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 37 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.13.1293828810415522206118845309426655161.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 53x^16 - 899x^15 - 382x^14 + 2557x^13 + 1438x^12 - 4294x^11 - 3019x^10 + 4030x^9 + 3533x^8 - 1774x^7 - 2183x^6 + 69x^5 + 551x^4 + 110x^3 - 36x^2 - 13x - 1	\( 3^{3}\cdot 7^{14}\cdot 113\cdot 7985768699\cdot 78297036161 \)	21T159	Trivial (GRH)
21.13.2730915542462327937504442529336180736.1	x^21 - 6x^19 - 4x^18 - 45x^17 - 60x^16 + 223x^15 + 486x^14 + 891x^13 + 1584x^12 - 918x^11 - 7428x^10 - 12146x^9 - 13032x^8 - 9933x^7 + 1246x^6 + 16092x^5 + 21528x^4 + 14992x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{24}\cdot 8388019^{3} \)	21T152	Trivial (GRH)
21.13.4645990340334022941969904782035730432.1	x^21 - 42x^19 - 28x^18 + 729x^17 + 972x^16 - 6453x^15 - 13554x^14 + 27333x^13 + 94976x^12 - 14553x^11 - 328686x^10 - 312847x^9 + 372276x^8 + 958311x^7 + 546750x^6 - 438804x^5 - 927144x^4 - 695216x^3 - 284256x^2 - 63168x - 6016	\( 2^{14}\cdot 3^{21}\cdot 47^{2}\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.13.16865213361316368677229831448817302529.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 54x^16 - 898x^15 - 396x^14 + 2541x^13 + 1511x^12 - 4209x^11 - 3210x^10 + 3829x^9 + 3846x^8 - 1479x^7 - 2499x^6 - 303x^5 + 537x^4 + 190x^3 - 15x^2 - 12x - 1	\( 7^{14}\cdot 41\cdot 167\cdot 5406197\cdot 671780022444019 \)	21T159	Trivial (GRH)
21.13.23781039465164875759312968407942873088.1	x^21 - 21x^19 - 10x^18 + 189x^17 + 180x^16 - 929x^15 - 1350x^14 + 2595x^13 + 5496x^12 - 3663x^11 - 13302x^10 + 495x^9 + 19764x^8 + 6885x^7 - 17594x^6 - 11664x^5 + 7392x^4 + 8032x^3 + 576x^2 - 768x - 128	\( 2^{14}\cdot 3^{21}\cdot 17\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.13.25192291127470187521040280871398560021.1	x^21 - 2x^20 - 15x^19 + 58x^18 + 22x^17 - 451x^16 + 666x^15 + 864x^14 - 3424x^13 + 1655x^12 + 5377x^11 - 4629x^10 - 8530x^9 + 10138x^8 + 6523x^7 - 9568x^6 - 4336x^5 + 6971x^4 - 397x^3 - 845x^2 - 78x - 1	\( 29^{19}\cdot 41^{2}\cdot 1567^{2} \)	21T112	Trivial (GRH)
21.13.30991632631127242005516305991156547228.1	x^21 - 5x^20 - 6x^19 + 63x^18 - 19x^17 - 327x^16 + 261x^15 + 911x^14 - 932x^13 - 1507x^12 + 1644x^11 + 1590x^10 - 1570x^9 - 1166x^8 + 816x^7 + 619x^6 - 241x^5 - 199x^4 + 49x^3 + 24x^2 - 3x - 1	\( 2^{2}\cdot 31\cdot 43\cdot 15053\cdot 102413451780923\cdot 3770285596717141 \)	21T164	Trivial (GRH)
