Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 16.0.105...889.2 | $x^{16} - 3 x^{15} + 34 x^{14} - 31 x^{13} + 473 x^{12} + 101 x^{11} + 3660 x^{10} + 2113 x^{9} + 15141 x^{8} + 6850 x^{7} + 32800 x^{6} + 14640 x^{5} + 41808 x^{4} + 19840 x^{3} + 26112 x^{2} + 9216 x + 4096$ | $17^{14}\cdot 89^{4}$ | $C_2^2 : C_8$ (as 16T24) | $[140]$ |
| 16.0.106...816.2 | $x^{16} + 24 x^{14} + 276 x^{12} + 1776 x^{10} + 6881 x^{8} + 15072 x^{6} + 16704 x^{4} + 3072 x^{2} + 256$ | $2^{48}\cdot 3^{8}\cdot 7^{8}$ | $C_4\times C_2^2$ (as 16T2) | $[4, 4, 8]$ |
| 16.0.114...441.1 | $x^{16} - 2 x^{15} - 2 x^{14} + 4 x^{13} + 59 x^{12} - 72 x^{11} - 18 x^{10} - 59 x^{9} + 1164 x^{8} - 538 x^{7} + 1415 x^{6} - 1654 x^{5} + 8638 x^{4} - 979 x^{3} + 18540 x^{2} + 6613 x + 35029$ | $3^{4}\cdot 7^{8}\cdot 89^{2}\cdot 1327^{4}$ | $C_2^5:S_4$ (as 16T1045) | $[3, 39]$ |
| 16.0.120...000.1 | $x^{16} + 33 x^{14} + 422 x^{12} + 2723 x^{10} + 9543 x^{8} + 18119 x^{6} + 17608 x^{4} + 7531 x^{2} + 941$ | $2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941$ | $C_2\wr D_4$ (as 16T1461) | $[2, 76]$ |
| 16.0.122...625.1 | $x^{16} - 6 x^{15} + 27 x^{14} - 92 x^{13} + 309 x^{12} - 824 x^{11} + 2046 x^{10} - 4678 x^{9} + 10025 x^{8} - 16676 x^{7} + 32508 x^{6} - 37970 x^{5} + 63804 x^{4} - 45560 x^{3} + 68140 x^{2} - 20900 x + 28775$ | $5^{8}\cdot 29^{8}\cdot 89^{4}$ | $C_2\wr C_2^2$ (as 16T150) | $[182]$ |
| 16.0.127...000.1 | $x^{16} - 8 x^{15} + 62 x^{14} - 294 x^{13} + 1232 x^{12} - 3774 x^{11} + 10008 x^{10} - 19892 x^{9} + 34425 x^{8} - 44976 x^{7} + 56189 x^{6} - 53874 x^{5} + 61418 x^{4} - 48694 x^{3} + 51225 x^{2} - 22708 x + 13921$ | $2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2}\cdot 181^{2}$ | $C_2^6:(C_2\times C_4)$ (as 16T797) | $[2, 2, 40]$ |
| 16.0.134...000.1 | $x^{16} + 37 x^{14} + 427 x^{12} + 2397 x^{10} + 7503 x^{8} + 13536 x^{6} + 13518 x^{4} + 6409 x^{2} + 841$ | $2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{2}$ | $C_2\wr D_4$ (as 16T1445) | $[152]$ |
| 16.0.135...976.6 | $x^{16} - 8 x^{15} + 24 x^{14} - 20 x^{13} - 22 x^{12} - 92 x^{11} + 932 x^{10} - 3152 x^{9} + 7935 x^{8} - 16684 x^{7} + 31292 x^{6} - 47960 x^{5} + 66166 x^{4} - 73676 x^{3} + 76948 x^{2} - 54308 x + 37993$ | $2^{32}\cdot 3^{8}\cdot 7^{8}\cdot 17^{4}$ | $C_2^2 \times D_4$ (as 16T25) | $[2, 4, 4, 4]$ |
