Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
12.0.334...264.5 | $x^{12} + 732 x^{10} + 200934 x^{8} + 25421872 x^{6} + 1453813305 x^{4} + 30405466836 x^{2} + 51520374361$ | $2^{24}\cdot 3^{18}\cdot 61^{6}$ | $C_6\times C_2$ (as 12T2) | $[42, 27090]$ |
12.0.365...296.10 | $x^{12} - 2 x^{11} + 549 x^{10} - 912 x^{9} + 127439 x^{8} - 169318 x^{7} + 16003958 x^{6} - 15988294 x^{5} + 1146467101 x^{4} - 767614604 x^{3} + 44414596734 x^{2} - 14988666216 x + 726950311489$ | $2^{12}\cdot 3^{6}\cdot 13^{10}\cdot 31^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 4, 8, 10360]$ |
12.0.511...504.16 | $x^{12} + 828 x^{10} + 252333 x^{8} + 34164936 x^{6} + 1949372406 x^{4} + 37536752376 x^{2} + 107918163081$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 6, 109368]$ |
12.0.587...456.6 | $x^{12} + 804 x^{10} + 242406 x^{8} + 33685456 x^{6} + 2115867705 x^{4} + 48604503852 x^{2} + 90458382169$ | $2^{24}\cdot 3^{18}\cdot 67^{6}$ | $C_6\times C_2$ (as 12T2) | $[14, 80808]$ |
12.0.606...832.1 | $x^{12} + 858 x^{10} + 283140 x^{8} + 44849376 x^{6} + 3453401952 x^{4} + 113962264416 x^{2} + 1074501350208$ | $2^{18}\cdot 3^{6}\cdot 11^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 18, 14274]$ |
12.0.957...000.1 | $x^{12} + 780 x^{10} + 212940 x^{8} + 26364000 x^{6} + 1542294000 x^{4} + 40099644000 x^{2} + 347530248000$ | $2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 13^{6}$ | $C_{12}$ (as 12T1) | $[2, 26, 24362]$ |
12.0.988...625.3 | $x^{12} - x^{11} + 66 x^{10} - 222 x^{9} - 1767 x^{8} - 8113 x^{7} + 37220 x^{6} + 82432 x^{5} + 428416 x^{4} - 639536 x^{3} - 3977856 x^{2} - 6304000 x + 28891136$ | $5^{9}\cdot 7^{10}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 4, 136140]$ |
12.0.186...000.1 | $x^{12} + 378 x^{10} - 4 x^{9} + 52314 x^{8} + 36 x^{7} + 3043978 x^{6} - 41448 x^{5} + 63815355 x^{4} - 247416 x^{3} + 740590164 x^{2} + 128427012 x + 3754358271$ | $2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{9}$ | $C_{12}$ (as 12T1) | $[6, 266934]$ |
12.0.197...648.1 | $x^{12} + 696 x^{10} + 151380 x^{8} + 13462728 x^{6} + 534704436 x^{4} + 8860816368 x^{2} + 42827279112$ | $2^{33}\cdot 3^{18}\cdot 29^{6}$ | $C_{12}$ (as 12T1) | $[2, 533234]$ |
12.0.205...056.12 | $x^{12} + 812 x^{10} + 206045 x^{8} + 18438084 x^{6} + 623821842 x^{4} + 8040370408 x^{2} + 29146342729$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 4, 52, 1872]$ |
12.0.205...056.16 | $x^{12} + 604 x^{10} + 143581 x^{8} + 16983632 x^{6} + 1039094758 x^{4} + 30891844344 x^{2} + 371530478089$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 4, 52, 936]$ |
12.0.205...056.17 | $x^{12} + 1044 x^{10} + 401157 x^{8} + 68484312 x^{6} + 4926919446 x^{4} + 119621020968 x^{2} + 433626201009$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 2, 2, 18, 1638]$ |
12.0.291...000.1 | $x^{12} + 1155 x^{10} + 495495 x^{8} + 100623600 x^{6} + 10169272575 x^{4} + 479408564250 x^{2} + 7910241310125$ | $2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 11^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 4, 86312]$ |
