| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 22.2.124...336.1 |
$x^{22} + 11 x^{20} + 55 x^{18} + 154 x^{16} + 253 x^{14} + 253 x^{12} + 209 x^{10} + 187 x^{8} + 77 x^{6} + 33 x^{2} - 4$ |
$22$ |
[2,10] |
$2^{20}\cdot 11^{26}$ |
$2$ |
$31.944819765$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$11$ |
$264400573.794$ |
| 22.2.124...336.2 |
$x^{22} - 44 x^{16} - 11 x^{14} - 88 x^{12} + 264 x^{10} - 275 x^{8} + 154 x^{6} - 55 x^{4} + 11 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{20}\cdot 11^{26}$ |
$2$ |
$31.944819765$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$11$ |
$65776820.1374$ |
| 22.2.124...336.3 |
$x^{22} + 22 x^{18} - 22 x^{16} - 22 x^{14} + 44 x^{12} + 55 x^{10} + 11 x^{8} + 11 x^{6} - 11 x^{2} - 4$ |
$22$ |
[2,10] |
$2^{20}\cdot 11^{26}$ |
$2$ |
$31.94481976502052$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$11$ |
$106904434.64071207$ |
| 22.2.124...336.4 |
$x^{22} + 22 x^{18} + 22 x^{16} + 132 x^{14} + 253 x^{12} - 44 x^{10} - 286 x^{8} - 165 x^{6} - 55 x^{4} - 11 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{20}\cdot 11^{26}$ |
$2$ |
$31.94481976502052$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$11$ |
$189131827.4987893$ |
| 22.10.241...104.1 |
$x^{22} - 11 x^{20} + 33 x^{18} - 11 x^{16} - 22 x^{14} - 22 x^{12} - 80 x^{11} - 22 x^{10} - 22 x^{8} - 11 x^{6} + 33 x^{4} - 11 x^{2} + 1$ |
$22$ |
[10,6] |
$2^{20}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$50.0255405753$ |
$66.49824652345667$ |
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$636267844897$ |
| 22.10.385...664.1 |
$x^{22} - 132 x^{18} + 4400 x^{14} - 3696 x^{12} - 32384 x^{10} + 9152 x^{8} + 57728 x^{6} + 30976 x^{4} + 2816 x^{2} - 256$ |
$22$ |
[10,6] |
$2^{24}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$56.7445971042$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$549685991097$ |
| 22.14.385...664.1 |
$x^{22} - 220 x^{18} - 572 x^{16} + 6468 x^{14} - 880 x^{12} - 27676 x^{10} + 33396 x^{8} - 15136 x^{6} + 2904 x^{4} - 176 x^{2} - 4$ |
$22$ |
[14,4] |
$2^{24}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$56.7445971042$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$1551542190850$ |
| 22.14.154...656.1 |
$x^{22} - 33 x^{20} + 143 x^{18} - 22 x^{17} + 385 x^{16} - 2222 x^{15} - 902 x^{14} + 14586 x^{13} - 3234 x^{12} + 94 x^{11} - 39512 x^{10} - 28006 x^{9} + 136862 x^{8} - 99286 x^{7} - 30151 x^{6} + 136136 x^{5} - 99561 x^{4} - 13794 x^{3} + 44385 x^{2} - 17182 x + 2039$ |
$22$ |
[14,4] |
$2^{26}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$60.4353275196$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$4502089440930$ |
| 22.10.154...656.1 |
$x^{22} - 11 x^{20} - 253 x^{18} - 605 x^{16} + 3234 x^{14} + 9042 x^{12} - 462 x^{10} - 16918 x^{8} - 13475 x^{6} - 1859 x^{4} + 583 x^{2} - 25$ |
$22$ |
[10,6] |
$2^{26}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$60.4353275196$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$2239953990090$ |
| 22.10.154...656.2 |
