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Results (12 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.6.127...000.1 | $x^{20} - 4 x^{19} - 8 x^{18} + 70 x^{17} - 94 x^{16} - 164 x^{15} + 333 x^{14} + 254 x^{13} - 59 x^{12} - 1812 x^{11} + 4724 x^{10} - 10976 x^{9} + 6000 x^{8} + 22592 x^{7} - 42880 x^{6} + 41600 x^{5} - 26816 x^{4} - 1280 x^{3} + 11520 x^{2} - 6144 x + 4096$ | $-\,2^{42}\cdot 5^{8}\cdot 11^{10}\cdot 13^{4}$ | $C_5:D_5^3.(C_2\times S_4)$ (as 20T884) | trivial |
| 21.3.534...875.1 | $x^{21} - 7 x^{19} + 21 x^{17} - 42 x^{15} - 19 x^{14} + 70 x^{13} + 70 x^{12} - 70 x^{11} - 35 x^{10} + 56 x^{9} - 175 x^{8} + 83 x^{7} + 14 x^{5} + 7 x^{4} - 28 x^{3} + 7 x^{2} + 7 x - 1$ | $-\,5^{9}\cdot 7^{23}$ | $F_7$ (as 21T4) | trivial |
| 21.11.423...000.1 | $x^{21} - 3 x^{20} - 15 x^{19} + 44 x^{18} + 94 x^{17} - 281 x^{16} - 298 x^{15} + 1078 x^{14} + 279 x^{13} - 2291 x^{12} + 635 x^{11} + 3408 x^{10} - 3777 x^{9} - 1738 x^{8} + 4305 x^{7} - 1372 x^{6} - 1831 x^{5} + 1718 x^{4} + 569 x^{3} - 294 x^{2} - 34 x + 3$ | $-\,2^{24}\cdot 3^{5}\cdot 5^{8}\cdot 113^{8}$ | $S_7$ (as 21T38) | trivial |
| 21.5.211...000.1 | $x^{21} - 16 x^{18} + 100 x^{15} - 302 x^{12} + 421 x^{9} - 162 x^{6} - 88 x^{3} - 8$ | $2^{24}\cdot 3^{18}\cdot 5^{6}\cdot 113^{6}$ | $C_3^6:A_7.C_2$ (as 21T129) | trivial |
| 21.7.201...000.1 | $x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 4 x^{14} + 2940 x^{13} + 56 x^{12} - 5733 x^{11} - 308 x^{10} + 7007 x^{9} + 840 x^{8} - 5141 x^{7} - 1176 x^{6} + 2030 x^{5} + 784 x^{4} - 287 x^{3} - 196 x^{2} - 28 x + 4$ | $-\,2^{14}\cdot 5^{7}\cdot 7^{31}$ | $C_7^2:(C_3\times S_3)$ (as 21T26) | trivial |
| 21.5.127...000.1 | $x^{21} - 18 x^{18} - 351 x^{15} + 351 x^{12} + 19359 x^{9} + 99630 x^{6} + 40095 x^{3} + 2187$ | $2^{18}\cdot 3^{36}\cdot 5^{6}\cdot 113^{6}$ | $C_3:S_7$ (as 21T58) | trivial |
| 21.21.703...000.1 | $x^{21} - 264 x^{19} - 168 x^{18} + 27342 x^{17} + 36048 x^{16} - 1401434 x^{15} - 2849472 x^{14} + 36431502 x^{13} + 102067252 x^{12} - 423314766 x^{11} - 1630146408 x^{10} + 1072584806 x^{9} + 9577784340 x^{8} + 9612576270 x^{7} - 2154284640 x^{6} - 5409788400 x^{5} - 324408000 x^{4} + 928545600 x^{3} + 75600000 x^{2} - 39456000 x - 4672000$ | $2^{33}\cdot 3^{28}\cdot 5^{6}\cdot 73^{12}$ | $C_3^6.C_7:C_6$ (as 21T79) | trivial |