12.0.295...328.1 | $x^{12} + 744 x^{10} + 172980 x^{8} + 16444632 x^{6} + 698181876 x^{4} + 12367793232 x^{2} + 63900265032$ | $2^{33}\cdot 3^{18}\cdot 31^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 323986]$ |
12.0.298...096.10 | $x^{12} + 60 x^{10} + 2683 x^{8} + 80840 x^{6} + 1655491 x^{4} + 20639500 x^{2} + 122655625$ | $2^{24}\cdot 3^{6}\cdot 11^{6}\cdot 13^{10}$ | $C_6\times C_2$ (as 12T2) | $[4, 4, 81528]$ |
12.0.313...352.1 | $x^{12} + 924 x^{10} + 289674 x^{8} + 38236968 x^{6} + 2324405160 x^{4} + 61364296224 x^{2} + 506255443848$ | $2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 204980]$ |
12.0.318...968.1 | $x^{12} + 1131 x^{10} + 491985 x^{8} + 102726468 x^{6} + 10426736502 x^{4} + 453563037837 x^{2} + 5637140613117$ | $2^{12}\cdot 3^{6}\cdot 13^{11}\cdot 29^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 162370]$ |
12.0.640...928.1 | $x^{12} + 714 x^{10} + 197064 x^{8} + 26655048 x^{6} + 1835265600 x^{4} + 59903069184 x^{2} + 718836830208$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 17^{9}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 134660]$ |
12.0.760...416.1 | $x^{12} - 4 x^{11} + 60 x^{10} - 244 x^{9} + 3108 x^{8} - 5680 x^{7} + 94940 x^{6} - 80056 x^{5} + 2043880 x^{4} + 521392 x^{3} + 29720144 x^{2} + 19294176 x + 194070672$ | $2^{16}\cdot 17^{6}\cdot 37^{10}$ | $C_6\times S_3$ (as 12T18) | $[2, 6, 107784]$ |
12.0.853...488.1 | $x^{12} + 1092 x^{10} + 404586 x^{8} + 63115416 x^{6} + 4534344360 x^{4} + 141471544032 x^{2} + 1379347554312$ | $2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 96434]$ |
12.0.108...864.16 | $x^{12} - 6 x^{11} + 111 x^{10} - 500 x^{9} + 9519 x^{8} - 35142 x^{7} + 504889 x^{6} - 1393704 x^{5} + 19106076 x^{4} - 35929344 x^{3} + 476053380 x^{2} - 458315280 x + 6075013344$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 17^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 6, 6, 24180]$ |
12.0.132...176.1 | $x^{12} - 2 x^{11} + 23 x^{10} + 24 x^{9} + 1107 x^{8} - 3398 x^{7} + 34971 x^{6} - 76766 x^{5} + 638234 x^{4} - 1642978 x^{3} + 9051364 x^{2} - 15698396 x + 46350852$ | $2^{8}\cdot 37^{10}\cdot 47^{6}$ | $C_6\times S_3$ (as 12T18) | $[6, 30, 15330]$ |
12.0.143...000.20 | $x^{12} - 2 x^{11} + 151 x^{10} - 214 x^{9} + 11149 x^{8} - 15346 x^{7} + 515448 x^{6} - 732598 x^{5} + 15029687 x^{4} - 18766796 x^{3} + 248996314 x^{2} - 193232084 x + 1771822921$ | $2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 37^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 262104]$ |
12.0.208...201.1 | $x^{12} - x^{11} + 25 x^{10} - 665 x^{9} + 9567 x^{8} - 36895 x^{7} - 32397 x^{6} + 1439117 x^{5} - 3804588 x^{4} - 649236 x^{3} + 100982464 x^{2} + 76425536 x + 14992384$ | $7^{10}\cdot 97^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 12, 26676]$ |
12.0.210...336.11 | $x^{12} - 9 x^{10} - 112 x^{9} + 2139 x^{8} + 7056 x^{7} + 56293 x^{6} + 2688 x^{5} + 1618164 x^{4} + 5742912 x^{3} + 49780692 x^{2} + 107430624 x + 392457024$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 100104]$ |
