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 |
|---|---|---|---|---|
| 12.0.170...125.1 | $x^{12} - x^{11} + 263 x^{10} - 81 x^{9} + 28463 x^{8} + 5828 x^{7} + 1619354 x^{6} + 768444 x^{5} + 51291336 x^{4} + 23582808 x^{3} + 866225088 x^{2} + 233929177 x + 6145345751$ | $5^{9}\cdot 7^{8}\cdot 73^{6}$ | $C_{12}$ (as 12T1) | $[5, 5, 4810]$ |
| 12.0.216...000.1 | $x^{12} - 4 x^{11} + 283 x^{10} - 926 x^{9} + 32574 x^{8} - 84412 x^{7} + 1935477 x^{6} - 3748466 x^{5} + 62575025 x^{4} - 81302524 x^{3} + 1065197590 x^{2} - 709042578 x + 7573971901$ | $2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 19^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 25012]$ |
| 12.0.240...125.1 | $x^{12} - x^{11} + 339 x^{10} - 339 x^{9} + 44279 x^{8} - 44279 x^{7} + 2786135 x^{6} - 2786135 x^{5} + 85955767 x^{4} - 85955767 x^{3} + 1167160983 x^{2} - 1167160983 x + 5183066071$ | $3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 4, 1588]$ |
| 12.0.309...976.17 | $x^{12} - 2 x^{11} + 243 x^{10} - 402 x^{9} + 25439 x^{8} - 33658 x^{7} + 1465592 x^{6} - 1462780 x^{5} + 48950518 x^{4} - 32947364 x^{3} + 898179909 x^{2} - 307522146 x + 7073009371$ | $2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 13^{10}$ | $C_6\times C_2$ (as 12T2) | $[2, 30, 2340]$ |
| 12.0.367...000.7 | $x^{12} - 6 x^{11} + 285 x^{10} - 1370 x^{9} + 30606 x^{8} - 114270 x^{7} + 1536671 x^{6} - 4215756 x^{5} + 37645887 x^{4} - 68396122 x^{3} + 416049516 x^{2} - 382535442 x + 1914274729$ | $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 23^{6}$ | $C_6\times C_2$ (as 12T2) | $[20, 5320]$ |
| 12.0.373...533.1 | $x^{12} - x^{11} + 365 x^{10} - 365 x^{9} + 51325 x^{8} - 51325 x^{7} + 3475837 x^{6} - 3475837 x^{5} + 115343229 x^{4} - 115343229 x^{3} + 1681486717 x^{2} - 1681486717 x + 7946060669$ | $13^{11}\cdot 113^{6}$ | $C_{12}$ (as 12T1) | $[2, 51140]$ |
| 12.0.478...125.1 | $x^{12} + 318 x^{10} - x^{9} + 35199 x^{8} - 5601 x^{7} + 1766048 x^{6} - 870237 x^{5} + 42372270 x^{4} - 39182024 x^{3} + 490256874 x^{2} - 445296567 x + 2516315671$ | $3^{18}\cdot 5^{9}\cdot 43^{6}$ | $C_{12}$ (as 12T1) | $[2, 52090]$ |
| 12.0.533...784.5 | $x^{12} + 183 x^{10} + 14617 x^{8} + 651967 x^{6} + 17056201 x^{4} + 246520835 x^{2} + 1526699329$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 43^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 8, 8, 1008]$ |
| 12.0.533...784.6 | $x^{12} + 473 x^{10} + 81356 x^{8} + 6201546 x^{6} + 205128060 x^{4} + 2352135088 x^{2} + 6321363049$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 43^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 2, 14, 504]$ |
| 12.0.559...125.1 | $x^{12} - x^{11} + 323 x^{10} - 101 x^{9} + 42703 x^{8} + 8448 x^{7} + 2950734 x^{6} + 1390204 x^{5} + 112725316 x^{4} + 52702688 x^{3} + 2278832068 x^{2} + 640091877 x + 19212337691$ | $5^{9}\cdot 7^{8}\cdot 89^{6}$ | $C_{12}$ (as 12T1) | $[2, 77890]$ |
| 12.0.576...944.6 | $x^{12} + 372 x^{10} + 51894 x^{8} + 3336592 x^{6} + 96969705 x^{4} + 1030649436 x^{2} + 887503681$ | $2^{24}\cdot 3^{18}\cdot 31^{6}$ | $C_6\times C_2$ (as 12T2) | $[3, 6, 6552]$ |