| 16.0.135...576.1 | $x^{16} - 8 x^{15} + 44 x^{14} - 168 x^{13} + 587 x^{12} - 1702 x^{11} + 4239 x^{10} - 8644 x^{9} + 15457 x^{8} - 23538 x^{7} + 30978 x^{6} - 33521 x^{5} + 31435 x^{4} - 23817 x^{3} + 13277 x^{2} - 4620 x + 6466$ | $2^{4}\cdot 43^{2}\cdot 2777^{6}$ | $C_2^7.S_4$ (as 16T1537) | $[2, 90]$ |
| 16.0.138...625.1 | $x^{16} - 4 x^{15} + 45 x^{14} - 160 x^{13} + 846 x^{12} - 2460 x^{11} + 8219 x^{10} - 18505 x^{9} + 42209 x^{8} - 70521 x^{7} + 109939 x^{6} - 126586 x^{5} + 122135 x^{4} - 81341 x^{3} + 42543 x^{2} - 26360 x + 15151$ | $5^{10}\cdot 29^{8}\cdot 41^{4}$ | $C_4^2:C_2^2$ (as 16T175) | $[2, 52]$ |
| 16.0.150...000.1 | $x^{16} + 23 x^{14} + 216 x^{12} + 1089 x^{10} + 3243 x^{8} + 5873 x^{6} + 6349 x^{4} + 3764 x^{2} + 941$ | $2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3}$ | $C_4\wr D_4$ (as 16T1432) | $[130]$ |
| 16.0.156...625.1 | $x^{16} - 4 x^{15} + 62 x^{14} - 162 x^{13} + 1357 x^{12} - 2204 x^{11} + 13752 x^{10} - 12451 x^{9} + 72905 x^{8} - 32084 x^{7} + 221779 x^{6} - 14352 x^{5} + 393392 x^{4} + 80477 x^{3} + 366837 x^{2} + 106495 x + 130321$ | $3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61^{4}$ | $D_4^2:C_4$ (as 16T542) | $[2, 4, 16]$ |
| 16.0.187...000.1 | $x^{16} + 27 x^{14} + 293 x^{12} + 1661 x^{10} + 5333 x^{8} + 9812 x^{6} + 9932 x^{4} + 4901 x^{2} + 841$ | $2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 1109^{2}$ | $C_2\wr D_4$ (as 16T1445) | $[136]$ |
| 16.0.190...000.8 | $x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 217 x^{12} - 364 x^{11} + 992 x^{10} - 1496 x^{9} + 3255 x^{8} - 64 x^{7} + 3914 x^{6} + 14828 x^{5} + 30557 x^{4} - 2068 x^{3} + 18942 x^{2} - 33280 x + 53551$ | $2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}$ | $C_2 \times (C_2^2:C_4)$ (as 16T21) | $[6, 24]$ |
| 16.0.198...736.1 | $x^{16} + 22 x^{14} + 206 x^{12} + 1112 x^{10} + 4217 x^{8} + 12912 x^{6} + 29016 x^{4} + 31136 x^{2} + 13456$ | $2^{32}\cdot 389^{4}\cdot 449^{2}$ | $C_2^5:S_4$ (as 16T1045) | $[2, 56]$ |
| 16.0.209...488.1 | $x^{16} - 3 x^{15} + 26 x^{14} - 61 x^{13} + 302 x^{12} - 481 x^{11} + 1800 x^{10} - 1694 x^{9} + 6221 x^{8} - 1408 x^{7} + 12724 x^{6} + 4447 x^{5} + 29261 x^{4} + 14047 x^{3} + 63157 x^{2} + 36221 x + 38659$ | $2^{8}\cdot 13^{4}\cdot 17^{15}$ | $\OD_{32}:C_2$ (as 16T104) | $[2, 2, 50]$ |