12.0.210...336.15 | $x^{12} + 111 x^{10} + 10851 x^{8} + 594845 x^{6} + 25800888 x^{4} + 675452112 x^{2} + 11307344896$ | $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 200208]$ |
12.0.371...808.1 | $x^{12} + 195 x^{10} - 52 x^{9} + 20787 x^{8} + 25428 x^{7} + 942422 x^{6} + 204828 x^{5} + 4214691 x^{4} + 12075388 x^{3} + 427391367 x^{2} - 807602328 x + 3678675897$ | $2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 6, 6, 17862]$ |
12.0.371...808.2 | $x^{12} + 195 x^{10} - 52 x^{9} + 20787 x^{8} - 3354 x^{7} + 943592 x^{6} - 589134 x^{5} + 3543930 x^{4} - 6234410 x^{3} + 456229527 x^{2} + 1474874154 x + 3926087841$ | $2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[3, 6, 6, 30, 390]$ |
12.0.450...152.2 | $x^{12} + 247 x^{10} + 23959 x^{8} + 1147562 x^{6} + 27702779 x^{4} + 296048519 x^{2} + 816061077$ | $2^{12}\cdot 13^{11}\cdot 19^{10}$ | $C_{12}$ (as 12T1) | $[2, 2, 10, 30270]$ |
12.0.519...504.1 | $x^{12} - 2 x^{11} + 41 x^{10} - 6 x^{9} + 1878 x^{8} - 4406 x^{7} + 63987 x^{6} - 136784 x^{5} + 1352954 x^{4} - 3084580 x^{3} + 19917769 x^{2} - 31791008 x + 115888143$ | $2^{8}\cdot 37^{10}\cdot 59^{6}$ | $C_6\times S_3$ (as 12T18) | $[3, 18, 108234]$ |
12.0.568...472.1 | $x^{12} - 4 x^{11} + 475 x^{10} - 1566 x^{9} + 77422 x^{8} - 202300 x^{7} + 4485909 x^{6} - 8624434 x^{5} + 27197377 x^{4} - 28351612 x^{3} + 150014294 x^{2} - 117500690 x + 370936189$ | $2^{12}\cdot 3^{6}\cdot 7^{8}\cdot 53^{9}$ | $C_{12}$ (as 12T1) | $[3, 6, 250926]$ |
12.0.886...873.1 | $x^{12} - x^{11} + 40 x^{10} + 362 x^{9} + 3865 x^{8} + 5787 x^{7} + 216950 x^{6} + 605452 x^{5} + 4161656 x^{4} + 6762912 x^{3} + 84181376 x^{2} + 235215360 x + 276287488$ | $7^{10}\cdot 73^{11}$ | $C_{12}$ (as 12T1) | $[1147854]$ |
12.0.967...888.2 | $x^{12} + 546 x^{10} + 95004 x^{8} + 6722352 x^{6} + 217120176 x^{4} + 3125539872 x^{2} + 15721812288$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 4, 15864]$ |
12.0.101...568.1 | $x^{12} + 1092 x^{10} + 286650 x^{8} + 29857464 x^{6} + 1314691560 x^{4} + 22086818208 x^{2} + 115955795592$ | $2^{33}\cdot 3^{6}\cdot 7^{6}\cdot 13^{10}$ | $C_{12}$ (as 12T1) | $[2, 2, 10, 45370]$ |
12.0.131...184.1 | $x^{12} + 354 x^{10} - 4 x^{9} + 49098 x^{8} + 36 x^{7} + 3301706 x^{6} + 13800 x^{5} + 111289299 x^{4} + 2865640 x^{3} + 1955645292 x^{2} + 154582308 x + 14516726199$ | $2^{18}\cdot 3^{16}\cdot 61^{9}$ | $C_{12}$ (as 12T1) | $[3, 3, 3, 41574]$ |
12.0.133...656.1 | $x^{12} - 3 x^{11} + 66 x^{10} - 215 x^{9} + 7368 x^{8} - 81525 x^{7} + 626863 x^{6} - 3211590 x^{5} + 8049024 x^{4} - 8441862 x^{3} + 28565064 x^{2} - 11968884 x + 43082964$ | $2^{8}\cdot 3^{18}\cdot 7^{10}\cdot 41^{6}$ | $C_6\times S_3$ (as 12T18) | $[6, 168, 1176]$ |
12.0.152...000.15 | $x^{12} + 228 x^{10} + 26334 x^{8} + 1542876 x^{6} + 57419577 x^{4} + 588796776 x^{2} + 2100205584$ | $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 6, 12, 11856]$ |
12.0.157...824.1 | $x^{12} - 2 x^{11} + 59 x^{10} - 36 x^{9} + 2919 x^{8} - 5774 x^{7} + 107367 x^{6} - 217538 x^{5} + 2536754 x^{4} - 5263138 x^{3} + 39484456 x^{2} - 58187108 x + 254779596$ | $2^{8}\cdot 37^{10}\cdot 71^{6}$ | $C_6\times S_3$ (as 12T18) | $[2, 6, 6, 6, 7686]$ |