| 12.0.594...125.1 | $x^{12} - x^{11} + 408 x^{10} - 409 x^{9} + 61794 x^{8} - 62203 x^{7} + 4441807 x^{6} - 4781629 x^{5} + 160998290 x^{4} - 185075146 x^{3} + 2829532400 x^{2} - 2683767652 x + 19664734321$ | $5^{9}\cdot 7^{10}\cdot 47^{6}$ | $C_{12}$ (as 12T1) | $[2, 93314]$ |
| 12.0.651...912.1 | $x^{12} + 403 x^{10} + 62465 x^{8} + 4647396 x^{6} + 168080822 x^{4} + 2605252741 x^{2} + 11537547853$ | $2^{12}\cdot 13^{11}\cdot 31^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 16946]$ |
| 12.0.682...000.1 | $x^{12} - 4 x^{11} + 343 x^{10} - 1126 x^{9} + 47714 x^{8} - 124252 x^{7} + 3418417 x^{6} - 6656386 x^{5} + 132905105 x^{4} - 173414484 x^{3} + 2704663170 x^{2} - 1800348698 x + 22837898761$ | $2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 23^{6}$ | $C_{12}$ (as 12T1) | $[2, 62770]$ |
| 12.0.728...125.1 | $x^{12} - x^{11} + 338 x^{10} - 106 x^{9} + 46713 x^{8} + 9178 x^{7} + 3370404 x^{6} + 1585644 x^{5} + 134261761 x^{4} + 62972433 x^{3} + 2825933888 x^{2} + 799850077 x + 24768500401$ | $3^{6}\cdot 5^{9}\cdot 7^{8}\cdot 31^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 25012]$ |
| 12.0.765...000.16 | $x^{12} - 6 x^{11} + 321 x^{10} - 1550 x^{9} + 38814 x^{8} - 146022 x^{7} + 2195273 x^{6} - 6081186 x^{5} + 60554802 x^{4} - 111141586 x^{3} + 753351309 x^{2} - 698770170 x + 3841091281$ | $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{6}$ | $C_6\times C_2$ (as 12T2) | $[4, 45752]$ |
| 12.0.799...336.15 | $x^{12} + 506 x^{10} + 93104 x^{8} + 7592208 x^{6} + 268647360 x^{4} + 3295407616 x^{2} + 9474296896$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6}$ | $C_6\times C_2$ (as 12T2) | $[4, 31992]$ |
| 12.0.799...336.16 | $x^{12} - 2 x^{11} + 265 x^{10} - 436 x^{9} + 30354 x^{8} - 40216 x^{7} + 1919630 x^{6} - 1949106 x^{5} + 70585208 x^{4} - 49564380 x^{3} + 1429811640 x^{2} - 529942832 x + 12452899201$ | $2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6}$ | $C_6\times C_2$ (as 12T2) | $[10, 17640]$ |
| 12.0.815...125.1 | $x^{12} + 348 x^{10} - x^{9} + 42174 x^{8} - 6651 x^{7} + 2316848 x^{6} - 1132947 x^{5} + 60795645 x^{4} - 55917689 x^{3} + 763654464 x^{2} - 700201812 x + 4170430441$ | $3^{18}\cdot 5^{9}\cdot 47^{6}$ | $C_{12}$ (as 12T1) | $[18, 7578]$ |
| 12.0.825...677.1 | $x^{12} - x^{11} + 417 x^{10} - 417 x^{9} + 66977 x^{8} - 66977 x^{7} + 5178785 x^{6} - 5178785 x^{5} + 196019617 x^{4} - 196019617 x^{3} + 3249472929 x^{2} - 3249472929 x + 17208116641$ | $3^{6}\cdot 13^{11}\cdot 43^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 14290]$ |
| 12.0.909...264.5 | $x^{12} + 201 x^{10} + 17560 x^{8} + 853159 x^{6} + 24229669 x^{4} + 379269698 x^{2} + 2540260801$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 47^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 25544]$ |
| 12.0.909...264.6 | $x^{12} + 517 x^{10} + 97196 x^{8} + 8098194 x^{6} + 292780860 x^{4} + 3669520112 x^{2} + 10779215329$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 47^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 4, 25956]$ |
