Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 22.2.412...237.1 | $x^{22} - 7 x^{20} - 3 x^{19} + 17 x^{18} + 12 x^{17} - 15 x^{16} - 16 x^{15} - x^{14} - x^{13} - 28 x^{12} - 42 x^{11} + 3 x^{10} + 25 x^{9} - 16 x^{8} - 47 x^{7} - 35 x^{6} + 7 x^{5} + 16 x^{4} - 7 x^{3} - 5 x^{2} + 2 x + 1$ | $1070197\cdot 6205948139^{2}$ | $C_2^{10}.(C_2\times S_{11})$ (as 22T53) | trivial |
| 22.2.147...704.1 | $x^{22} - 2 x^{20} + 6 x^{18} - 14 x^{16} + 22 x^{14} - 31 x^{12} + 38 x^{10} - 34 x^{8} + 27 x^{6} - 17 x^{4} + 6 x^{2} - 1$ | $2^{22}\cdot 12917^{2}\cdot 459847^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.147...704.2 | $x^{22} + x^{18} - 2 x^{16} - 2 x^{14} - x^{12} + 3 x^{8} + x^{6} + x^{4} - 1$ | $2^{22}\cdot 12917^{2}\cdot 459847^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.178...033.1 | $x^{22} - 11 x^{21} + 65 x^{20} - 265 x^{19} + 825 x^{18} - 2067 x^{17} + 4301 x^{16} - 7582 x^{15} + 11469 x^{14} - 15003 x^{13} + 17039 x^{12} - 16811 x^{11} + 14374 x^{10} - 10594 x^{9} + 6680 x^{8} - 3576 x^{7} + 1630 x^{6} - 656 x^{5} + 261 x^{4} - 113 x^{3} + 48 x^{2} - 15 x + 1$ | $149\cdot 33797\cdot 64661^{2}\cdot 92179^{2}$ | $C_2^{10}.(C_2\times S_{11})$ (as 22T53) | trivial |
| 22.2.289...513.1 | $x^{22} - x^{21} + x^{20} - 3 x^{19} + 3 x^{18} + x^{17} + 5 x^{16} - 4 x^{15} - 18 x^{14} + 11 x^{13} + 16 x^{12} + 32 x^{11} - 45 x^{10} - 81 x^{9} + 100 x^{8} + 75 x^{7} - 101 x^{6} - 41 x^{5} + 53 x^{4} + 15 x^{3} - 15 x^{2} - 4 x + 1$ | $359753\cdot 28385393161^{2}$ | $C_2^{10}.(C_2\times S_{11})$ (as 22T53) | trivial |
| 22.2.635...313.1 | $x^{22} - x^{21} + 5 x^{20} - 8 x^{19} + 16 x^{18} - 27 x^{17} + 41 x^{16} - 61 x^{15} + 80 x^{14} - 104 x^{13} + 121 x^{12} - 138 x^{11} + 143 x^{10} - 142 x^{9} + 131 x^{8} - 112 x^{7} + 89 x^{6} - 64 x^{5} + 43 x^{4} - 24 x^{3} + 12 x^{2} - 4 x + 1$ | $60821\cdot 1487459\cdot 7024799976319967$ | $S_{22}$ (as 22T59) | trivial |
| 22.2.716...264.1 | $x^{22} + 4 x^{20} + x^{18} - 20 x^{16} - 7 x^{14} + 93 x^{12} + 46 x^{10} - 121 x^{8} - 80 x^{6} - 34 x^{4} - 9 x^{2} - 1$ | $2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ | $C_2^{10}.A_{11}$ (as 22T49) | trivial |