21.13.40453417591156198845459427294648145741.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 45x^16 - 907x^15 - 270x^14 + 2685x^13 + 854x^12 - 5055x^11 - 1653x^10 + 6124x^9 + 2244x^8 - 4458x^7 - 2040x^6 + 1560x^5 + 960x^4 - 80x^3 - 123x^2 - 21x - 1	\( 7^{14}\cdot 59646183107903161080974909 \)	21T159	Trivial (GRH)
21.13.45756205480679415294398559964416419984.1	x^21 - 5x^20 - 6x^19 + 63x^18 - 19x^17 - 327x^16 + 261x^15 + 911x^14 - 932x^13 - 1507x^12 + 1644x^11 + 1590x^10 - 1570x^9 - 1166x^8 + 816x^7 + 619x^6 - 241x^5 - 200x^4 + 49x^3 + 25x^2 - 3x - 1	\( 2^{4}\cdot 103\cdot 426103\cdot 1287491\cdot 50609727688176358507171 \)	21T164	Trivial (GRH)
21.13.57940968764052746135454872365001378937.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 48x^16 - 904x^15 - 312x^14 + 2637x^13 + 1073x^12 - 4770x^11 - 2166x^10 + 5341x^9 + 2733x^8 - 3453x^7 - 2099x^6 + 1011x^5 + 825x^4 - x^3 - 90x^2 - 18x - 1	\( 3^{28}\cdot 661493771\cdot 3828819218040827 \)	21T159	Trivial (GRH)
21.13.101589114585925847727528969484632342528.1	x^21 - 60x^19 - 8x^18 + 1224x^17 + 192x^16 - 10767x^15 - 4410x^14 + 45264x^13 + 54600x^12 - 156366x^11 - 233310x^10 + 726860x^9 + 270576x^8 - 2019843x^7 - 331208x^6 + 2676384x^5 + 103680x^4 - 922000x^3 + 242208x^2 - 161472x - 107648	\( 2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 29^{2}\cdot 53\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.13.8866863017363332031653762708238323679232.1	x^21 + 24x^19 - 16x^18 - 36x^17 + 48x^16 - 3472x^15 + 6912x^14 - 11088x^13 + 18304x^12 + 107136x^11 - 407040x^10 + 691648x^9 - 928512x^8 - 63744x^7 + 4379648x^6 - 10036224x^5 + 11501568x^4 - 7729152x^3 + 3096576x^2 - 688128x + 65536	\( 2^{38}\cdot 3^{21}\cdot 11\cdot 809^{6} \)	21T147	Trivial (GRH)
21.13.12897255297983028409678200302892107169792.1	x^21 - 9x^19 - 6x^18 - 36x^17 - 48x^16 + 362x^15 + 756x^14 + 828x^13 + 976x^12 - 3024x^11 - 12576x^10 - 18674x^9 - 17352x^8 - 9186x^7 + 11260x^6 + 36504x^5 + 44208x^4 + 30112x^3 + 12096x^2 + 2688x + 256	\( 2^{42}\cdot 3^{21}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.13.21658684236689624719937096086082755356533.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 57x^16 - 895x^15 - 438x^14 + 2493x^13 + 1730x^12 - 3910x^11 - 3695x^10 + 2962x^9 + 4125x^8 - 418x^7 - 2147x^6 - 599x^5 + 347x^4 + 190x^3 + 4x^2 - 9x - 1	\( 229^{7}\cdot 92077\cdot 82827653\cdot 85991827177 \)	21T162	Trivial (GRH)
21.13.30442588627548161668838591975407708094464.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 44x^16 - 908x^15 - 256x^14 + 2701x^13 + 781x^12 - 5138x^11 - 1458x^10 + 6313x^9 + 1901x^8 - 4745x^7 - 1695x^6 + 1879x^5 + 877x^4 - 201x^3 - 146x^2 - 22x - 1	\( 2^{14}\cdot 37^{7}\cdot 113\cdot 8273\cdot 385537\cdot 54305277821449 \)	21T162	Trivial (GRH)
