Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (17 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.0.402...936.1 | $x^{12} - 2 x^{11} + 77 x^{10} - 66 x^{9} + 4230 x^{8} - 7502 x^{7} + 168351 x^{6} - 322268 x^{5} + 4364918 x^{4} - 8373052 x^{3} + 72211609 x^{2} - 98828804 x + 508991091$ | $2^{8}\cdot 37^{10}\cdot 83^{6}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 349182]$ |
| 12.0.132...384.1 | $x^{12} + 1092 x^{10} + 424242 x^{8} + 70309512 x^{6} + 4510403352 x^{4} + 61163496576 x^{2} + 222991914600$ | $2^{33}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 4820212]$ |
| 12.0.166...416.1 | $x^{12} + 1422 x^{8} - 924300 x^{6} - 11027847 x^{4} + 657177300 x^{2} + 225275535424$ | $2^{12}\cdot 3^{16}\cdot 79^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 4, 4, 168, 2520]$ |
| 12.0.253...016.1 | $x^{12} - 2 x^{11} + 481 x^{10} - 838 x^{9} + 119477 x^{8} - 156478 x^{7} + 18193295 x^{6} - 15155658 x^{5} + 1765848274 x^{4} - 806865152 x^{3} + 102482964344 x^{2} - 21056399040 x + 2803797460864$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6}\cdot 19^{8}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 2, 2, 6, 153072]$ |
| 12.0.355...000.2 | $x^{12} + 780 x^{10} + 226980 x^{8} + 29335800 x^{6} + 1451174400 x^{4} + 4672512000 x^{2} + 3833856000$ | $2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 1467420]$ |
| 12.0.418...384.1 | $x^{12} - 2 x^{11} - 33 x^{10} + 256 x^{9} + 1545 x^{8} - 13802 x^{7} + 81119 x^{6} - 370046 x^{5} + 2556757 x^{4} - 7921528 x^{3} + 24439295 x^{2} - 52458066 x + 247704597$ | $2^{12}\cdot 47^{6}\cdot 79^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 30, 30, 7440]$ |
| 12.0.841...832.1 | $x^{12} + 1236 x^{10} + 391194 x^{8} + 50258232 x^{6} + 2784225960 x^{4} + 60139280736 x^{2} + 405940144968$ | $2^{33}\cdot 3^{6}\cdot 103^{10}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 639132]$ |
| 12.0.912...361.1 | $x^{12} - 4 x^{11} - 367 x^{10} + 788 x^{9} + 53059 x^{8} - 36136 x^{7} - 3642675 x^{6} - 265142 x^{5} + 128044633 x^{4} + 49855354 x^{3} - 2174288521 x^{2} - 388898690 x + 17877187700$ | $7^{10}\cdot 11^{6}\cdot 67^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 6, 6, 150612]$ |
| 12.0.173...656.1 | $x^{12} + 762 x^{10} + 202311 x^{8} + 24967184 x^{6} + 1472174475 x^{4} + 33659206875 x^{2} + 252015625$ | $2^{12}\cdot 3^{18}\cdot 127^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 8, 8, 8, 15960]$ |
| 12.0.182...000.2 | $x^{12} + 1095 x^{10} + 160965 x^{8} + 9460800 x^{6} + 262241550 x^{4} + 3368192625 x^{2} + 15971752125$ | $2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 73^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 1372628]$ |
| 12.0.207...576.1 | $x^{12} - 6 x^{11} - 105 x^{10} + 476 x^{9} + 4659 x^{8} - 11886 x^{7} - 23927 x^{6} + 12144 x^{5} + 756936 x^{4} + 454128 x^{3} + 14513724 x^{2} + 475632 x + 57241872$ | $2^{18}\cdot 3^{18}\cdot 13^{10}\cdot 23^{6}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 2, 6, 6, 118188]$ |
| 12.0.230...744.1 | $x^{12} - 6 x^{11} - 369 x^{10} + 568 x^{9} + 58059 x^{8} + 114606 x^{7} - 3548525 x^{6} - 9052842 x^{5} + 135909666 x^{4} + 393289626 x^{3} - 1893538260 x^{2} + 975185460 x + 49479090012$ | $2^{8}\cdot 3^{18}\cdot 13^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 12, 283476]$ |
| 12.0.274...856.1 | $x^{12} + 798 x^{10} + 166383 x^{8} + 11626860 x^{6} + 174325095 x^{4} + 743627871 x^{2} + 1432809$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[6, 6, 327894]$ |