$x^{22} + 33 x^{20} + 363 x^{18} + 1243 x^{16} - 2310 x^{14} - 14278 x^{12} + 9878 x^{10} + 25718 x^{8} - 7051 x^{6} - 363 x^{4} + 143 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{26}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$60.4353275196$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$720857418211$ |
| 22.10.617...624.1 |
$x^{22} - 88 x^{18} - 66 x^{17} - 616 x^{16} + 638 x^{15} + 44 x^{14} - 748 x^{13} + 5742 x^{12} - 11648 x^{11} + 23980 x^{10} + 49368 x^{9} - 145508 x^{8} - 89232 x^{7} + 242308 x^{6} + 64240 x^{5} - 174680 x^{4} + 21120 x^{3} + 76296 x^{2} - 33704 x - 27476$ |
$22$ |
[10,6] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$2473904084450$ |
| 22.14.617...624.1 |
$x^{22} - 33 x^{20} - 44 x^{19} + 253 x^{18} + 660 x^{17} + 1177 x^{16} + 2992 x^{15} - 2266 x^{14} - 27214 x^{13} - 75812 x^{12} - 258772 x^{11} - 808192 x^{10} - 1679018 x^{9} - 2491038 x^{8} - 3007114 x^{7} - 3012009 x^{6} - 2244528 x^{5} - 1081113 x^{4} - 281710 x^{3} - 22011 x^{2} + 4268 x + 561$ |
$22$ |
[14,4] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$10182928874900$ |
| 22.6.617...624.1 |
$x^{22} + 22 x^{20} - 44 x^{19} + 176 x^{18} - 242 x^{17} + 506 x^{16} - 726 x^{15} + 528 x^{14} - 5214 x^{13} + 3894 x^{12} + 316 x^{11} - 23716 x^{10} - 10472 x^{9} + 82962 x^{8} + 101090 x^{7} - 82456 x^{6} - 170368 x^{5} - 12100 x^{4} + 75504 x^{3} + 37510 x^{2} + 6776 x + 242$ |
$22$ |
[6,8] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$13$ |
$629593387255$ |
| 22.10.617...624.2 |
$x^{22} - 11 x^{20} - 165 x^{18} - 165 x^{16} + 1650 x^{14} + 3234 x^{12} - 1386 x^{10} - 5610 x^{8} - 1815 x^{6} + 1265 x^{4} + 495 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$3989928450040$ |
| 22.6.617...624.2 |
$x^{22} - 308 x^{18} - 3080 x^{16} - 7040 x^{14} + 42944 x^{12} + 292600 x^{10} + 659120 x^{8} + 536096 x^{6} - 125532 x^{4} - 335060 x^{2} - 70756$ |
$22$ |
[6,8] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$13$ |
$1003327194150$ |
| 22.10.617...624.3 |
$x^{22} - 11 x^{20} - 77 x^{18} + 1023 x^{16} + 242 x^{14} - 23474 x^{12} + 26906 x^{10} + 168850 x^{8} - 176627 x^{6} - 388443 x^{4} - 145761 x^{2} - 9409$ |
$22$ |
[10,6] |
$2^{28}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$64.3661070622$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$5990176821720$ |
| 22.10.246...496.1 |
$x^{22} - 132 x^{18} - 44 x^{16} + 5280 x^{14} + 3344 x^{12} - 61600 x^{10} - 57904 x^{8} + 6512 x^{6} + 6336 x^{4} - 880 x^{2} - 16$ |
$22$ |
[10,6] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$5708333064240$ |
| 22.6.246...496.1 |
$x^{22} - 22 x^{18} + 88 x^{16} - 484 x^{15} - 1232 x^{14} - 352 x^{13} - 8448 x^{12} - 11888 x^{11} + 8712 x^{10} - 54208 x^{9} + 42592 x^{8} + 256608 x^{7} - 547888 x^{6} - 399168 x^{5} + 878944 x^{4} - 1636800 x^{3} - 2798048 x^{2} + 297088 x + 734816$ |
$22$ |
[6,8] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$13$ |
$1781125148300$ |
| 22.14.246...496.1 |