| 22.2.890...989.1 | $x^{22} - 2 x^{21} + 6 x^{20} - 10 x^{19} + 17 x^{18} - 21 x^{17} + 22 x^{16} - 15 x^{15} - 5 x^{14} + 38 x^{13} - 83 x^{12} + 135 x^{11} - 185 x^{10} + 221 x^{9} - 234 x^{8} + 222 x^{7} - 187 x^{6} + 138 x^{5} - 88 x^{4} + 47 x^{3} - 20 x^{2} + 6 x - 1$ | $34092855421\cdot 26129523845912209$ | $S_{22}$ (as 22T59) | trivial |
| 22.2.172...125.1 | $x^{22} + 3 x^{20} - 8 x^{19} - 13 x^{18} - 13 x^{17} - 10 x^{16} + 79 x^{15} + 45 x^{14} + 111 x^{13} + 59 x^{12} - 172 x^{11} + 31 x^{10} - 94 x^{9} - 96 x^{8} + 55 x^{7} - 26 x^{6} + x^{5} + 20 x^{4} - 4 x^{3} + 3 x^{2} - 1$ | $5^{11}\cdot 12917^{2}\cdot 459847^{2}$ | $C_2\times S_{11}$ (as 22T47) | trivial |
| 22.2.173...125.1 | $x^{22} - x^{21} + 2 x^{20} + x^{19} - 13 x^{18} + 3 x^{17} - 35 x^{16} - 18 x^{15} + 37 x^{14} + 27 x^{13} + 152 x^{12} + 277 x^{11} + 160 x^{10} + 72 x^{9} - 42 x^{8} - 69 x^{7} - 31 x^{6} - 22 x^{5} + 3 x^{4} + 4 x^{3} + x^{2} + x - 1$ | $5^{11}\cdot 64661^{2}\cdot 92179^{2}$ | $C_2\times S_{11}$ (as 22T47) | trivial |
| 22.2.176...672.1 | $x^{22} - 5 x^{21} + 17 x^{20} - 40 x^{19} + 70 x^{18} - 93 x^{17} + 99 x^{16} - 86 x^{15} + 53 x^{14} + 37 x^{13} - 283 x^{12} + 778 x^{11} - 1493 x^{10} + 2198 x^{9} - 2575 x^{8} + 2425 x^{7} - 1840 x^{6} + 1108 x^{5} - 512 x^{4} + 173 x^{3} - 33 x^{2} + x + 1$ | $2^{16}\cdot 37^{5}\cdot 4441^{4}$ | $C_2^{11}.A_{11}$ (as 22T52) | trivial |
| 22.2.286...056.1 | $x^{22} - 5 x^{20} + 9 x^{18} - 6 x^{16} - 12 x^{14} + 37 x^{12} - 45 x^{10} + 75 x^{8} - 54 x^{6} - 17 x^{4} + 44 x^{2} - 16$ | $2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ | $C_2^{10}.A_{11}$ (as 22T49) | trivial |
| 22.2.302...024.1 | $x^{22} + 3 x^{20} - 11 x^{16} - 24 x^{14} - 24 x^{12} + x^{10} + 11 x^{8} - 9 x^{6} - 5 x^{4} + 5 x^{2} - 1$ | $2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.311...696.1 | $x^{22} + 2 x^{16} - x^{14} - x^{12} + x^{10} + x^{8} - 2 x^{6} - x^{4} + 2 x^{2} - 1$ | $2^{22}\cdot 1559^{2}\cdot 17480927^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.107...089.1 | $x^{22} - x^{21} + x^{20} - 11 x^{19} - 5 x^{18} + 22 x^{17} + 22 x^{16} + 62 x^{15} - 83 x^{14} - 148 x^{13} + 44 x^{12} + 72 x^{11} + 52 x^{10} + 25 x^{9} + 50 x^{8} - 75 x^{7} - 65 x^{6} + 60 x^{5} - 17 x^{3} + 17 x^{2} - 7 x + 1$ | $167^{10}\cdot 639361$ | $C_2^{10}.D_{22}$ (as 22T32) | trivial |