| 12.0.274...856.18 | $x^{12} + 64638 x^{8} - 1550780 x^{6} + 933713865 x^{4} + 50119658820 x^{2} + 624972464704$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 6, 12, 12, 912]$ |
| 12.0.274...856.21 | $x^{12} + 64638 x^{8} - 1550780 x^{6} + 536348169 x^{4} + 50119658820 x^{2} + 1100619202816$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 2, 2, 12, 12, 5928]$ |
| 12.0.274...856.23 | $x^{12} + 45486 x^{8} - 2101932 x^{6} + 854750169 x^{4} + 47804239476 x^{2} + 1417566459456$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 4, 4, 4, 12, 13416]$ |
| 12.0.274...856.31 | $x^{12} + 7182 x^{8} + 4184180 x^{6} + 167001849 x^{4} - 15025390380 x^{2} + 4790180067904$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 4, 4, 12, 6384]$ |
| 12.0.300...744.2 | $x^{12} - 6 x^{11} - 153 x^{10} + 212 x^{9} + 13059 x^{8} + 31698 x^{7} - 313383 x^{6} - 1147464 x^{5} + 7323048 x^{4} + 44510576 x^{3} + 130678764 x^{2} + 535140720 x + 1969894000$ | $2^{18}\cdot 3^{18}\cdot 13^{6}\cdot 19^{10}$ | $C_6\times S_3$ (as 12T18) | $[42, 749112]$ |
| 12.0.317...984.1 | $x^{12} + 1092 x^{10} + 384930 x^{8} + 54427464 x^{6} + 2733815448 x^{4} + 23518325376 x^{2} + 449513064$ | $2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 814, 4884]$ |
| 12.0.317...984.2 | $x^{12} + 1092 x^{10} + 247338 x^{8} + 22407840 x^{6} + 889945056 x^{4} + 13314502656 x^{2} + 17178086016$ | $2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 709644]$ |
| 12.0.466...776.1 | $x^{12} + 1241 x^{10} + 465050 x^{8} + 58121633 x^{6} + 2059220588 x^{4} + 9110533718 x^{2} + 10098039121$ | $2^{12}\cdot 3^{8}\cdot 107^{8}\cdot 317^{4}$ | $C_2^5:S_4$ (as 12T184) | $[2, 2, 2, 2, 2, 2, 1386364]$ |
| 12.0.466...776.2 | $x^{12} + 1419 x^{10} + 631560 x^{8} + 94820723 x^{6} + 5360083260 x^{4} + 113149006176 x^{2} + 646274503744$ | $2^{12}\cdot 3^{8}\cdot 107^{8}\cdot 317^{4}$ | $C_2^5:S_4$ (as 12T184) | $[2, 2, 2, 2, 2, 2, 410844]$ |
| 12.0.597...136.1 | $x^{12} - 2 x^{11} + 223 x^{10} + 9112 x^{9} - 21670 x^{8} - 26020 x^{7} + 7804782 x^{6} - 68604576 x^{5} + 539755077 x^{4} - 2463841322 x^{3} + 8931195747 x^{2} - 20412720936 x + 20785096368$ | $2^{18}\cdot 7^{10}\cdot 19^{8}\cdot 41^{6}$ | $C_6\times S_3$ (as 12T18) | $[3, 3, 3, 42, 21294]$ |
| 12.0.784...336.1 | $x^{12} - 6 x^{11} - 393 x^{10} + 688 x^{9} + 62187 x^{8} + 97374 x^{7} - 3967909 x^{6} - 9955650 x^{5} + 133133706 x^{4} + 364479098 x^{3} - 1900721436 x^{2} - 1258966476 x + 27667585644$ | $2^{8}\cdot 3^{16}\cdot 23^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 3, 3, 3, 332955]$ |
| 12.0.115...904.1 | $x^{12} - 6 x^{11} - 351 x^{10} + 478 x^{9} + 55278 x^{8} + 126270 x^{7} - 3238565 x^{6} - 8189760 x^{5} + 140539986 x^{4} + 428985876 x^{3} - 1763760087 x^{2} + 3332863368 x + 72485894151$ | $2^{8}\cdot 3^{18}\cdot 17^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 6, 1114230]$ |
| 12.0.118...176.3 | $x^{12} + 80802 x^{8} + 1466758305 x^{4} + 42363518976$ | $2^{24}\cdot 3^{18}\cdot 67^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 4, 4, 16, 16, 336]$ |
| 12.0.118...176.5 | $x^{12} + 804 x^{10} + 242406 x^{8} + 33685456 x^{6} + 2115867705 x^{4} + 48604503852 x^{2} + 348339581209$ | $2^{24}\cdot 3^{18}\cdot 67^{10}$ | $C_6\times C_2$ (as 12T2) | $[30, 469560]$ |