| 16.0.225...000.9 | $x^{16} - 8 x^{15} + 38 x^{14} - 126 x^{13} + 392 x^{12} - 1078 x^{11} + 2868 x^{10} - 6508 x^{9} + 14535 x^{8} - 27518 x^{7} + 52626 x^{6} - 80626 x^{5} + 131167 x^{4} - 151166 x^{3} + 199323 x^{2} - 133920 x + 139681$ | $2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 11^{8}$ | $C_4\times C_2^2$ (as 16T2) | $[2, 4, 4, 8]$ |
| 16.0.225...433.1 | $x^{16} - x^{15} + 35 x^{14} - 52 x^{13} + 426 x^{12} - 834 x^{11} + 2908 x^{10} - 5441 x^{9} + 12734 x^{8} - 20894 x^{7} + 36823 x^{6} - 49114 x^{5} + 65638 x^{4} - 66318 x^{3} + 63428 x^{2} - 39339 x + 19211$ | $17^{15}\cdot 53^{4}$ | $C_{16} : C_2$ (as 16T22) | $[9, 18]$ |
| 16.0.239...000.1 | $x^{16} + 32 x^{14} + 390 x^{12} + 2472 x^{10} + 9054 x^{8} + 19658 x^{6} + 24455 x^{4} + 15458 x^{2} + 3481$ | $2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2}$ | $C_2^7:(C_2\times C_4)$ (as 16T1102) | $[2, 122]$ |
| 16.0.239...000.2 | $x^{16} + 36 x^{14} + 527 x^{12} + 4038 x^{10} + 17390 x^{8} + 42102 x^{6} + 53962 x^{4} + 30444 x^{2} + 3481$ | $2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2}$ | $C_2^7:(C_2\times C_4)$ (as 16T1102) | $[2, 106]$ |
| 16.0.239...000.3 | $x^{16} + 32 x^{14} + 418 x^{12} + 2884 x^{10} + 11340 x^{8} + 25514 x^{6} + 31183 x^{4} + 18172 x^{2} + 3481$ | $2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2}$ | $C_2^4.C_2^4$ (as 16T464) | $[2, 112]$ |
| 16.0.246...000.1 | $x^{16} + 24 x^{14} + 234 x^{12} + 1217 x^{10} + 3710 x^{8} + 6827 x^{6} + 7451 x^{4} + 4436 x^{2} + 1109$ | $2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3}$ | $C_4\wr D_4$ (as 16T1432) | $[146]$ |
| 16.0.246...000.2 | $x^{16} + 35 x^{14} + 391 x^{12} + 2107 x^{10} + 6265 x^{8} + 10736 x^{6} + 10474 x^{4} + 5361 x^{2} + 1109$ | $2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3}$ | $C_2^2.C_2\wr D_4$ (as 16T1741) | $[186]$ |
| 16.0.250...184.1 | $x^{16} + 17 x^{14} + 104 x^{12} + 291 x^{10} + 407 x^{8} + 291 x^{6} + 104 x^{4} + 17 x^{2} + 1$ | $2^{16}\cdot 3^{8}\cdot 137^{2}\cdot 1327^{4}$ | $C_2^5:S_4$ (as 16T1045) | $[6, 18]$ |
