Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (13 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 22.0.138...683.1 | $x^{22} - x^{21} + 116 x^{20} - 116 x^{19} + 5866 x^{18} - 5866 x^{17} + 169741 x^{16} - 169741 x^{15} + 3102241 x^{14} - 3102241 x^{13} + 37314741 x^{12} - 37314741 x^{11} + 298939741 x^{10} - 298939741 x^{9} + 1583705366 x^{8} - 1583705366 x^{7} + 5438002241 x^{6} - 5438002241 x^{5} + 11861830366 x^{4} - 11861830366 x^{3} + 16803236616 x^{2} - 16803236616 x + 17926283491$ | $-\,3^{11}\cdot 7^{11}\cdot 23^{21}$ | $C_{22}$ (as 22T1) | $[2, 1433434]$ |
| 22.0.436...031.1 | $x^{22} - 9 x^{21} + 103 x^{20} - 633 x^{19} + 4455 x^{18} - 21547 x^{17} + 115721 x^{16} - 463428 x^{15} + 2047836 x^{14} - 6940762 x^{13} + 26133577 x^{12} - 75415028 x^{11} + 246269894 x^{10} - 601120919 x^{9} + 1716577617 x^{8} - 3469345651 x^{7} + 8681282523 x^{6} - 13884271574 x^{5} + 30359360950 x^{4} - 34852602875 x^{3} + 66136100859 x^{2} - 41797446694 x + 68117781041$ | $-\,23^{20}\cdot 31^{11}$ | $C_{22}$ (as 22T1) | $[3128667]$ |
| 22.0.600...952.1 | $x^{22} + 138 x^{20} + 8280 x^{18} + 283176 x^{16} + 6080832 x^{14} + 85131648 x^{12} + 781208064 x^{10} + 4603547520 x^{8} + 16572771072 x^{6} + 33145542144 x^{4} + 30595885056 x^{2} + 8344332288$ | $-\,2^{33}\cdot 3^{11}\cdot 23^{21}$ | $C_{22}$ (as 22T1) | $[2, 3189916]$ |
| 22.0.165...875.1 | $x^{22} - 9 x^{21} + 114 x^{20} - 723 x^{19} + 5545 x^{18} - 27862 x^{17} + 161687 x^{16} - 673652 x^{15} + 3199234 x^{14} - 11272660 x^{13} + 45446261 x^{12} - 136089890 x^{11} + 474573050 x^{10} - 1198919315 x^{9} + 3649189205 x^{8} - 7608385175 x^{7} + 20266939465 x^{6} - 33305104255 x^{5} + 77468338075 x^{4} - 90946009745 x^{3} + 183517941560 x^{2} - 117944870669 x + 204320499769$ | $-\,5^{11}\cdot 7^{11}\cdot 23^{20}$ | $C_{22}$ (as 22T1) | $[6263182]$ |
| 22.0.948...211.1 | $x^{22} - 9 x^{21} + 8 x^{20} + 69 x^{19} + 341 x^{18} - 1536 x^{17} - 1667 x^{16} + 252 x^{15} + 45513 x^{14} + 12225 x^{13} + 72521 x^{12} - 276013 x^{11} + 757511 x^{10} + 840645 x^{9} + 11788951 x^{8} + 27209924 x^{7} + 94723994 x^{6} + 160917509 x^{5} + 349577039 x^{4} + 428625612 x^{3} + 683809164 x^{2} + 522560028 x + 589202287$ | $-\,11^{11}\cdot 67^{20}$ | $C_{22}$ (as 22T1) | $[23, 117139]$ |
| 22.0.191...064.1 | $x^{22} + 134 x^{20} + 6968 x^{18} + 181704 x^{16} + 2564224 x^{14} + 19630464 x^{12} + 77539904 x^{10} + 145088768 x^{8} + 131212800 x^{6} + 54371840 x^{4} + 8027136 x^{2} + 137216$ | $-\,2^{33}\cdot 67^{21}$ | $C_{22}$ (as 22T1) | $[1397102]$ |
