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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.11.3913912048328213377158221353159.1	x^21 - 2x^20 - 9x^19 + 12x^18 + 25x^17 + 8x^16 - 79x^15 + 7x^14 + 170x^13 - 132x^12 - 294x^11 - 136x^10 + 534x^9 + 158x^8 - 345x^7 + 242x^6 + 243x^5 - 58x^4 - 53x^3 - 6x^2 + 2x + 1	\( -\,7^{5}\cdot 17^{8}\cdot 2017^{5} \)	21T38	Trivial (GRH)
21.11.34428615704115413560094117894967.1	x^21 - 6x^20 - x^19 + 71x^18 - 93x^17 - 305x^16 + 665x^15 + 567x^14 - 2100x^13 - 214x^12 + 3718x^11 - 982x^10 - 3941x^9 + 1934x^8 + 2506x^7 - 1669x^6 - 928x^5 + 820x^4 + 128x^3 - 214x^2 + 45x - 1	\( -\,3^{9}\cdot 280909^{5} \)	21T38	Trivial (GRH)
21.11.2103209751169770458112224890011648.1	x^21 - 21x^19 - 14x^18 + 162x^17 + 216x^16 - 495x^15 - 1134x^14 + 54x^13 + 1992x^12 + 2889x^11 + 3390x^10 - 974x^9 - 15336x^8 - 26253x^7 - 15618x^6 + 7452x^5 + 19224x^4 + 14736x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.11.2279162600361785110437461456142336.1	x^21 - 21x^19 - 16x^18 + 189x^17 + 288x^16 - 873x^15 - 2160x^14 + 1755x^13 + 8584x^12 + 1377x^11 - 18768x^10 - 14529x^9 + 20304x^8 + 28701x^7 - 5168x^6 - 22680x^5 - 7224x^4 + 4800x^3 + 4032x^2 + 1152x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.11.1398884674421463279959586376937816064.1	x^21 - 3x^19 - 2x^18 - 54x^17 - 72x^16 + 111x^15 + 270x^14 + 828x^13 + 1768x^12 + 513x^11 - 3282x^10 - 6730x^9 - 9432x^8 - 8733x^7 + 1406x^6 + 16092x^5 + 21528x^4 + 14992x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.11.1398884674421463279959586376937816064.2	x^21 - 3x^19 - 2x^18 - 54x^17 - 72x^16 + 84x^15 + 216x^14 + 954x^13 + 2192x^12 + 1188x^11 - 2280x^10 - 7076x^9 - 14544x^8 - 18213x^7 - 7202x^6 + 11772x^5 + 20376x^4 + 14864x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.11.5396811891984762047839189745295633479.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 60x^16 - 892x^15 - 480x^14 + 2445x^13 + 1949x^12 - 3615x^11 - 4188x^10 + 2119x^9 + 4464x^8 + 627x^7 - 1945x^6 - 1065x^5 + 75x^4 + 180x^3 + 27x^2 - 6x - 1	\( -\,7^{14}\cdot 13\cdot 97\cdot 10039\cdot 628578004368802949 \)	21T159	Trivial (GRH)
21.11.145147030291169283887309482380107366400.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 56x^16 - 896x^15 - 424x^14 + 2509x^13 + 1657x^12 - 4006x^11 - 3526x^10 + 3229x^9 + 3977x^8 - 757x^7 - 2159x^6 - 441x^5 + 389x^4 + 167x^3 - 6x^2 - 10x - 1	\( -\,2^{14}\cdot 3^{3}\cdot 5^{2}\cdot 37^{7}\cdot 138252302841813371149 \)	21T162	Trivial (GRH)
21.11.152136328493452883717548161594456983867.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 57x^16 - 895x^15 - 438x^14 + 2493x^13 + 1730x^12 - 3915x^11 - 3705x^10 + 2992x^9 + 4200x^8 - 438x^7 - 2312x^6 - 744x^5 + 312x^4 + 200x^3 + 9x^2 - 9x - 1	\( -\,7^{15}\cdot 223\cdot 80317\cdot 1789163334752592959 \)	21T159	Trivial (GRH)
