Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
Results (12 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 22.0.489...811.1 | $x^{22} - 9 x^{21} + 48 x^{20} - 183 x^{19} + 655 x^{18} - 2122 x^{17} + 6491 x^{16} - 17468 x^{15} + 45646 x^{14} - 108112 x^{13} + 251537 x^{12} - 521318 x^{11} + 1081334 x^{10} - 1963079 x^{9} + 3653567 x^{8} - 5688311 x^{7} + 9483883 x^{6} - 12150619 x^{5} + 18112705 x^{4} - 17363285 x^{3} + 23145134 x^{2} - 12720749 x + 15354571$ | $-\,11^{11}\cdot 23^{20}$ | $C_{22}$ (as 22T1) | $[15499]$ |
| 22.0.148...375.1 | $x^{22} - 9 x^{21} + 59 x^{20} - 273 x^{19} + 1195 x^{18} - 4387 x^{17} + 15557 x^{16} - 47572 x^{15} + 143444 x^{14} - 378050 x^{13} + 996721 x^{12} - 2278940 x^{11} + 5312470 x^{10} - 10499975 x^{9} + 21744445 x^{8} - 36444035 x^{7} + 67020055 x^{6} - 91292990 x^{5} + 148564990 x^{4} - 149610555 x^{3} + 214516775 x^{2} - 122653854 x + 155003209$ | $-\,3^{11}\cdot 5^{11}\cdot 23^{20}$ | $C_{22}$ (as 22T1) | $[91498]$ |
| 22.0.497...411.1 | $x^{22} - 11 x^{19} + 33 x^{18} + 462 x^{17} + 583 x^{16} + 1023 x^{15} + 5214 x^{14} + 8239 x^{13} + 31647 x^{12} - 7140 x^{11} + 18271 x^{10} + 320529 x^{9} - 276177 x^{8} - 359084 x^{7} + 861894 x^{6} - 236907 x^{5} - 210870 x^{4} - 339471 x^{3} + 277992 x^{2} - 96228 x + 177147$ | $-\,11^{41}$ | $C_{22}$ (as 22T1) | $[23651]$ |
| 22.0.139...704.1 | $x^{22} + 61 x^{20} + 1466 x^{18} + 18767 x^{16} + 142812 x^{14} + 672568 x^{12} + 1953909 x^{10} + 3334358 x^{8} + 2944762 x^{6} + 969293 x^{4} + 57019 x^{2} + 841$ | $-\,2^{22}\cdot 67^{20}$ | $C_{22}$ (as 22T1) | $[36961]$ |
| 22.0.172...547.1 | $x^{22} - x^{21} + 41 x^{20} + 2 x^{19} + 1137 x^{18} + 120 x^{17} + 15187 x^{16} + 4521 x^{15} + 143572 x^{14} + 41908 x^{13} + 810728 x^{12} + 310631 x^{11} + 3278352 x^{10} + 1130011 x^{9} + 7018057 x^{8} + 3087160 x^{7} + 10139143 x^{6} + 2471155 x^{5} + 430399 x^{4} + 38213 x^{3} + 2468 x^{2} + 57 x + 1$ | $-\,3^{11}\cdot 89^{20}$ | $C_{22}$ (as 22T1) | $[26687]$ |
| 22.0.174...947.1 | $x^{22} + 20 x^{20} + 257 x^{18} - 4 x^{17} + 1934 x^{16} - 106 x^{15} + 10498 x^{14} - 1280 x^{13} + 38977 x^{12} - 9695 x^{11} + 107932 x^{10} - 38992 x^{9} + 209993 x^{8} - 108043 x^{7} + 304613 x^{6} - 168141 x^{5} + 295910 x^{4} - 171702 x^{3} + 186586 x^{2} - 69384 x + 31329$ | $-\,3^{11}\cdot 74843^{8}$ | $C_2\times \PSL(2,11)$ (as 22T13) | $[2, 2, 2, 3580]$ |
