \)	16T1263	$[2]$ (GRH)
16.0.2371212900396504113756570569.16	x^16 - 6x^15 + 11x^14 - 3x^13 - 11x^12 + 72x^11 - 401x^10 - 21x^9 + 2454x^8 + 693x^7 - 234x^6 - 6788x^5 - 46828x^4 - 16858x^3 + 122847x^2 + 122304x + 35347	\( 13^{6}\cdot 53^{12} \)	16T1263	$[2, 2]$ (GRH)
16.0.3999625222217600929630104481.3	x^16 - 3x^15 + 3x^14 - 17x^13 + 63x^12 - 250x^11 + 581x^10 - 196x^9 + 3806x^8 - 7934x^7 + 9993x^6 - 11599x^5 + 33390x^4 - 33334x^3 + 28225x^2 - 23863x + 7693	\( 37^{12}\cdot 157^{4} \)	16T1263	Trivial (GRH)
16.0.4466413296812760910104974161.25	x^16 - 6x^15 + 8x^14 - 109x^13 + 949x^12 - 2325x^11 + 2477x^10 - 5012x^9 + 79004x^8 - 169455x^7 - 120419x^6 + 323596x^5 + 1892735x^4 - 5978037x^3 + 15222337x^2 - 16161808x + 10626213	\( 13^{12}\cdot 61^{8} \)	16T1263	$[2, 2]$ (GRH)
16.0.14870286751307494933959540736.1	x^16 + 64x^14 + 1592x^12 + 19760x^10 + 132106x^8 + 474032x^6 + 838456x^4 + 582336x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	$[2, 1388]$ (GRH)
16.16.14870286751307494933959540736.1	x^16 - 44x^14 + 814x^12 - 8192x^10 + 48401x^8 - 168576x^6 + 328238x^4 - 314084x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	Trivial (GRH)
16.8.14870286751307494933959540736.1	x^16 + 44x^14 + 498x^12 - 808x^10 - 21423x^8 + 46536x^6 + 119298x^4 - 324868x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	Trivial (GRH)
16.0.14870286751307494933959540736.2	x^16 + 44x^14 + 814x^12 + 8192x^10 + 48401x^8 + 168576x^6 + 328238x^4 + 314084x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	$[2, 1332]$ (GRH)
16.16.14870286751307494933959540736.2	x^16 - 64x^14 + 1592x^12 - 19760x^10 + 132106x^8 - 474032x^6 + 838456x^4 - 582336x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	Trivial (GRH)
16.8.14870286751307494933959540736.2	x^16 + 12x^14 - 170x^12 - 1224x^10 + 7901x^8 + 26184x^6 - 88294x^4 - 198156x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	$[2]$ (GRH)
16.8.14870286751307494933959540736.3	x^16 - 44x^14 + 498x^12 + 808x^10 - 21423x^8 - 46536x^6 + 119298x^4 + 324868x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	$[2]$ (GRH)
16.8.14870286751307494933959540736.4	x^16 - 12x^14 - 262x^12 + 1416x^10 + 11357x^8 - 40968x^6 - 57290x^4 + 101100x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	Trivial (GRH)
16.0.39412645190614083168888797209.2	x^16 - 4x^15 + 14x^14 - 58x^13 + 364x^12 - 1372x^11 + 2941x^10 - 4491x^9 + 7272x^8 - 12138x^7 + 19032x^6 - 25678x^5 + 28026x^4 - 31363x^3 + 31792x^2 - 37204x + 31147	\( 13^{4}\cdot 53^{14} \)	16T1263	Trivial (GRH)
16.0.400734980167009195224860426161.1	x^16 - 7x^15 + 40x^14 - 190x^13 + 687x^12 - 1801x^11 + 3509x^10 - 5178x^9 + 5891x^8 - 5178x^7 + 3509x^6 - 1801x^5 + 687x^4 - 190x^3 + 40x^2 - 7x + 1	\( 13^{8}\cdot 53^{12} \)	16T1263	$[2, 4]$ (GRH)
16.0.400734980167009195224860426161.7	x^16 - 2x^15 + 4x^14 + 25x^13 - 43x^12 + 90x^11 + 321x^10 - 649x^9 + 858x^8 + 1747x^7 - 1058x^6 + 190x^5 + 13223x^4 - 15324x^3 + 20364x^2 - 2977x + 3809	\( 13^{8}\cdot 53^{12} \)	16T1263	$[2, 4]$ (GRH)
16.0.400734980167009195224860426161.8	x^16 - x^15 + 14x^14 - 72x^13 + 202x^12 - 775x^11 + 2524x^10 - 5518x^9 + 11732x^8 - 21375x^7 + 23344x^6 - 15249x^5 + 12020x^4 - 4293x^3 - 3816x^2 - 2862x + 4293	\( 13^{8}\cdot 53^{12} \)	16T1263	$[2, 4]$ (GRH)
16.0.400734980167009195224860426161.16	x^16 - 7x^15 + 24x^14 - 77x^13 + 248x^12 - 568x^11 + 752x^10 + 123x^9 - 2986x^8 + 3502x^7 + 9176x^6 - 23827x^5 + 1080x^4 + 39331x^3 - 19619x^2 + 5183x + 37181	\( 13^{8}\cdot 53^{12} \)	16T1263	$[2, 4]$ (GRH)