21.11.1214922588597965135114544770664959361024.1	x^21 - 21x^19 - 12x^18 + 189x^17 + 216x^16 - 925x^15 - 1620x^14 + 2535x^13 + 6616x^12 - 3303x^11 - 16212x^10 - 665x^9 + 24840x^8 + 9225x^7 - 23660x^6 - 14796x^5 + 12360x^4 + 11024x^3 - 2016x^2 - 3264x - 640	\( -\,2^{14}\cdot 3^{21}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.11.6074612942989825675572723853324796805120.1	x^21 - 6x^19 - 4x^18 - 63x^17 - 84x^16 + 242x^15 + 540x^14 + 1413x^13 + 2888x^12 + 378x^11 - 6852x^10 - 11321x^9 - 10116x^8 - 5073x^7 + 5566x^6 + 18252x^5 + 22104x^4 + 15056x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 5\cdot 577^{9} \)	21T131	Trivial (GRH)
21.11.10343288728827978523071854146763992353792.1	x^21 - 21x^19 - x^18 + 189x^17 + 18x^16 - 1101x^15 - 135x^14 + 5175x^13 + 1640x^12 - 19143x^11 - 14415x^10 + 45479x^9 + 60858x^8 - 49671x^7 - 122905x^6 - 9180x^5 + 109356x^4 + 53424x^3 - 30384x^2 - 19008x + 6208	\( -\,2^{10}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.11.21976304547105974485649436224048259658411.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 45x^16 - 907x^15 - 270x^14 + 2685x^13 + 854x^12 - 5050x^11 - 1643x^10 + 6094x^9 + 2169x^8 - 4438x^7 - 1895x^6 + 1645x^5 + 935x^4 - 110x^3 - 128x^2 - 21x - 1	\( -\,53\cdot 229^{7}\cdot 12555396112941725258843 \)	21T162	Trivial (GRH)
21.11.103178042383864227277425602423136857358336.1	x^21 - 72x^17 - 96x^16 - 86x^15 - 108x^14 + 1143x^13 + 3224x^12 + 4212x^11 + 4680x^10 + 186x^9 - 14616x^8 - 32574x^7 - 46204x^6 - 53784x^5 - 48816x^4 - 30624x^3 - 12096x^2 - 2688x - 256	\( -\,2^{45}\cdot 3^{21}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.11.237714117824906601657941050896630528000000.1	x^21 - 3x^19 - 2x^18 - 90x^17 - 120x^16 + 68x^15 + 216x^14 + 1521x^13 + 3704x^12 + 2700x^11 - 1608x^10 - 9151x^9 - 23292x^8 - 32793x^7 - 20162x^6 + 5292x^5 + 18648x^4 + 14672x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.11.482108591396798180036901678675500279119872.1	x^21 - 12x^19 - 14x^18 - 171x^17 + 762x^16 + 2775x^15 - 11556x^14 - 7095x^13 + 67730x^12 - 4464x^11 - 219000x^10 - 105816x^9 + 1080900x^8 - 492591x^7 - 3230200x^6 + 5102568x^5 - 1202184x^4 - 1646784x^3 + 1253952x^2 - 358272x + 39808	\( -\,2^{14}\cdot 3^{28}\cdot 23^{3}\cdot 239^{3}\cdot 311^{2}\cdot 431^{3} \)	21T149	Trivial (GRH)
21.11.756401169658892313445973964168187656575911.1	x^21 - x^20 - 10x^19 + 40x^18 - 74x^17 + 11x^16 + 323x^15 - 1158x^14 + 2738x^13 - 4870x^12 + 7701x^11 - 11657x^10 + 15330x^9 - 18587x^8 + 21309x^7 - 19493x^6 + 16136x^5 - 15807x^4 + 11731x^3 - 3775x^2 + 70x + 41	\( -\,29^{18}\cdot 41^{3}\cdot 3671\cdot 3769^{2} \)	21T123	Trivial (GRH)
21.11.5144587239008449606268116987075998504714240.1	x^21 - 72x^17 - 96x^16 - 86x^15 - 108x^14 + 1224x^13 + 3440x^12 + 4914x^11 + 6396x^10 + 2362x^9 - 13176x^8 - 32094x^7 - 46140x^6 - 53784x^5 - 48816x^4 - 30624x^3 - 12096x^2 - 2688x - 256	\( -\,2^{32}\cdot 3^{21}\cdot 5\cdot 73^{12} \)	21T137	Trivial (GRH)