| 12.0.138...000.1 | $x^{12} - 2 x^{11} - 99 x^{10} - 106 x^{9} + 4082 x^{8} + 14090 x^{7} - 22661 x^{6} - 35264 x^{5} + 892106 x^{4} + 1721560 x^{3} - 3073903 x^{2} + 2278368 x + 47551339$ | $2^{8}\cdot 5^{6}\cdot 19^{6}\cdot 97^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 12, 267612]$ |
| 12.0.143...104.1 | $x^{12} - 318 x^{10} - 1332 x^{9} + 46575 x^{8} + 346320 x^{7} - 1501832 x^{6} - 11068920 x^{5} + 146211555 x^{4} + 915488928 x^{3} + 545148774 x^{2} + 13551484284 x + 183940728157$ | $2^{16}\cdot 3^{18}\cdot 7^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 6, 82812]$ |
| 12.0.227...000.2 | $x^{12} - 2 x^{11} + 263 x^{10} - 820 x^{9} + 52859 x^{8} - 291274 x^{7} + 8434721 x^{6} - 37166640 x^{5} + 892977008 x^{4} - 4209452296 x^{3} + 83515868324 x^{2} - 336370274912 x + 2998191573664$ | $2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 13^{8}\cdot 17^{6}$ | $C_6\times S_3$ (as 12T18) | $[4, 12, 709740]$ |
| 12.0.242...681.1 | $x^{12} - 4 x^{11} - 355 x^{10} + 748 x^{9} + 50999 x^{8} - 30536 x^{7} - 3501679 x^{6} - 320614 x^{5} + 127974329 x^{4} + 50632666 x^{3} - 2305644145 x^{2} - 123051698 x + 24154857412$ | $7^{10}\cdot 19^{6}\cdot 67^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 419034]$ |
| 12.0.279...416.1 | $x^{12} + 1047 x^{10} + 298395 x^{8} + 30228984 x^{6} + 840352563 x^{4} + 783107838 x^{2} + 185472909$ | $2^{12}\cdot 3^{6}\cdot 349^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 4, 4, 4, 4, 31076]$ |
| 12.0.300...000.1 | $x^{12} + 1392 x^{10} + 629609 x^{8} - 412720 x^{7} + 99222500 x^{6} - 148785560 x^{5} + 4391308468 x^{4} - 1487855600 x^{3} + 11116778728 x^{2} - 58262444240 x + 122794061636$ | $2^{24}\cdot 5^{6}\cdot 7^{10}\cdot 67^{8}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 2, 2, 4, 8, 35184]$ |
| 12.0.329...000.1 | $x^{12} - 2 x^{11} - 359 x^{10} + 1052 x^{9} + 50065 x^{8} - 174468 x^{7} - 3230464 x^{6} + 10576888 x^{5} + 114207080 x^{4} - 297299312 x^{3} - 2056643472 x^{2} + 2305129248 x + 24433473744$ | $2^{12}\cdot 5^{6}\cdot 7^{10}\cdot 67^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 6, 6, 150, 2100]$ |
| 12.0.423...384.1 | $x^{12} - 2 x^{11} - 133 x^{10} + 600 x^{9} + 7087 x^{8} - 53362 x^{7} - 73635 x^{6} + 1629932 x^{5} - 2918404 x^{4} - 21088072 x^{3} + 127645924 x^{2} - 312129232 x + 378133648$ | $2^{18}\cdot 23^{6}\cdot 127^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 6, 36, 44964]$ |
| 12.0.470...344.1 | $x^{12} - 6 x^{11} - 381 x^{10} + 628 x^{9} + 60063 x^{8} + 106230 x^{7} - 3756945 x^{6} - 9540870 x^{5} + 134066346 x^{4} + 376355866 x^{3} - 1917591072 x^{2} - 261317892 x + 37452592916$ | $2^{8}\cdot 3^{16}\cdot 31^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 3, 9, 160659]$ |
| 12.0.746...464.3 | $x^{12} - 4 x^{11} - 268 x^{10} + 2292 x^{9} + 32602 x^{8} - 462836 x^{7} + 38710 x^{6} + 26496976 x^{5} - 73875215 x^{4} - 1177757340 x^{3} + 12510915458 x^{2} - 57170141008 x + 146620788217$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 43^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 6, 1172580]$ |
| 12.0.883...856.1 | $x^{12} - 4 x^{11} - 84 x^{10} - 80 x^{9} + 6854 x^{8} + 25816 x^{7} - 98480 x^{6} - 1156624 x^{5} + 1204337 x^{4} + 39287276 x^{3} + 256880276 x^{2} + 778821408 x + 1637642776$ | $2^{24}\cdot 13^{6}\cdot 127^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 8, 8, 105504]$ |