| 16.0.252...000.1 | $x^{16} + 35 x^{14} + 475 x^{12} + 3225 x^{10} + 11775 x^{8} + 22875 x^{6} + 21250 x^{4} + 6875 x^{2} + 625$ | $2^{12}\cdot 3^{12}\cdot 5^{12}\cdot 83^{4}$ | $C_2^4:S_4$ (as 16T747) | $[2, 2, 30]$ |
| 16.0.260...625.4 | $x^{16} - 2 x^{15} - 10 x^{14} + 129 x^{12} + 128 x^{11} - 262 x^{10} - 1405 x^{9} - 604 x^{8} + 2918 x^{7} + 16953 x^{6} + 35934 x^{5} + 72154 x^{4} + 89871 x^{3} + 113604 x^{2} + 78021 x + 62631$ | $3^{8}\cdot 5^{12}\cdot 7^{8}\cdot 41^{4}$ | $C_2 \times (C_2^2:C_4)$ (as 16T21) | $[2, 84]$ |
| 16.0.260...625.5 | $x^{16} - 2 x^{15} - 14 x^{14} + 22 x^{13} + 115 x^{12} - 212 x^{11} + 158 x^{10} + 941 x^{9} + 1308 x^{8} - 2306 x^{7} + 9713 x^{6} - 536 x^{5} + 13484 x^{4} - 5339 x^{3} + 55722 x^{2} - 49691 x + 74281$ | $3^{8}\cdot 5^{12}\cdot 7^{8}\cdot 41^{4}$ | $C_2 \times (C_2^2:C_4)$ (as 16T21) | $[2, 84]$ |
| 16.0.260...625.10 | $x^{16} - 2 x^{15} - 6 x^{14} - 46 x^{13} + 27 x^{12} + 428 x^{11} + 3903 x^{10} + 879 x^{9} - 37189 x^{8} - 75054 x^{7} + 2008 x^{6} - 571448 x^{5} + 4969552 x^{4} + 8915296 x^{3} - 26589056 x^{2} + 34339712 x + 181063936$ | $3^{8}\cdot 5^{12}\cdot 7^{8}\cdot 41^{4}$ | $C_2 \times (C_2^2:C_4)$ (as 16T21) | $[2, 84]$ |
| 16.0.263...000.1 | $x^{16} + 20 x^{14} + 167 x^{12} + 755 x^{10} + 2004 x^{8} + 3165 x^{6} + 2868 x^{4} + 1340 x^{2} + 241$ | $2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 241\cdot 1021^{2}$ | $C_4^4.C_2\wr C_4$ (as 16T1771) | $[2, 52]$ |
| 16.0.265...104.1 | $x^{16} + 24 x^{14} + 276 x^{12} + 1776 x^{10} + 6850 x^{8} + 14784 x^{6} + 17024 x^{4} + 6144 x^{2} + 1024$ | $2^{62}\cdot 7^{8}$ | $C_8\times C_2$ (as 16T5) | $[136]$ |
| 16.0.317...112.1 | $x^{16} + 34 x^{14} + 425 x^{12} + 2584 x^{10} + 8670 x^{8} + 16898 x^{6} + 19040 x^{4} + 11492 x^{2} + 2873$ | $2^{16}\cdot 13^{2}\cdot 17^{15}$ | $C_2^4.C_8$ (as 16T306) | $[2, 2, 50]$ |
| 16.0.331...376.2 | $x^{16} + 27 x^{14} + 295 x^{12} + 1688 x^{10} + 5432 x^{8} + 9729 x^{6} + 8855 x^{4} + 3249 x^{2} + 361$ | $2^{16}\cdot 3^{2}\cdot 19^{6}\cdot 103^{6}$ | $C_{2440}.D_6$ (as 16T1757) | $[196]$ |
| 16.0.333...456.1 | $x^{16} - 2 x^{14} - 2 x^{13} + 57 x^{12} + 12 x^{11} + 171 x^{10} + 128 x^{9} + 1436 x^{8} + 684 x^{7} + 5805 x^{6} + 1084 x^{5} + 18353 x^{4} + 1488 x^{3} + 40675 x^{2} + 2430 x + 42947$ | $2^{24}\cdot 3^{4}\cdot 89^{2}\cdot 1327^{4}$ | $C_2^5:S_4$ (as 16T1045) | $[140]$ |