21.13.36068680148646461612743213200732662710272.1	x^21 - 3x^19 - 2x^18 - 108x^17 - 144x^16 + 141x^15 + 378x^14 + 2520x^13 + 6104x^12 + 2646x^11 - 8652x^10 - 21233x^9 - 36324x^8 - 49287x^7 - 49534x^6 - 39852x^5 - 27864x^4 - 15696x^3 - 6048x^2 - 1344x - 128	\( 2^{14}\cdot 3^{21}\cdot 29^{18} \)	21T123	Trivial (GRH)
21.13.70218440916863154295349403985322359078912.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 50x^16 - 902x^15 - 340x^14 + 2605x^13 + 1219x^12 - 4584x^11 - 2516x^10 + 4843x^9 + 3119x^8 - 2799x^7 - 2259x^6 + 563x^5 + 741x^4 + 71x^3 - 64x^2 - 16x - 1	\( 2^{14}\cdot 37^{7}\cdot 3637897767851\cdot 12409911498371 \)	21T162	Trivial (GRH)
21.13.165492619661247656369149666348223877660672.1	x^21 - 6x^19 - 4x^18 - 63x^17 - 84x^16 + 269x^15 + 594x^14 + 1692x^13 + 3544x^12 + 54x^11 - 9804x^10 - 22883x^9 - 42156x^8 - 52446x^7 - 27556x^6 + 17064x^5 + 39024x^4 + 29536x^3 + 12096x^2 + 2688x + 256	\( 2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.13.185774792348382807570141316603039633686528.1	x^21 - 24x^19 - 16x^18 + 162x^17 + 216x^16 - 9x^15 - 162x^14 - 1890x^13 - 4776x^12 - 3780x^11 + 1128x^10 + 9800x^9 + 26208x^8 + 42027x^7 + 44894x^6 + 37692x^5 + 27288x^4 + 15632x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 1009^{9} \)	21T131	Trivial (GRH)
21.13.960590898533608949920374968680596595802112.1	x^21 - 21x^19 - 20x^18 + 189x^17 + 360x^16 - 801x^15 - 2700x^14 + 675x^13 + 10344x^12 + 7857x^11 - 18828x^10 - 33233x^9 + 4536x^8 + 51237x^7 + 34828x^6 - 20304x^5 - 37896x^4 - 15392x^3 + 1440x^2 + 2112x + 320	\( 2^{24}\cdot 3^{21}\cdot 73^{12}\cdot 239 \)	21T137	Trivial (GRH)
21.13.2057834895603379842507246794830399401885696.1	x^21 - 21x^19 - 14x^18 + 117x^17 + 156x^16 + 133x^15 + 162x^14 - 1593x^13 - 4512x^12 - 3321x^11 + 2034x^10 + 8709x^9 + 18180x^8 + 23313x^7 + 11554x^6 - 9612x^5 - 19800x^4 - 14800x^3 - 6048x^2 - 1344x - 128	\( 2^{33}\cdot 3^{21}\cdot 73^{12} \)	21T137	Trivial (GRH)
21.13.2469302026241064308075329448353362630033408.1	x^21 + 24x^19 - 16x^18 - 297x^17 + 396x^16 - 7881x^15 + 15498x^14 + 14859x^13 - 64880x^12 + 659124x^11 - 2003016x^10 + 1978298x^9 + 876312x^8 - 11936907x^7 + 41795214x^6 - 77901372x^5 + 84911832x^4 - 56319248x^3 + 22504608x^2 - 5001024x + 476288	\( 2^{14}\cdot 3^{29}\cdot 61^{2}\cdot 8388019^{3} \)	21T149	Trivial (GRH)
21.13.9211785278619203955690014672704286619549696.1	x^21 - 6x^19 - 4x^18 - 126x^17 - 168x^16 + 862x^15 + 1836x^14 + 1548x^13 + 1136x^12 - 8370x^11 - 30396x^10 - 35873x^9 - 6948x^8 + 27087x^7 + 39230x^6 + 35532x^5 + 26712x^4 + 15568x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{19}\cdot 7\cdot 1601^{9} \)	21T131	Trivial (GRH)