| 22.2.315...616.1 | $x^{22} - 2 x^{21} + x^{20} - x^{19} - 7 x^{17} + 5 x^{16} + 45 x^{15} + 31 x^{14} - 38 x^{13} - 205 x^{12} - 278 x^{11} - 123 x^{10} + 249 x^{9} + 532 x^{8} + 371 x^{7} + 205 x^{6} + 153 x^{5} + 236 x^{4} + 94 x^{3} + 34 x^{2} + 5 x + 25$ | $2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4}$ | $C_2^{11}.A_{11}$ (as 22T52) | trivial |
| 22.2.707...496.1 | $x^{22} - 3 x^{20} + x^{18} + x^{16} + 6 x^{14} - 8 x^{12} + 5 x^{6} - x^{2} - 1$ | $2^{22}\cdot 167^{10}$ | $C_2^{10}.D_{11}$ (as 22T30) | trivial |
| 22.2.707...496.2 | $x^{22} - 6 x^{20} + 15 x^{18} - 27 x^{16} + 57 x^{14} - 109 x^{12} + 140 x^{10} - 129 x^{8} + 89 x^{6} - 41 x^{4} + 10 x^{2} - 1$ | $2^{22}\cdot 167^{10}$ | $C_2^{10}.D_{11}$ (as 22T30) | trivial |
| 22.2.104...544.1 | $x^{22} + 2 x^{20} - x^{18} + 2 x^{16} - 18 x^{12} - 24 x^{10} + 3 x^{8} + 36 x^{6} + 27 x^{4} + 4 x^{2} - 1$ | $2^{22}\cdot 19457^{2}\cdot 8095783^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.126...136.1 | $x^{22} - 4 x^{21} + 14 x^{20} - 38 x^{19} + 89 x^{18} - 184 x^{17} + 341 x^{16} - 572 x^{15} + 876 x^{14} - 1228 x^{13} + 1579 x^{12} - 1862 x^{11} + 2008 x^{10} - 1978 x^{9} + 1765 x^{8} - 1416 x^{7} + 1009 x^{6} - 628 x^{5} + 333 x^{4} - 144 x^{3} + 47 x^{2} - 10 x + 1$ | $2^{33}\cdot 11^{2}\cdot 121975057867858073$ | $S_{11}\wr C_2$ (as 22T57) | trivial |
| 22.2.168...256.1 | $x^{22} + x^{20} - 12 x^{14} - 14 x^{12} + 16 x^{10} + 28 x^{8} + x^{6} - 14 x^{4} - 7 x^{2} - 1$ | $2^{22}\cdot 200601609583^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.347...005.1 | $x^{22} - x - 1$ | $5\cdot 69454092876521107983605569601$ | $S_{22}$ (as 22T59) | trivial |
| 22.2.499...501.1 | $x^{22} - 2 x^{21} + 5 x^{20} - 4 x^{19} + 4 x^{18} - 14 x^{17} + 63 x^{16} - 228 x^{15} + 497 x^{14} - 686 x^{13} + 792 x^{12} - 793 x^{11} + 1821 x^{10} - 3315 x^{9} + 78 x^{8} + 1215 x^{7} + 1528 x^{6} + 168 x^{5} - 351 x^{4} - 826 x^{3} - 4 x^{2} + 39 x - 5$ | $3^{11}\cdot 167^{11}$ | $D_{22}$ (as 22T3) | trivial |
| 22.2.639...073.1 | $x^{22} - x^{21} + 14 x^{19} - 11 x^{18} - 42 x^{17} + 99 x^{16} + 27 x^{15} - 297 x^{14} + 205 x^{13} + 473 x^{12} - 780 x^{11} - 121 x^{10} + 1273 x^{9} - 891 x^{8} - 915 x^{7} + 1485 x^{6} - 27 x^{5} - 1166 x^{4} + 1016 x^{3} - 429 x^{2} + 98 x - 8$ | $3^{21}\cdot 11^{19}$ | $C_2\times F_{11}$ (as 22T6) | trivial |