12.0.175...000.1 | $x^{12} + 780 x^{10} + 216450 x^{8} + 25623000 x^{6} + 1174095000 x^{4} + 11372400000 x^{2} + 29615625000$ | $2^{33}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 4, 4, 4616]$ |
12.0.175...000.2 | $x^{12} + 780 x^{10} + 216450 x^{8} + 28431000 x^{6} + 1890135000 x^{4} + 60652800000 x^{2} + 740390625000$ | $2^{33}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 2, 126, 252]$ |
12.0.218...000.36 | $x^{12} + 102 x^{10} - 52 x^{9} + 8703 x^{8} + 3198 x^{7} + 471412 x^{6} + 83538 x^{5} + 17475255 x^{4} + 13489866 x^{3} + 462875499 x^{2} + 458844750 x + 5314031919$ | $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 30, 21720]$ |
12.0.218...000.37 | $x^{12} + 102 x^{10} - 52 x^{9} + 8703 x^{8} + 2496 x^{7} + 470242 x^{6} + 300456 x^{5} + 18065637 x^{4} + 14790204 x^{3} + 438168960 x^{2} + 279668376 x + 5374163484$ | $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 4, 12, 5928]$ |
12.0.276...376.1 | $x^{12} + 861 x^{10} + 242802 x^{8} + 27005265 x^{6} + 1307690244 x^{4} + 26260555104 x^{2} + 157563330624$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 41^{9}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 42260]$ |
12.0.305...000.1 | $x^{12} + 930 x^{10} + 306900 x^{8} + 46872000 x^{6} + 3487276800 x^{4} + 119563776000 x^{2} + 1434765312000$ | $2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 31^{10}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 59060]$ |
12.0.315...000.1 | $x^{12} + 312 x^{10} - 52 x^{9} + 45123 x^{8} + 35256 x^{7} + 2843672 x^{6} + 794976 x^{5} + 38233377 x^{4} + 26701324 x^{3} + 1641488550 x^{2} - 2628689544 x + 17237397684$ | $2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 6, 6, 28254]$ |
12.0.315...000.2 | $x^{12} + 312 x^{10} - 52 x^{9} + 45123 x^{8} - 6162 x^{7} + 2844842 x^{6} - 1148862 x^{5} + 37302525 x^{4} - 15701114 x^{3} + 1693748589 x^{2} + 4707053910 x + 17866171479$ | $2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[3, 6, 144534]$ |
12.0.330...224.15 | $x^{12} - 2 x^{11} + 145 x^{10} - 880 x^{9} + 13350 x^{8} - 77392 x^{7} + 789272 x^{6} - 3718848 x^{5} + 22127456 x^{4} - 62065824 x^{3} + 227928720 x^{2} - 351879680 x + 1003941856$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 4, 38064]$ |
12.0.330...224.22 | $x^{12} - 2 x^{11} + 121 x^{10} - 840 x^{9} + 11938 x^{8} - 75536 x^{7} + 810648 x^{6} - 3407360 x^{5} + 20369536 x^{4} - 53662112 x^{3} + 232061456 x^{2} - 360419200 x + 2117917600$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 2, 102480]$ |
12.0.330...224.23 | $x^{12} - 4 x^{11} - 164 x^{10} + 760 x^{9} + 11031 x^{8} - 57920 x^{7} - 73396 x^{6} + 501456 x^{5} + 8722892 x^{4} - 27044448 x^{3} + 36508032 x^{2} - 129311488 x + 2287368448$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 2, 38064]$ |
12.0.330...224.27 | $x^{12} - 2 x^{11} + 73 x^{10} - 760 x^{9} + 10554 x^{8} - 73744 x^{7} + 842072 x^{6} - 2403456 x^{5} + 14402624 x^{4} - 55312800 x^{3} + 287379984 x^{2} - 84951680 x + 7114036000$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 40, 7320]$ |