21.13.10423848562958827406082788615011739523268608.1	x^21 - 24x^19 - 16x^18 + 135x^17 + 180x^16 + 519x^15 + 918x^14 - 4653x^13 - 13904x^12 - 7236x^11 + 16440x^10 + 49612x^9 + 101808x^8 + 105621x^7 - 51646x^6 - 286524x^5 - 369432x^4 - 255248x^3 - 102816x^2 - 22848x - 2176	\( 2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 29^{18} \)	21T123	Trivial (GRH)
21.13.24120549315626845915803563870253630169042944.1	x^21 - 21x^19 - 3x^18 + 189x^17 + 54x^16 - 1021x^15 - 405x^14 + 3975x^13 + 2216x^12 - 11943x^11 - 10797x^10 + 23903x^9 + 36558x^8 - 17487x^7 - 64299x^6 - 27972x^5 + 34740x^4 + 45128x^3 + 20304x^2 + 3936x + 256	\( 2^{12}\cdot 3^{21}\cdot 11\cdot 53\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.13.83737838586499625317207823358068174759018496.1	x^21 - 27x^19 - 18x^18 + 171x^17 + 228x^16 + 589x^15 + 1026x^14 - 5067x^13 - 15184x^12 - 15093x^11 - 6006x^10 + 26188x^9 + 105696x^8 + 177387x^7 + 165758x^6 + 98172x^5 + 43416x^4 + 17424x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{31}\cdot 587^{9} \)	21T122	Trivial (GRH)
21.13.6782764925506469650693833692003522155480498176.1	x^21 - 6x^19 - 4x^18 - 126x^17 - 168x^16 + 322x^15 + 756x^14 + 4554x^13 + 10912x^12 + 5454x^11 - 13020x^10 - 60139x^9 - 164556x^8 - 259701x^7 - 251642x^6 - 171396x^5 - 97416x^4 - 48624x^3 - 18144x^2 - 4032x - 384	\( 2^{14}\cdot 3^{35}\cdot 587^{9} \)	21T122	Trivial (GRH)
21.13.14848842777743746917666586040678292200394276864.1	x^21 + 36x^19 - 24x^18 - 108x^17 + 144x^16 - 7608x^15 + 15120x^14 + 6768x^13 - 42688x^12 + 402624x^11 - 1212288x^10 - 86528x^9 + 5658624x^8 - 8884608x^7 + 761600x^6 + 13312512x^5 - 18994176x^4 + 13400064x^3 - 5419008x^2 + 1204224x - 114688	\( 2^{14}\cdot 3^{21}\cdot 7^{3}\cdot 43^{18} \)	21T123	Trivial (GRH)
21.13.16463709752408337616228606991569162841980108800.1	x^21 - 3x^19 - 2x^18 - 108x^17 - 144x^16 + 195x^15 + 486x^14 + 3321x^13 + 8064x^12 + 1674x^11 - 17508x^10 - 42797x^9 - 79956x^8 - 97365x^7 - 40522x^6 + 56700x^5 + 101304x^4 + 74256x^3 + 30240x^2 + 6720x + 640	\( 2^{15}\cdot 3^{21}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.13.1482492148218678638085477396433249728399446900736.1	x^21 - 6x^19 - 4x^18 - 81x^17 - 108x^16 + 342x^15 + 756x^14 + 2610x^13 + 5728x^12 - 216x^11 - 16944x^10 - 42271x^9 - 84348x^8 - 108792x^7 - 59304x^6 + 31968x^5 + 77472x^4 + 59008x^3 + 24192x^2 + 5376x + 512	\( 2^{39}\cdot 3^{39}\cdot 13^{16} \)	21T142	Trivial (GRH)