16.0.400734980167009195224860426161.24	x^16 - 3x^15 + 4x^14 + 18x^13 + 233x^12 + 43x^11 - 1562x^10 - 4148x^9 + 2746x^8 + 21927x^7 + 16015x^6 - 77351x^5 - 163680x^4 + 28422x^3 + 600746x^2 + 915879x + 590327	\( 13^{8}\cdot 53^{12} \)	16T1263	$[2, 2, 2]$ (GRH)
16.0.754823847161356593807740633209.11	x^16 - 6x^15 + 26x^14 - 179x^13 + 1233x^12 - 5490x^11 + 1168x^10 + 11629x^9 + 194597x^8 - 120954x^7 - 1006648x^6 - 1701847x^5 - 6362725x^4 + 29579481x^3 + 22641411x^2 - 81236989x + 134139983	\( 13^{14}\cdot 61^{8} \)	16T1263	$[2, 2, 2]$ (GRH)
16.0.5475486929215895672663613034489.1	x^16 - 4x^15 + 63x^14 - 55x^13 + 1046x^12 - 1005x^11 + 9225x^10 - 13208x^9 + 60260x^8 - 83761x^7 + 250634x^6 - 324957x^5 + 635768x^4 - 609071x^3 + 843018x^2 - 527756x + 463589	\( 37^{14}\cdot 157^{4} \)	16T1263	Trivial (GRH)
16.0.6660737037213780055542206728321.1	x^16 - 2x^15 - 36x^14 + 148x^13 + 598x^12 - 2366x^11 - 1565x^10 + 26712x^9 + 23245x^8 - 71338x^7 - 138822x^6 + 492020x^5 + 1599079x^4 + 582089x^3 + 1912174x^2 + 289887x + 11219	\( 13^{6}\cdot 53^{14} \)	16T1263	$[2, 2]$ (GRH)
16.0.6660737037213780055542206728321.3	x^16 - 7x^15 - 14x^14 + 199x^13 - 295x^12 - 3517x^11 + 27213x^10 - 94769x^9 + 237730x^8 - 498936x^7 + 1163887x^6 - 2147609x^5 + 2952893x^4 - 3154489x^3 + 4335539x^2 - 3500744x + 999947	\( 13^{6}\cdot 53^{14} \)	16T1263	$[2, 2]$ (GRH)
16.0.98586762102441645314452445352169.10	x^16 - 3x^15 + x^14 - 108x^13 + 880x^12 - 2766x^11 + 24860x^10 - 125210x^9 + 274990x^8 + 248849x^7 - 2139347x^6 + 4196569x^5 + 2080962x^4 - 19749908x^3 + 50035370x^2 - 52490006x + 39371633	\( 37^{12}\cdot 157^{6} \)	16T1263	$[2]$ (GRH)
16.0.98586762102441645314452445352169.12	x^16 - 5x^15 + 80x^14 - 371x^13 + 2451x^12 - 11500x^11 + 42902x^10 - 179757x^9 + 579189x^8 - 1860278x^7 + 5475094x^6 - 12157062x^5 + 27751164x^4 - 84988496x^3 + 244561025x^2 - 279329589x + 104368793	\( 37^{12}\cdot 157^{6} \)	16T1263	$[2]$ (GRH)
16.0.1125664559289128829386632937086249.1	x^16 - 3x^15 + 36x^14 - 13x^13 + 709x^12 + 1918x^11 + 11517x^10 + 39721x^9 + 86739x^8 + 46024x^7 - 10053x^6 - 557115x^5 - 1554137x^4 - 1401668x^3 + 12988290x^2 - 3587532x + 281867	\( 13^{8}\cdot 53^{14} \)	16T1263	$[2, 2, 4]$ (GRH)
16.0.1125664559289128829386632937086249.5	x^16 - 7x^15 + 79x^14 - 205x^13 + 1262x^12 - 1287x^11 + 10037x^10 - 12012x^9 + 161280x^8 - 11026x^7 + 1042184x^6 + 13506x^5 + 4631732x^4 - 2571426x^3 + 7697352x^2 + 313326x + 3286543	\( 13^{8}\cdot 53^{14} \)	16T1263	$[2, 2, 4]$ (GRH)
16.0.1125664559289128829386632937086249.7	x^16 - 4x^15 + 52x^14 - 191x^13 + 1004x^12 - 4675x^11 + 10357x^10 - 54485x^9 + 114330x^8 - 122429x^7 + 565267x^6 + 1246730x^5 - 2654985x^4 - 4063001x^3 + 7510735x^2 - 4096578x + 4962179	\( 13^{8}\cdot 53^{14} \)	16T1263	$[2, 2, 4]$ (GRH)
16.0.1125664559289128829386632937086249.14	x^16 - 8x^15 + 9x^14 - 29x^13 + 667x^12 - 1975x^11 + 1940x^10 - 6845x^9 + 26459x^8 - 30297x^7 - 365599x^6 - 1459696x^5 + 8653181x^4 - 3692254x^3 + 42347991x^2 + 13550329x + 43741763	\( 13^{8}\cdot 53^{14} \)	16T1263	$[2, 2, 2, 2]$ (GRH)
16.0.1125664559289128829386632937086249.15	x^16 - 4x^15 + 34x^14 - 22x^13 - 267x^12 + 86x^11 + 7067x^10 + 6134x^9 - 14475x^8 - 79428x^7 + 521094x^6 + 872096x^5 + 1808447x^4 - 6469998x^3 + 1831385x^2 + 4379232x + 65951899	\( 13^{8}\cdot 53^{14} \)	16T1263	$[2, 2, 4]$ (GRH)