| 16.0.344...000.1 | $x^{16} - 2 x^{15} + 21 x^{14} - 6 x^{13} + 262 x^{12} - 136 x^{11} + 1281 x^{10} - 660 x^{9} + 4473 x^{8} - 2484 x^{7} + 7293 x^{6} - 1864 x^{5} + 6700 x^{4} - 2094 x^{3} + 2571 x^{2} + 322 x + 49$ | $2^{24}\cdot 3^{8}\cdot 5^{4}\cdot 29^{8}$ | $C_2^2 \times D_4$ (as 16T25) | $[3, 3, 12]$ |
| 16.0.350...000.1 | $x^{16} - 4 x^{15} + 34 x^{14} - 64 x^{13} + 539 x^{12} - 1000 x^{11} + 4842 x^{10} - 4648 x^{9} + 19562 x^{8} - 22604 x^{7} + 45816 x^{6} - 21740 x^{5} + 19433 x^{4} + 3616 x^{3} + 4684 x^{2} - 68 x + 1$ | $2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8}$ | $C_2^4$ (as 16T3) | $[4, 8, 8]$ |
| 16.0.352...976.14 | $x^{16} - 8 x^{15} + 32 x^{14} - 74 x^{13} + 88 x^{12} + 52 x^{11} - 494 x^{10} + 1356 x^{9} - 2844 x^{8} + 5424 x^{7} - 7904 x^{6} + 3328 x^{5} + 22528 x^{4} - 75776 x^{3} + 131072 x^{2} - 131072 x + 65536$ | $2^{20}\cdot 3^{8}\cdot 8461^{4}$ | $C_2^4:S_4$ (as 16T747) | $[2, 60]$ |
| 16.0.352...000.1 | $x^{16} + 34 x^{14} + 443 x^{12} + 2832 x^{10} + 9661 x^{8} + 18056 x^{6} + 17887 x^{4} + 8278 x^{2} + 1249$ | $2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1249^{3}$ | $D_8\wr C_2$ (as 16T972) | $[2, 92]$ |
| 16.0.356...264.2 | $x^{16} + 18 x^{14} + 129 x^{12} + 478 x^{10} + 990 x^{8} + 1154 x^{6} + 726 x^{4} + 223 x^{2} + 25$ | $2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4}$ | $C_2^7.A_8$ (as 16T1938) | $[2, 60]$ |
| 16.0.360...449.1 | $x^{16} - 6 x^{15} + 24 x^{14} - 68 x^{13} + 229 x^{12} - 610 x^{11} + 1652 x^{10} - 3427 x^{9} + 8268 x^{8} - 14574 x^{7} + 31149 x^{6} - 43150 x^{5} + 84686 x^{4} - 84235 x^{3} + 155680 x^{2} - 83057 x + 153851$ | $11^{8}\cdot 17^{14}$ | $C_8\times C_2$ (as 16T5) | $[17, 17]$ |
| 16.0.366...776.2 | $x^{16} + 30 x^{14} + 301 x^{12} + 1164 x^{10} + 1698 x^{8} + 1062 x^{6} + 304 x^{4} + 36 x^{2} + 1$ | $2^{16}\cdot 3^{12}\cdot 241^{2}\cdot 367^{4}$ | $C_2^5:S_4$ (as 16T1045) | $[2, 56]$ |
| 16.0.373...625.1 | $x^{16} - x^{15} + 22 x^{14} - 15 x^{13} + 370 x^{12} - 219 x^{11} + 1996 x^{10} + 855 x^{9} + 6474 x^{8} + 2315 x^{7} + 9134 x^{6} + 8383 x^{5} + 7555 x^{4} + 3230 x^{3} + 1088 x^{2} + 152 x + 16$ | $3^{8}\cdot 5^{12}\cdot 13^{12}$ | $C_4\times C_2^2$ (as 16T2) | $[2, 104]$ |