$x^{22} - 11 x^{20} - 55 x^{18} - 154 x^{17} + 517 x^{16} + 1628 x^{15} + 3058 x^{14} + 2332 x^{13} - 6160 x^{12} - 33934 x^{11} - 105996 x^{10} - 79684 x^{9} + 136972 x^{8} + 243364 x^{7} + 221111 x^{6} + 106920 x^{5} - 143297 x^{4} - 191466 x^{3} - 62843 x^{2} - 5258 x + 245$ |
$22$ |
[14,4] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$15569759718900$ |
| 22.14.246...496.2 |
$x^{22} - 44 x^{20} - 22 x^{19} + 660 x^{18} + 704 x^{17} - 4048 x^{16} - 8448 x^{15} + 10516 x^{14} + 48312 x^{13} - 15180 x^{12} - 118720 x^{11} + 17776 x^{10} + 67408 x^{9} + 84392 x^{8} + 3696 x^{7} - 151976 x^{6} - 9328 x^{5} + 131648 x^{4} + 71104 x^{3} + 8976 x^{2} - 704 x - 48$ |
$22$ |
[14,4] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$16857324277000$ |
| 22.10.246...496.2 |
$x^{22} + 33 x^{20} + 275 x^{18} - 341 x^{16} - 7062 x^{14} - 1430 x^{12} + 44902 x^{10} + 9878 x^{8} - 41371 x^{6} + 10373 x^{4} + 1463 x^{2} - 81$ |
$22$ |
[10,6] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$6858150642190$ |
| 22.10.246...496.3 |
$x^{22} - 11 x^{20} - 165 x^{18} + 1683 x^{16} + 8118 x^{14} - 63734 x^{12} - 113718 x^{10} + 74822 x^{8} + 126665 x^{6} - 20383 x^{4} - 18293 x^{2} - 1369$ |
$22$ |
[10,6] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$9881793618560$ |
| 22.14.246...496.3 |
$x^{22} - 11 x^{20} - 44 x^{19} - 33 x^{18} + 748 x^{17} + 869 x^{16} - 3630 x^{15} - 6578 x^{14} + 7018 x^{13} + 25894 x^{12} - 17722 x^{11} - 24992 x^{10} - 3784 x^{9} + 25476 x^{8} + 25014 x^{7} - 29799 x^{6} - 9218 x^{5} + 10329 x^{4} + 1870 x^{3} - 1133 x^{2} - 264 x - 13$ |
$22$ |
[14,4] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$12066789286700$ |
| 22.14.246...496.4 |
$x^{22} - 22 x^{20} - 22 x^{19} - 44 x^{18} - 374 x^{17} + 2970 x^{16} + 15444 x^{15} + 2442 x^{14} - 88748 x^{13} - 127732 x^{12} + 115336 x^{11} + 383570 x^{10} + 156442 x^{9} - 287386 x^{8} - 325028 x^{7} - 118162 x^{6} + 23628 x^{5} + 120978 x^{4} + 79508 x^{3} - 17270 x^{2} - 9416 x + 1554$ |
$22$ |
[14,4] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$17981000875800$ |
| 22.10.246...496.4 |
$x^{22} + 33 x^{20} + 187 x^{18} - 2145 x^{16} - 8294 x^{14} + 73194 x^{12} - 117986 x^{10} - 11638 x^{8} + 90805 x^{6} - 1155 x^{4} - 7381 x^{2} - 169$ |
$22$ |
[10,6] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885197$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$3771900828509.023$ |
| 22.14.246...496.5 |
$x^{22} - 11 x^{20} - 121 x^{18} + 1551 x^{16} - 594 x^{14} - 35574 x^{12} + 88462 x^{10} + 100738 x^{8} - 410399 x^{6} + 75361 x^{4} + 481415 x^{2} - 303601$ |
$22$ |
[14,4] |
$2^{30}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$68.5525487885197$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$17$ |
$20091585541845.836$ |
| 22.18.395...936.1 |
$x^{22} - 33 x^{20} + 429 x^{18} - 2673 x^{16} + 6578 x^{14} + 12122 x^{12} - 121726 x^{10} + 319682 x^{8} - 379335 x^{6} + 172667 x^{4} + 11253 x^{2} - 20449$ |
$22$ |
[18,2] |
$2^{34}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$77.7600145192$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$84012537963800$ |