21.13.7581538340984039472273273519617599488731840102400.1	x^21 - 6x^19 - 4x^18 - 432x^17 - 576x^16 + 1752x^15 + 3888x^14 + 50544x^13 + 128448x^12 - 74304x^11 - 617088x^10 - 1868864x^9 - 4518144x^8 - 5331840x^7 + 699136x^6 + 10160640x^5 + 13741056x^4 + 9590784x^3 + 3870720x^2 + 860160x + 81920	\( 2^{14}\cdot 3^{22}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9}\cdot 307 \)	21T142	Trivial (GRH)
21.13.8830806594437225156672627375869213526379397644288.1	x^21 - 12x^19 - 8x^18 - 324x^17 - 432x^16 + 2880x^15 + 6048x^14 + 37728x^13 + 90752x^12 - 96768x^11 - 582144x^10 - 1895872x^9 - 4845312x^8 - 6218496x^7 - 1158144x^6 + 7271424x^5 + 10764288x^4 + 7647232x^3 + 3096576x^2 + 688128x + 65536	\( 2^{35}\cdot 3^{40}\cdot 7\cdot 13^{15}\cdot 59 \)	21T142	Trivial (GRH)
21.13.79356206645831716224655747338287777368449179467776.1	x^21 - 30x^19 - 20x^18 - 621x^17 - 828x^16 + 17247x^15 + 35046x^14 + 66051x^13 + 119024x^12 - 1844262x^11 - 6476388x^10 - 4483504x^9 + 11041056x^8 + 23943879x^7 + 14457846x^6 - 7997076x^5 - 19421064x^4 - 14795696x^3 - 6066144x^2 - 1348032x - 128384	\( 2^{14}\cdot 3^{28}\cdot 17^{2}\cdot 29^{18}\cdot 59^{2} \)	21T120	Trivial (GRH)
21.13.218227930326934861214217295120255573869289271660544.1	x^21 + 24x^19 - 16x^18 - 459x^17 + 612x^16 - 11355x^15 + 22302x^14 + 46044x^13 - 159128x^12 + 1546074x^11 - 4684332x^10 + 4473917x^9 + 2650860x^8 - 37055628x^7 + 136617936x^6 - 258599088x^5 + 283109760x^4 - 187999040x^3 + 75140352x^2 - 16697856x + 1590272	\( 2^{12}\cdot 3^{28}\cdot 149^{6}\cdot 211^{6}\cdot 1553^{2} \)	21T148	Trivial (GRH)
21.13.508239433358075553521104351093444483806919881916416.1	x^21 - 9x^19 - 6x^18 - 135x^17 - 180x^16 + 993x^15 + 2106x^14 + 4887x^13 + 9600x^12 - 23031x^11 - 103602x^10 - 97025x^9 + 87948x^8 + 258951x^7 + 196462x^6 - 6804x^5 - 122472x^4 - 101808x^3 - 42336x^2 - 9408x - 896	\( 2^{32}\cdot 3^{22}\cdot 7^{14}\cdot 11^{18} \)	21T127	Trivial (GRH)
21.13.1403514779847325853897324257959386241063870491787264.1	x^21 + 15x^19 - 10x^18 - 540x^17 + 720x^16 - 6774x^15 + 13068x^14 + 74556x^13 - 220112x^12 + 892728x^11 - 2334288x^10 - 783346x^9 + 13135176x^8 - 39968658x^7 + 94308324x^6 - 155188008x^5 + 162971856x^4 - 106988384x^3 + 42662592x^2 - 9480576x + 902912	\( 2^{44}\cdot 3^{28}\cdot 809^{6}\cdot 3527^{2} \)	21T145	Trivial (GRH)
21.13.10017279497047013285784312521273620782624202478075904.1	x^21 + 33x^19 - 22x^18 - 540x^17 + 720x^16 - 21597x^15 + 42714x^14 - 65736x^13 + 105688x^12 + 1371762x^11 - 4859580x^10 + 9685343x^9 - 16976412x^8 - 2163123x^7 + 96125046x^6 - 220676508x^5 + 253088568x^4 - 170110352x^3 + 68154912x^2 - 15145536x + 1442432	\( 2^{14}\cdot 3^{28}\cdot 29^{18}\cdot 59^{2}\cdot 191^{2} \)	21T120	Trivial (GRH)