| 22.2.823...125.1 | $x^{22} - x^{21} + 14 x^{20} - 11 x^{19} + 83 x^{18} - 46 x^{17} + 290 x^{16} - 162 x^{15} + 710 x^{14} - 312 x^{13} + 966 x^{12} - 47 x^{11} + 930 x^{10} + 311 x^{9} + 628 x^{8} + 309 x^{7} + 259 x^{6} + 141 x^{5} + 87 x^{4} + 44 x^{3} + 16 x^{2} + 2 x - 1$ | $5^{11}\cdot 167^{10}$ | $D_{22}$ (as 22T3) | trivial |
| 22.2.162...408.1 | $x^{22} - 10 x^{20} + 45 x^{18} - 125 x^{16} + 250 x^{14} - 392 x^{12} + 498 x^{10} - 516 x^{8} + 428 x^{6} - 264 x^{4} + 107 x^{2} - 23$ | $2^{22}\cdot 23\cdot 167^{10}$ | $C_2^{10}.D_{22}$ (as 22T32) | trivial |
| 22.2.397...125.1 | $x^{22} - x^{11} - 1$ | $5^{11}\cdot 11^{22}$ | $C_2\times F_{11}$ (as 22T6) | trivial |
| 22.2.109...056.1 | $x^{22} + 12 x^{20} + 64 x^{18} + 200 x^{16} + 406 x^{14} + 557 x^{12} + 507 x^{10} + 271 x^{8} + 51 x^{6} - 18 x^{4} - 9 x^{2} - 1$ | $2^{22}\cdot 1619043113033^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.109...056.2 | $x^{22} + 10 x^{20} + 44 x^{18} + 112 x^{16} + 182 x^{14} + 199 x^{12} + 151 x^{10} + 67 x^{8} - 13 x^{6} - 36 x^{4} - 13 x^{2} - 1$ | $2^{22}\cdot 1619043113033^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.128...337.1 | $x^{22} - 11 x^{21} + 75 x^{20} - 365 x^{19} + 1409 x^{18} - 4473 x^{17} + 12052 x^{16} - 27974 x^{15} + 56686 x^{14} - 100938 x^{13} + 158847 x^{12} - 221312 x^{11} + 273270 x^{10} - 298381 x^{9} + 287150 x^{8} - 241819 x^{7} + 176511 x^{6} - 109912 x^{5} + 57096 x^{4} - 23845 x^{3} + 7532 x^{2} - 1599 x + 163$ | $31\cdot 43^{2}\cdot 547^{2}\cdot 632447\cdot 34374601^{2}$ | $C_2^{10}.(C_2\times S_{11})$ (as 22T53) | trivial |
| 22.2.529...892.1 | $x^{22} - 4 x^{21} + 8 x^{20} - 17 x^{19} + 25 x^{18} + 9 x^{17} - 75 x^{16} + 78 x^{15} - 51 x^{14} - 5 x^{13} + 143 x^{12} - 112 x^{11} + 22 x^{10} + 109 x^{9} + 123 x^{8} + 246 x^{7} + 108 x^{6} - 39 x^{5} - 82 x^{4} - 107 x^{3} - 65 x^{2} - 4 x + 8$ | $2^{2}\cdot 3^{20}\cdot 11^{18}\cdot 683$ | $C_2\times C_2^{10}.F_{11}$ (as 22T37) | trivial |