| 22.0.192...343.1 | $x^{22} - 9 x^{21} - 23 x^{20} + 427 x^{19} - 333 x^{18} - 8101 x^{17} + 19825 x^{16} + 54452 x^{15} - 199899 x^{14} - 268055 x^{13} + 1619754 x^{12} - 923591 x^{11} - 3715861 x^{10} + 3187790 x^{9} + 19675195 x^{8} - 56103742 x^{7} + 59561975 x^{6} - 21663766 x^{5} + 150503099 x^{4} - 437293737 x^{3} + 963528183 x^{2} - 867599298 x + 639704333$ | $-\,7^{11}\cdot 89^{20}$ | $C_{22}$ (as 22T1) | $[1084931]$ |
| 22.0.206...560.1 | $x^{22} + 44 x^{20} + 858 x^{18} + 9768 x^{16} + 71984 x^{14} + 359744 x^{12} + 1241240 x^{10} + 2950112 x^{8} + 4723312 x^{6} + 4842816 x^{4} + 2857888 x^{2} + 734760$ | $-\,2^{43}\cdot 5\cdot 7^{10}\cdot 11^{22}\cdot 13\cdot 157$ | $C_2\times C_2^{10}.F_{11}$ (as 22T37) | $[2, 2, 499520]$ |
| 22.0.835...992.1 | $x^{22} - 2 x^{21} - 57 x^{20} + 78 x^{19} + 1486 x^{18} - 1192 x^{17} - 19345 x^{16} + 8722 x^{15} + 166656 x^{14} - 5440 x^{13} - 680544 x^{12} - 318952 x^{11} + 1977573 x^{10} + 2955478 x^{9} + 10118056 x^{8} - 4737470 x^{7} + 447202 x^{6} + 4776110 x^{5} + 248446153 x^{4} + 188456410 x^{3} + 890303175 x^{2} + 263009438 x + 762593971$ | $-\,2^{33}\cdot 89^{20}$ | $C_{22}$ (as 22T1) | $[1293259]$ |
| 22.0.171...527.1 | $x^{22} - x^{21} + 136 x^{20} - 141 x^{19} + 6933 x^{18} - 11219 x^{17} + 176727 x^{16} - 447777 x^{15} + 2849200 x^{14} - 9627703 x^{13} + 31913346 x^{12} - 114648803 x^{11} + 293038974 x^{10} - 732575214 x^{9} + 2085803018 x^{8} - 3042652387 x^{7} + 8079316286 x^{6} - 13226651538 x^{5} + 17433518072 x^{4} - 19326356701 x^{3} + 19500553636 x^{2} - 6880449063 x + 7438698677$ | $-\,7^{11}\cdot 89^{21}$ | $C_{22}$ (as 22T1) | $[6596678]$ |
| 22.0.168...147.1 | $x^{22} - x^{21} + 91 x^{20} - 140 x^{19} + 5866 x^{18} - 6595 x^{17} + 171038 x^{16} + 105438 x^{15} + 3197216 x^{14} + 5217907 x^{13} + 46857656 x^{12} + 117294960 x^{11} + 496574452 x^{10} + 1287274232 x^{9} + 4044314069 x^{8} + 9224730377 x^{7} + 18936907588 x^{6} + 27784386063 x^{5} + 32870636944 x^{4} + 26173775028 x^{3} + 15505412182 x^{2} + 4564257710 x + 939238609$ | $-\,3^{11}\cdot 199^{20}$ | $C_{22}$ (as 22T1) | $[3608231]$ |
| 22.0.397...304.1 | $x^{22} + 181 x^{20} + 13028 x^{18} + 490585 x^{16} + 10635319 x^{14} + 137334967 x^{12} + 1056115843 x^{10} + 4729178714 x^{8} + 11925395238 x^{6} + 15697884460 x^{4} + 8830679464 x^{2} + 939238609$ | $-\,2^{22}\cdot 199^{20}$ | $C_{22}$ (as 22T1) | $[2097569]$ |
| 22.0.116...819.1 | $x^{22} - x^{21} + 10 x^{20} - 130 x^{19} + 1885 x^{18} - 3051 x^{17} + 19486 x^{16} - 173956 x^{15} + 1407458 x^{14} - 2060852 x^{13} - 21380891 x^{12} + 232972284 x^{11} - 992590046 x^{10} + 2186797028 x^{9} + 1727107332 x^{8} - 33713397579 x^{7} + 156515778679 x^{6} - 463698132550 x^{5} + 1062844895210 x^{4} - 1843489099333 x^{3} + 2553256282724 x^{2} - 2451856901550 x + 1515754471721$ | $-\,419^{21}$ | $C_{22}$ (as 22T1) | $[5829723]$ |