| 12.0.984...776.5 | $x^{12} - 2 x^{11} - 353 x^{10} + 1042 x^{9} + 49065 x^{8} - 173128 x^{7} - 3159246 x^{6} + 10378032 x^{5} + 114580543 x^{4} - 298637654 x^{3} - 2114803145 x^{2} + 2202525150 x + 28296601375$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 67^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 2, 6, 6, 6, 19290]$ |
| 12.0.115...752.1 | $x^{12} + 1191 x^{10} + 403749 x^{8} + 39960432 x^{6} + 826306272 x^{4} + 493931520 x^{2} + 74089728$ | $2^{12}\cdot 3^{6}\cdot 397^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 2, 4, 4, 11908]$ |
| 12.0.122...000.1 | $x^{12} - 264 x^{10} - 1332 x^{9} + 41472 x^{8} + 346320 x^{7} - 451748 x^{6} - 3516480 x^{5} + 219344376 x^{4} + 1374245712 x^{3} + 4479083712 x^{2} + 36662777856 x + 412946670736$ | $2^{22}\cdot 3^{18}\cdot 5^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 1189032]$ |
| 12.0.133...256.1 | $x^{12} - 6 x^{11} - 705 x^{10} + 164 x^{9} + 191247 x^{8} + 882426 x^{7} - 20245807 x^{6} - 178600680 x^{5} + 406915920 x^{4} + 9630102544 x^{3} + 37486393872 x^{2} + 53879884608 x + 52111361152$ | $2^{12}\cdot 3^{18}\cdot 7^{6}\cdot 61^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 1819188]$ |
| 12.0.196...984.1 | $x^{12} - 6 x^{11} - 921 x^{10} - 1028 x^{9} + 295971 x^{8} + 2075754 x^{7} - 28211583 x^{6} - 352600800 x^{5} - 60482568 x^{4} + 15452035960 x^{3} + 84364121604 x^{2} + 179651020416 x + 159663973904$ | $2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 79^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 6, 12, 275436]$ |
| 12.0.199...704.2 | $x^{12} - 1474 x^{9} - 372587 x^{6} - 11969765874 x^{3} + 65944160601201$ | $2^{18}\cdot 3^{18}\cdot 13^{6}\cdot 67^{8}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 6, 444654]$ |
| 12.0.216...056.1 | $x^{12} - 246 x^{10} - 1332 x^{9} + 40311 x^{8} + 346320 x^{7} - 73208 x^{6} - 711288 x^{5} + 252900579 x^{4} + 1582213536 x^{3} + 6540737454 x^{2} + 47474838972 x + 524928803509$ | $2^{16}\cdot 3^{18}\cdot 11^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 2, 2, 6, 6, 233016]$ |
| 12.0.234...000.1 | $x^{12} - 6 x^{11} - 909 x^{10} - 1088 x^{9} + 290583 x^{8} + 2097666 x^{7} - 26961755 x^{6} - 349601628 x^{5} - 99728316 x^{4} + 15910199832 x^{3} + 93110276772 x^{2} + 225064184688 x + 252713068704$ | $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 79^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 1135764]$ |
| 12.0.253...224.14 | $x^{12} - 1092 x^{10} + 476658 x^{8} - 100979970 x^{6} + 11767011165 x^{4} - 724677216354 x^{2} + 18181585136169$ | $2^{24}\cdot 3^{18}\cdot 7^{10}\cdot 13^{10}$ | $C_6\times S_3$ (as 12T18) | $[6, 6, 12, 24, 3096]$ |
| 12.0.253...536.1 | $x^{12} - 2 x^{11} - 121 x^{10} + 580 x^{9} + 6491 x^{8} - 52554 x^{7} - 45007 x^{6} + 1556360 x^{5} - 2960768 x^{4} - 24484248 x^{3} + 166228260 x^{2} - 460288544 x + 655716544$ | $2^{18}\cdot 31^{6}\cdot 127^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 3, 9, 1053180]$ |
| 12.0.279...136.1 | $x^{12} - 2 x^{11} + 167 x^{10} - 1246 x^{9} + 24756 x^{8} - 132978 x^{7} + 1130569 x^{6} - 3335608 x^{5} + 25742792 x^{4} - 60568948 x^{3} + 342253035 x^{2} + 20074400 x + 1190281$ | $2^{8}\cdot 3^{6}\cdot 11^{6}\cdot 13^{10}\cdot 19^{10}$ | $C_6\times S_3$ (as 12T18) | $[3, 6, 6, 178662]$ |
| 12.0.283...216.1 | $x^{12} - 114 x^{10} - 686 x^{9} + 8664 x^{8} - 282492 x^{7} + 48223 x^{6} + 15768480 x^{5} + 119711742 x^{4} + 296911062 x^{3} + 7447669704 x^{2} + 6175179360 x + 16955122017$ | $2^{18}\cdot 3^{18}\cdot 7^{8}\cdot 13^{4}\cdot 19^{8}$ | $C_6\times S_3$ (as 12T18) | $[3, 3, 3, 3, 6, 42, 882]$ |