| 22.2.583...928.1 | $x^{22} - 8 x^{21} + 32 x^{20} - 90 x^{19} + 202 x^{18} - 378 x^{17} + 607 x^{16} - 856 x^{15} + 1073 x^{14} - 1210 x^{13} + 1241 x^{12} - 1164 x^{11} + 1007 x^{10} - 806 x^{9} + 595 x^{8} - 406 x^{7} + 253 x^{6} - 144 x^{5} + 73 x^{4} - 34 x^{3} + 14 x^{2} - 4 x + 1$ | $2^{33}\cdot 223\cdot 94616983\cdot 321748692401$ | $S_{11}\wr C_2$ (as 22T57) | trivial |
| 22.2.102...625.1 | $x^{22} - x^{21} - 11 x^{20} + 5 x^{19} + 71 x^{18} + 39 x^{17} - 241 x^{16} - 440 x^{15} + 36 x^{14} + 974 x^{13} + 1084 x^{12} - 1095 x^{11} - 6129 x^{10} - 12496 x^{9} - 16556 x^{8} - 15445 x^{7} - 9954 x^{6} - 3936 x^{5} - 451 x^{4} + 325 x^{3} + 155 x^{2} - 10 x - 5$ | $5^{16}\cdot 11^{20}$ | $C_{11}^2:C_4$ (as 22T8) | trivial |
| 22.2.145...953.1 | $x^{22} - 4 x^{21} + x^{20} + 6 x^{19} + 21 x^{18} - 27 x^{17} - 24 x^{16} - 255 x^{15} + 291 x^{14} + 226 x^{13} + 1112 x^{12} + 1378 x^{11} + 1776 x^{10} + 2229 x^{9} + 2715 x^{8} + 2358 x^{7} + 1791 x^{6} + 360 x^{5} - 828 x^{4} - 9 x^{3} + 405 x^{2} + 117 x - 72$ | $3^{20}\cdot 11^{19}\cdot 683$ | $C_2\times C_2^{10}.F_{11}$ (as 22T37) | trivial |
| 22.2.499...288.1 | $x^{22} - 8 x^{21} + 23 x^{20} - 8 x^{19} - 123 x^{18} + 364 x^{17} - 662 x^{16} + 1316 x^{15} - 2070 x^{14} + 1360 x^{13} - 62 x^{12} + 2204 x^{11} - 5167 x^{10} + 2080 x^{9} + 795 x^{8} + 8072 x^{7} - 22483 x^{6} + 26464 x^{5} - 17824 x^{4} + 7236 x^{3} - 1720 x^{2} + 224 x - 8$ | $2^{22}\cdot 3^{11}\cdot 11^{20}$ | $D_{11}^2$ (as 22T9) | trivial |
| 22.2.529...664.1 | $x^{22} + 5 x^{20} - 11 x^{18} - 34 x^{16} + 29 x^{14} + 127 x^{12} - 268 x^{10} + 239 x^{8} - 119 x^{6} + 29 x^{4} - 1$ | $2^{22}\cdot 1831^{8}$ | $C_2^{10}.\PSL(2,11)$ (as 22T39) | trivial |
| 22.2.529...664.2 | $x^{22} - 3 x^{20} - 5 x^{18} + 58 x^{16} - 141 x^{14} + 140 x^{12} - 16 x^{10} - 89 x^{8} + 13 x^{6} + 49 x^{4} + 21 x^{2} - 1$ | $2^{22}\cdot 1831^{8}$ | $C_2^{10}.\PSL(2,11)$ (as 22T39) | trivial |
| 22.2.529...664.3 | $x^{22} - 4 x^{20} + 11 x^{18} - 18 x^{16} + 10 x^{14} + 17 x^{12} - 25 x^{10} + 26 x^{8} - 4 x^{6} - 16 x^{4} + 4 x^{2} - 9$ | $2^{22}\cdot 1831^{8}$ | $C_2^{10}.\PSL(2,11)$ (as 22T39) | trivial |
| 22.2.124...336.1 | $x^{22} + 11 x^{20} + 55 x^{18} + 154 x^{16} + 253 x^{14} + 253 x^{12} + 209 x^{10} + 187 x^{8} + 77 x^{6} + 33 x^{2} - 4$ | $2^{20}\cdot 11^{26}$ | $C_2^{10}.F_{11}$ (as 22T34) | trivial |