| 16.0.396...000.1 | $x^{16} - 8 x^{15} + 20 x^{14} - 34 x^{12} - 160 x^{11} + 988 x^{10} - 2520 x^{9} + 6291 x^{8} - 13520 x^{7} + 25876 x^{6} - 37312 x^{5} + 55602 x^{4} - 61552 x^{3} + 73496 x^{2} - 47168 x + 55036$ | $2^{44}\cdot 5^{8}\cdot 7^{8}$ | $C_4\times C_2^2$ (as 16T2) | $[2, 8, 8]$ |
| 16.0.411...625.1 | $x^{16} - x^{15} + 12 x^{14} - 17 x^{13} + 2 x^{12} - 75 x^{11} - 142 x^{10} - 399 x^{9} + 470 x^{8} - 121 x^{7} + 3168 x^{6} + 5225 x^{5} + 8927 x^{4} + 11662 x^{3} + 12432 x^{2} + 7816 x + 4336$ | $5^{12}\cdot 17^{14}$ | $C_8\times C_2$ (as 16T5) | $[146]$ |
| 16.0.421...000.1 | $x^{16} - 2 x^{15} + 18 x^{14} - 12 x^{13} + 190 x^{12} - 142 x^{11} + 882 x^{10} - 288 x^{9} + 2502 x^{8} - 864 x^{7} + 3414 x^{6} + 770 x^{5} + 1501 x^{4} + 18 x^{3} + 240 x^{2} + 40 x + 16$ | $2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 19^{4}\cdot 149^{4}$ | $C_2^2\times S_4$ (as 16T182) | $[138]$ |
| 16.0.425...000.1 | $x^{16} - 2 x^{15} + 18 x^{14} - 24 x^{13} + 211 x^{12} - 274 x^{11} + 1026 x^{10} - 576 x^{9} + 2376 x^{8} - 1272 x^{7} + 3414 x^{6} - 982 x^{5} + 2611 x^{4} - 768 x^{3} + 1182 x^{2} + 34 x + 1$ | $2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 2837^{4}$ | $C_2^2\times S_4$ (as 16T182) | $[2, 60]$ |
| 16.0.441...928.1 | $x^{16} + 32 x^{14} + 392 x^{12} + 2352 x^{10} + 7418 x^{8} + 12240 x^{6} + 9800 x^{4} + 3136 x^{2} + 337$ | $2^{60}\cdot 337^{3}$ | $C_2^4.C_2\wr C_4$ (as 16T1251) | $[5, 30]$ |
| 16.0.441...928.2 | $x^{16} + 28 x^{14} + 322 x^{12} + 1968 x^{10} + 6901 x^{8} + 13920 x^{6} + 15086 x^{4} + 7020 x^{2} + 337$ | $2^{60}\cdot 337^{3}$ | $C_2^4.C_2\wr C_4$ (as 16T1251) | $[5, 30]$ |
| 16.0.480...288.1 | $x^{16} + 34 x^{14} + 476 x^{12} + 3536 x^{10} + 14960 x^{8} + 35904 x^{6} + 45696 x^{4} + 26112 x^{2} + 4352$ | $2^{24}\cdot 17^{15}$ | $C_{16}$ (as 16T1) | $[2, 194]$ |
| 16.0.494...000.1 | $x^{16} + 20 x^{14} + 164 x^{12} + 718 x^{10} + 1828 x^{8} + 2756 x^{6} + 2389 x^{4} + 1086 x^{2} + 199$ | $2^{40}\cdot 5^{8}\cdot 199\cdot 761^{2}$ | $C_4^4.C_2\wr C_2^2$ (as 16T1769) | $[126]$ |
| 16.0.495...616.1 | $x^{16} + 35 x^{14} + 486 x^{12} + 3428 x^{10} + 13207 x^{8} + 28366 x^{6} + 33276 x^{4} + 19631 x^{2} + 4489$ | $2^{16}\cdot 17^{14}\cdot 67^{2}$ | $C_2^7:C_8$ (as 16T1194) | $[2, 2, 78]$ |