| 12.0.937...125.1 | $x^{12} - x^{11} + 353 x^{10} - 111 x^{9} + 50903 x^{8} + 9938 x^{7} + 3828104 x^{6} + 1798584 x^{5} + 158746986 x^{4} + 74673288 x^{3} + 3473412138 x^{2} + 990002287 x + 31603168001$ | $5^{9}\cdot 7^{8}\cdot 97^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 44018]$ |
| 12.0.970...125.1 | $x^{12} - x^{11} + 443 x^{10} - 444 x^{9} + 72854 x^{8} - 73298 x^{7} + 5685112 x^{6} - 6113764 x^{5} + 223464715 x^{4} - 256778386 x^{3} + 4246142315 x^{2} - 4044668347 x + 31633408171$ | $3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 35906]$ |
| 12.0.991...453.1 | $x^{12} - x^{11} + 430 x^{10} - 430 x^{9} + 71215 x^{8} - 71215 x^{7} + 5677387 x^{6} - 5677387 x^{5} + 221515009 x^{4} - 221515009 x^{3} + 3782835772 x^{2} - 3782835772 x + 20571919369$ | $7^{6}\cdot 13^{11}\cdot 19^{6}$ | $C_{12}$ (as 12T1) | $[2, 50866]$ |
| 12.0.102...744.13 | $x^{12} - 2 x^{11} + 23 x^{10} - 70 x^{9} + 1683 x^{8} - 1182 x^{7} + 58064 x^{6} + 29528 x^{5} + 1326358 x^{4} + 312844 x^{3} + 19852557 x^{2} - 2851794 x + 125095671$ | $2^{18}\cdot 7^{10}\cdot 13^{10}$ | $C_6\times C_2$ (as 12T2) | $[3, 3, 17784]$ |
| 12.0.104...296.6 | $x^{12} - 4 x^{11} + 202 x^{10} - 656 x^{9} + 17604 x^{8} - 45212 x^{7} + 847622 x^{6} - 1633236 x^{5} + 23739599 x^{4} - 30808716 x^{3} + 365351184 x^{2} - 241593532 x + 2404591561$ | $2^{24}\cdot 3^{6}\cdot 7^{8}\cdot 23^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 12, 4836]$ |
| 12.0.104...896.1 | $x^{12} + 189 x^{10} + 15972 x^{8} + 773671 x^{6} + 22405545 x^{4} + 361326234 x^{2} + 2491307569$ | $2^{12}\cdot 3^{18}\cdot 137^{6}$ | $C_6\times C_2$ (as 12T2) | $[3, 68328]$ |
| 12.0.109...000.1 | $x^{12} + 455 x^{10} + 76895 x^{8} + 6151600 x^{6} + 244910575 x^{4} + 4548339250 x^{2} + 29564205125$ | $2^{12}\cdot 5^{9}\cdot 7^{10}\cdot 13^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 11258]$ |
| 12.0.113...632.1 | $x^{12} + 442 x^{10} + 75140 x^{8} + 6131424 x^{6} + 243213152 x^{4} + 4134623584 x^{2} + 20082457408$ | $2^{18}\cdot 13^{11}\cdot 17^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 34858]$ |
| 12.0.117...072.1 | $x^{12} + 364 x^{10} + 44954 x^{8} + 2337608 x^{6} + 55979560 x^{4} + 582187424 x^{2} + 1892109128$ | $2^{33}\cdot 7^{10}\cdot 13^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 4, 3656]$ |
| 12.0.118...533.1 | $x^{12} - x^{11} + 443 x^{10} - 443 x^{9} + 75583 x^{8} - 75583 x^{7} + 6207007 x^{6} - 6207007 x^{5} + 249420159 x^{4} - 249420159 x^{3} + 4384043743 x^{2} - 4384043743 x + 24466501151$ | $13^{11}\cdot 137^{6}$ | $C_{12}$ (as 12T1) | $[100402]$ |
| 12.0.119...000.19 | $x^{12} + 420 x^{10} + 66150 x^{8} + 4802000 x^{6} + 157565625 x^{4} + 1890787500 x^{2} + 1838265625$ | $2^{24}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 29212]$ |
| 12.0.119...125.1 | $x^{12} - x^{11} + 368 x^{10} - 116 x^{9} + 55273 x^{8} + 10728 x^{7} + 4325484 x^{6} + 2029774 x^{5} + 186438691 x^{4} + 87932303 x^{3} + 4234486768 x^{2} + 1214690007 x + 39941506541$ | $5^{9}\cdot 7^{8}\cdot 101^{6}$ | $C_{12}$ (as 12T1) | $[52, 5044]$ |