| 22.2.124...336.2 | $x^{22} - 44 x^{16} - 11 x^{14} - 88 x^{12} + 264 x^{10} - 275 x^{8} + 154 x^{6} - 55 x^{4} + 11 x^{2} - 1$ | $2^{20}\cdot 11^{26}$ | $C_2^{10}.F_{11}$ (as 22T34) | trivial |
| 22.2.124...336.3 | $x^{22} + 22 x^{18} - 22 x^{16} - 22 x^{14} + 44 x^{12} + 55 x^{10} + 11 x^{8} + 11 x^{6} - 11 x^{2} - 4$ | $2^{20}\cdot 11^{26}$ | $C_2^{10}.F_{11}$ (as 22T34) | trivial |
| 22.2.124...336.4 | $x^{22} + 22 x^{18} + 22 x^{16} + 132 x^{14} + 253 x^{12} - 44 x^{10} - 286 x^{8} - 165 x^{6} - 55 x^{4} - 11 x^{2} - 1$ | $2^{20}\cdot 11^{26}$ | $C_2^{10}.F_{11}$ (as 22T34) | trivial |
| 22.2.158...992.1 | $x^{22} + 9 x^{20} + 36 x^{18} + 79 x^{16} + 99 x^{14} + 68 x^{12} + 24 x^{10} + 3 x^{8} - 9 x^{6} - 15 x^{4} - 11 x^{2} - 3$ | $2^{22}\cdot 3\cdot 1831^{8}$ | $C_2^{11}.\PSL(2,11)$ (as 22T42) | trivial |
| 22.2.158...992.2 | $x^{22} + 13 x^{20} + 78 x^{18} + 280 x^{16} + 657 x^{14} + 1027 x^{12} + 1021 x^{10} + 513 x^{8} - 88 x^{6} - 299 x^{4} - 163 x^{2} - 27$ | $2^{22}\cdot 3\cdot 1831^{8}$ | $C_2^{11}.\PSL(2,11)$ (as 22T42) | trivial |
| 22.2.719...104.1 | $x^{22} + 24 x^{20} + 220 x^{18} + 980 x^{16} + 2267 x^{14} + 2696 x^{12} + 1324 x^{10} - 265 x^{8} - 563 x^{6} - 215 x^{4} - 29 x^{2} - 1$ | $2^{22}\cdot 23^{20}$ | $C_2^{10}:C_{11}$ (as 22T23) | trivial |
| 22.2.245...305.1 | $x^{22} - 4 x - 1$ | $5\cdot 549569\cdot 7345029585473\cdot 1214169483036053$ | $S_{22}$ (as 22T59) | trivial |
| 22.2.245...568.1 | $x^{22} - 2 x - 1$ | $2^{23}\cdot 19\cdot 37\cdot 68639\cdot 132989\cdot 10028509\cdot 45394463$ | $S_{22}$ (as 22T59) | trivial |
| 22.2.344...000.1 | $x^{22} - 22 x^{11} - 4$ | $2^{20}\cdot 5^{11}\cdot 11^{20}$ | $D_{11}:F_{11}$ (as 22T15) | trivial |
| 22.2.699...264.1 | $x^{22} + 16 x^{20} + 103 x^{18} + 331 x^{16} + 485 x^{14} - 75 x^{12} - 1440 x^{10} - 2340 x^{8} - 1825 x^{6} - 744 x^{4} - 144 x^{2} - 9$ | $2^{22}\cdot 3^{6}\cdot 4784137656827^{2}$ | $C_2^{10}.S_{11}$ (as 22T51) | trivial |
| 22.2.165...392.1 | $x^{22} + 23 x^{20} + 207 x^{18} + 897 x^{16} + 1679 x^{14} - 483 x^{12} - 7636 x^{10} - 13041 x^{8} - 9660 x^{6} - 3312 x^{4} - 483 x^{2} - 23$ | $2^{22}\cdot 23^{21}$ | $C_{15}\times C_{420}$ (as 22T28) | trivial |