21.11.8662051113659033903782726464178407348043696.1	x^21 - 3x^20 - 13x^19 + 37x^18 + 80x^17 - 188x^16 - 321x^15 + 511x^14 + 910x^13 - 802x^12 - 1758x^11 + 703x^10 + 2157x^9 - 238x^8 - 1551x^7 - 113x^6 + 576x^5 + 112x^4 - 83x^3 - 20x^2 + 4x + 1	\( -\,2^{4}\cdot 757\cdot 21211\cdot 754931\cdot 44661826147142180133953570063 \)	21T164	Trivial (GRH)
21.11.23681017647282083374222184484113019484225536.1	x^21 - 21x^19 - 14x^18 - 54x^17 - 72x^16 + 1947x^15 + 3942x^14 - 1098x^13 - 9352x^12 + 129303x^11 + 459714x^10 + 249230x^9 - 1062936x^8 - 7283943x^7 - 25324998x^6 - 47407788x^5 - 51752376x^4 - 34339664x^3 - 13722912x^2 - 3049536x - 290432	\( -\,2^{14}\cdot 3^{28}\cdot 107^{3}\cdot 2269^{2}\cdot 21557^{3} \)	21T149	Trivial (GRH)
21.11.139466544682494688544924733946513396963737600.1	x^21 + 12x^19 - 60x^18 - 288x^17 - 840x^16 - 3726x^15 + 594x^14 + 366x^13 + 17192x^12 + 75906x^11 - 86412x^10 + 32126x^9 + 10296x^8 - 447726x^7 + 531832x^6 - 214920x^5 + 43176x^4 - 2352x^3 - 5760x^2 + 1440x + 160	\( -\,2^{26}\cdot 3^{21}\cdot 5^{2}\cdot 73^{12}\cdot 347 \)	21T137	Trivial (GRH)
21.11.329274195048166752324572139831383256839602176.1	x^21 + 36x^19 - 24x^18 + 108x^17 - 144x^16 - 6648x^15 + 13392x^14 - 50400x^13 + 112576x^12 + 83808x^11 - 598848x^10 + 1555648x^9 - 3375360x^8 + 2618112x^7 + 6278144x^6 - 18828288x^5 + 22671360x^4 - 15421440x^3 + 6193152x^2 - 1376256x + 131072	\( -\,2^{14}\cdot 3^{21}\cdot 7^{12}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.11.822019128720178339889523873118173943471698952.1	x^21 - 3x^20 - 8x^19 + 27x^18 + 21x^17 - 99x^16 - 11x^15 + 205x^14 - 54x^13 - 287x^12 + 157x^11 + 287x^10 - 235x^9 - 184x^8 + 218x^7 + 54x^6 - 122x^5 + 8x^4 + 37x^3 - 7x^2 - 4x + 1	\( -\,2^{3}\cdot 102752391090022292486190484139771742933962369 \)	21T164	Trivial (GRH)
21.11.20999001542048815263956213456361659483283259392.1	x^21 + 21x^19 - 14x^18 - 99x^17 + 132x^16 - 3851x^15 + 7614x^14 - 13905x^13 + 24672x^12 + 86535x^11 - 356466x^10 + 760871x^9 - 1419660x^8 + 1233567x^7 + 1621218x^6 - 5701428x^5 + 7018920x^4 - 4799280x^3 + 1929312x^2 - 428736x + 40832	\( -\,2^{46}\cdot 3^{21}\cdot 11^{2}\cdot 29^{2}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.11.5085862618644065944682370862103067572913300652032.1	x^21 + 21x^19 - 14x^18 - 2457x^15 + 4914x^14 - 16884x^13 + 37016x^12 - 19278x^11 - 40572x^10 + 241311x^9 - 723996x^8 + 1097907x^7 - 806246x^6 + 111132x^5 + 297864x^4 - 272496x^3 + 114912x^2 - 25536x + 2432	\( -\,2^{14}\cdot 3^{21}\cdot 7^{36}\cdot 19^{2}\cdot 31 \)	21T123	Trivial (GRH)
21.11.5170674349462897470243377350710078541633750155264.1	x^21 - 3x^19 - 2x^18 - 207x^17 - 276x^16 + 745x^15 + 1674x^14 + 7029x^13 + 16016x^12 - 999x^11 - 48882x^10 - 79184x^9 - 73008x^8 - 35757x^7 + 55086x^6 + 166428x^5 + 199512x^4 + 135568x^3 + 54432x^2 + 12096x + 1152	\( -\,2^{14}\cdot 3^{23}\cdot 13\cdot 31^{12}\cdot 41^{9} \)	21T142	Trivial (GRH)