| 22.0.174...947.2 | $x^{22} - 4 x^{21} + 41 x^{20} - 62 x^{19} + 712 x^{18} - 691 x^{17} + 8218 x^{16} - 3289 x^{15} + 62044 x^{14} - 12972 x^{13} + 331973 x^{12} + 1202 x^{11} + 1201112 x^{10} + 23541 x^{9} + 2960817 x^{8} + 250587 x^{7} + 4248123 x^{6} - 781164 x^{5} + 3132885 x^{4} - 746848 x^{3} + 1635703 x^{2} - 490413 x + 335241$ | $-\,3^{11}\cdot 74843^{8}$ | $C_2\times \PSL(2,11)$ (as 22T13) | $[2, 2, 2, 3580]$ |
| 22.0.153...683.1 | $x^{22} - x^{21} + 47 x^{20} - 52 x^{19} + 792 x^{18} - 1785 x^{17} + 6826 x^{16} - 27519 x^{15} + 65725 x^{14} - 239894 x^{13} + 428795 x^{12} - 1132774 x^{11} + 3194187 x^{10} - 2353532 x^{9} + 12889600 x^{8} - 10825379 x^{7} + 17897782 x^{6} - 53427788 x^{5} + 50690086 x^{4} - 31652698 x^{3} + 43810715 x^{2} - 2705016 x + 8609149$ | $-\,3^{11}\cdot 89^{21}$ | $C_{22}$ (as 22T1) | $[51658]$ |
| 22.0.301...816.1 | $x^{22} + 66 x^{20} + 1815 x^{18} + 27225 x^{16} + 245025 x^{14} + 1367784 x^{12} + 4714281 x^{10} + 9653985 x^{8} + 10895445 x^{6} + 6145227 x^{4} + 1617165 x^{2} + 156816$ | $-\,2^{12}\cdot 3^{20}\cdot 11^{32}$ | $C_2^{10}.C_{11}:C_{10}$ (as 22T36) | $[2, 12506]$ |
| 22.0.801...947.1 | $x^{22} + 55 x^{20} - 66 x^{19} + 2200 x^{18} - 2211 x^{17} + 36520 x^{16} - 15048 x^{15} + 407473 x^{14} - 67485 x^{13} + 2823634 x^{12} + 317505 x^{11} + 14038057 x^{10} + 2608749 x^{9} + 46593316 x^{8} + 11785983 x^{7} + 109177024 x^{6} + 15287250 x^{5} + 140760675 x^{4} + 3952476 x^{3} + 120982653 x^{2} - 2670327 x + 59049$ | $-\,3^{11}\cdot 11^{40}$ | $C_{22}$ (as 22T1) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 178]$ |
| 22.0.528...000.2 | $x^{22} + 105 x^{20} + 4740 x^{18} + 120000 x^{16} + 1861425 x^{14} + 18118440 x^{12} + 108583200 x^{10} + 375108525 x^{8} + 650459700 x^{6} + 443168550 x^{4} + 84206925 x^{2} + 898425$ | $-\,2^{20}\cdot 3^{21}\cdot 5^{20}\cdot 11^{17}$ | $C_2^{10}.C_{11}:C_{10}$ (as 22T36) | $[2, 2, 21366]$ |
| 22.0.189...904.1 | $x^{22} + 110 x^{20} + 4675 x^{18} + 101783 x^{16} + 1279201 x^{14} + 9871136 x^{12} + 48063862 x^{10} + 147421505 x^{8} + 274663048 x^{6} + 281918538 x^{4} + 121207185 x^{2} + 59049$ | $-\,2^{22}\cdot 11^{40}$ | $C_{22}$ (as 22T1) | $[14411]$ |
| 22.0.243...375.1 | $x^{22} + 110 x^{20} - 22 x^{19} + 4895 x^{18} + 4026 x^{17} + 120120 x^{16} + 288222 x^{15} + 1882144 x^{14} + 6515520 x^{13} + 24762320 x^{12} + 60773360 x^{11} + 227012456 x^{10} + 397249116 x^{9} + 720148935 x^{8} + 1566072057 x^{7} + 1566926449 x^{6} + 1217292384 x^{5} + 714471362 x^{4} - 2592915589 x^{3} + 2027899907 x^{2} - 2522739483 x + 6490917711$ | $-\,5^{11}\cdot 11^{41}$ | $C_{22}$ (as 22T1) | $[88708]$ |