| 22.18.158...744.1 |
$x^{22} - 11 x^{20} - 319 x^{18} + 7183 x^{16} - 57794 x^{14} + 234762 x^{12} - 526174 x^{10} + 651002 x^{8} - 398827 x^{6} + 67529 x^{4} + 26565 x^{2} - 3721$ |
$22$ |
[18,2] |
$2^{36}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$82.8176105784$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$178623184551000$ |
| 22.2.158...744.1 |
$x^{22} + 55 x^{20} + 1199 x^{18} + 13299 x^{16} + 81114 x^{14} + 279642 x^{12} + 532422 x^{10} + 491194 x^{8} + 80201 x^{6} - 190157 x^{4} - 119053 x^{2} - 18225$ |
$22$ |
[2,10] |
$2^{36}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$82.8176105784$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
$[8]$ |
$2$ |
$11$ |
$712861842202$ |
| 22.6.158...744.1 |
$x^{22} + 11 x^{20} - 121 x^{18} - 1441 x^{16} + 110 x^{14} + 39314 x^{12} + 149490 x^{10} + 224906 x^{8} + 145937 x^{6} + 38907 x^{4} + 3267 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{36}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$82.8176105784$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$13$ |
$15251388917300$ |
| 22.2.632...976.1 |
$x^{22} + 55 x^{20} + 1177 x^{18} + 12639 x^{16} + 73898 x^{14} + 237402 x^{12} + 390258 x^{10} + 246906 x^{8} - 33011 x^{6} - 40249 x^{4} - 451 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{38}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$88.2041581953$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
$[20]$ |
$2$ |
$11$ |
$1583985040230$ |
| 22.18.113...984.1 |
$x^{22} - 33 x^{20} - 473 x^{18} - 1562 x^{17} + 23265 x^{16} + 76296 x^{15} - 108526 x^{14} - 1090342 x^{13} - 1720004 x^{12} + 3925524 x^{11} + 11886094 x^{10} - 3917782 x^{9} - 28429720 x^{8} - 3261940 x^{7} + 31213369 x^{6} + 8149526 x^{5} - 15186435 x^{4} - 4824908 x^{3} + 2175415 x^{2} + 1066868 x + 115123$ |
$22$ |
[18,2] |
$2^{22}\cdot 7^{16}\cdot 11^{22}$ |
$3$ |
$90.58148519459012$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$519373019408642.56$ |
| 22.22.101...616.1 |
$x^{22} - 55 x^{20} + 1221 x^{18} - 14333 x^{16} + 98318 x^{14} - 409706 x^{12} + 1039852 x^{10} - 1564134 x^{8} + 1316293 x^{6} - 561011 x^{4} + 96041 x^{2} - 1369$ |
$22$ |
[22,0] |
$2^{42}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$100.051081151$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$21$ |
$3806572397390000$ |
| 22.22.127...616.1 |
$x^{22} - 66 x^{20} + 1749 x^{18} - 24354 x^{16} + 196152 x^{14} - 948684 x^{12} + 2777841 x^{10} - 4888422 x^{8} + 5096619 x^{6} - 3028806 x^{4} + 931491 x^{2} - 112896$ |
$22$ |
[22,0] |
$2^{52}\cdot 3^{20}\cdot 11^{22}$ |
$3$ |
$153.696764314$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$21$ |
$1349827487610000000$ |
| 22.10.297...696.1 |
$x^{22} - 77 x^{20} + 385 x^{18} + 56595 x^{16} - 405328 x^{14} - 3856006 x^{12} + 12948936 x^{10} + 100520266 x^{8} - 11911361 x^{6} - 778886801 x^{4} - 1356442549 x^{2} - 697540921$ |
$22$ |
[10,6] |
$2^{40}\cdot 7^{16}\cdot 11^{22}$ |
$3$ |
$159.711690424$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$15$ |
$48791434660600000$ |