| 21.21.703...000.2 | $x^{21} - 267 x^{19} - 558 x^{18} + 27117 x^{17} + 103932 x^{16} - 1240915 x^{15} - 6753042 x^{14} + 24497415 x^{13} + 192716088 x^{12} - 162404217 x^{11} - 2785124154 x^{10} - 894491889 x^{9} + 22104443700 x^{8} + 18090773655 x^{7} - 101908889190 x^{6} - 96253071300 x^{5} + 276559255800 x^{4} + 216023379600 x^{3} - 410564052000 x^{2} - 163151640000 x + 237053584000$ | $2^{33}\cdot 3^{28}\cdot 5^{6}\cdot 73^{12}$ | $C_3^6.C_7:C_6$ (as 21T79) | trivial |
| 21.7.584...000.1 | $x^{21} - 4 x^{20} - 172 x^{19} + 41 x^{18} + 10346 x^{17} + 7360 x^{16} - 303161 x^{15} + 129476 x^{14} + 6812176 x^{13} - 5491771 x^{12} - 77585528 x^{11} + 135977776 x^{10} + 849006685 x^{9} + 1678570946 x^{8} + 3467537070 x^{7} + 1558417063 x^{6} + 80313040142 x^{5} + 398147180490 x^{4} + 561944975579 x^{3} + 709729046640 x^{2} + 1426262185102 x + 796675579415$ | $-\,2^{18}\cdot 5^{8}\cdot 29^{18}\cdot 83^{7}$ | $C_7^3:C_3^2:S_3$ (as 21T65) | $[14]$ |
| 21.9.139...000.1 | $x^{21} - x^{20} - 8907 x^{19} + 287403 x^{18} + 20737563 x^{17} - 1536048695 x^{16} - 1424880171 x^{15} + 2670255003655 x^{14} - 37268264741490 x^{13} - 2277204938680934 x^{12} + 51251307238942562 x^{11} + 2236315564988775294 x^{10} - 58383564684400836337 x^{9} - 1347435674438794900027 x^{8} + 11387278172766393483117 x^{7} + 66387826557099595391831 x^{6} + 40559284948933905553228907 x^{5} - 416437033528682812281227479 x^{4} - 10858579223880525420579598929 x^{3} - 15135666229270655154860400447 x^{2} + 4071371288467802705264508035412 x - 29218184349161717714466118551912$ | $2^{20}\cdot 3^{8}\cdot 5^{10}\cdot 7^{12}\cdot 13^{17}\cdot 79^{8}\cdot 5279^{7}$ | $C_7^3:(C_3^3:S_4)$ (as 21T110) | not computed |
| 27.27.169...625.1 | $x^{27} - 81 x^{25} - 9 x^{24} + 2655 x^{23} + 630 x^{22} - 46449 x^{21} - 15174 x^{20} + 480726 x^{19} + 168732 x^{18} - 3091932 x^{17} - 921699 x^{16} + 12697560 x^{15} + 2226852 x^{14} - 33544908 x^{13} - 151362 x^{12} + 55869750 x^{11} - 10353906 x^{10} - 55098225 x^{9} + 20237283 x^{8} + 28210356 x^{7} - 15002577 x^{6} - 5789232 x^{5} + 4425516 x^{4} + 47223 x^{3} - 428166 x^{2} + 79218 x - 3969$ | $3^{48}\cdot 5^{18}\cdot 11^{18}$ | $\He_3:C_4$ (as 27T32) | trivial |
| 27.27.141...625.1 | $x^{27} - 135 x^{25} - 10 x^{24} + 7473 x^{23} + 912 x^{22} - 224337 x^{21} - 34458 x^{20} + 4054797 x^{19} + 699843 x^{18} - 46248429 x^{17} - 8386056 x^{16} + 339464965 x^{15} + 62343726 x^{14} - 1609499231 x^{13} - 300390454 x^{12} + 4886317342 x^{11} + 964290791 x^{10} - 9266363476 x^{9} - 2025251746 x^{8} + 10382430425 x^{7} + 2594556582 x^{6} - 6061560373 x^{5} - 1762982686 x^{4} + 1295269083 x^{3} + 454776934 x^{2} + 31601315 x + 611801$ | $5^{18}\cdot 7^{18}\cdot 19^{18}\cdot 23^{12}$ | $C_3^2:C_{12}$ (as 27T33) | $[3, 3]$ |