| 12.0.134...000.1 | $x^{12} + 455 x^{10} + 79625 x^{8} + 6688500 x^{6} + 273113750 x^{4} + 4779490625 x^{2} + 23897453125$ | $2^{12}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 11290]$ |
| 12.0.140...117.1 | $x^{12} - x^{11} + 456 x^{10} - 456 x^{9} + 80081 x^{8} - 80081 x^{7} + 6768581 x^{6} - 6768581 x^{5} + 279882331 x^{4} - 279882331 x^{3} + 5059372956 x^{2} - 5059372956 x + 28956826081$ | $3^{6}\cdot 13^{11}\cdot 47^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 8660]$ |
| 12.0.142...000.1 | $x^{12} - 4 x^{11} + 388 x^{10} - 1276 x^{9} + 60959 x^{8} - 159172 x^{7} + 4926262 x^{6} - 9621256 x^{5} + 215720780 x^{4} - 282139524 x^{3} + 4928620860 x^{2} - 3280867988 x + 46545815161$ | $2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 13^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 27130]$ |
| 12.0.150...592.1 | $x^{12} - 4 x^{11} + 409 x^{10} - 1618 x^{9} + 64702 x^{8} - 232812 x^{7} + 4913521 x^{6} - 14897420 x^{5} + 177880768 x^{4} - 392841486 x^{3} + 2512428095 x^{2} - 2287314156 x + 6688402169$ | $2^{16}\cdot 11^{6}\cdot 37^{9}$ | $C_3 : C_4$ (as 12T5) | $[2, 2, 2, 22, 748]$ |
| 12.0.160...944.2 | $x^{12} + 144 x^{10} - 4 x^{9} + 9417 x^{8} + 36 x^{7} + 354874 x^{6} + 17724 x^{5} + 8053932 x^{4} + 638028 x^{3} + 103405548 x^{2} + 7102716 x + 582677873$ | $2^{24}\cdot 3^{16}\cdot 53^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 252, 252]$ |
| 12.0.162...000.1 | $x^{12} + 273 x^{10} - 4 x^{9} + 30834 x^{8} + 36 x^{7} + 1824563 x^{6} + 30672 x^{5} + 59716095 x^{4} + 2436664 x^{3} + 1053927204 x^{2} + 67270842 x + 7952847101$ | $2^{12}\cdot 3^{16}\cdot 5^{9}\cdot 19^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 2, 2, 14, 364]$ |
| 12.0.166...125.1 | $x^{12} - x^{11} + 469 x^{10} - 469 x^{9} + 84709 x^{8} - 84709 x^{7} + 7363045 x^{6} - 7363045 x^{5} + 313053157 x^{4} - 313053157 x^{3} + 5815475173 x^{2} - 5815475173 x + 34113645541$ | $5^{6}\cdot 13^{11}\cdot 29^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 2, 18, 1332]$ |
| 12.0.166...624.16 | $x^{12} + 468 x^{10} + 80613 x^{8} + 6169176 x^{6} + 198955926 x^{4} + 2165380776 x^{2} + 3518743761$ | $2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 12, 12, 228]$ |
| 12.0.166...216.5 | $x^{12} + 444 x^{10} + 73926 x^{8} + 5673136 x^{6} + 196786905 x^{4} + 2496382452 x^{2} + 2565726409$ | $2^{24}\cdot 3^{18}\cdot 37^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 2, 6, 6, 630]$ |
| 12.0.175...125.1 | $x^{12} - 3 x^{11} + 279 x^{10} - 831 x^{9} + 32505 x^{8} - 91308 x^{7} + 2005158 x^{6} - 4813584 x^{5} + 68420724 x^{4} - 119458244 x^{3} + 1226604198 x^{2} - 1176569685 x + 9174406301$ | $3^{16}\cdot 5^{9}\cdot 7^{6}\cdot 11^{6}$ | $C_{12}$ (as 12T1) | $[2, 2, 28564]$ |
| 12.0.186...064.5 | $x^{12} - 6 x^{11} + 241 x^{10} - 1150 x^{9} + 24665 x^{8} - 91826 x^{7} + 1372757 x^{6} - 3801644 x^{5} + 43884395 x^{4} - 81537580 x^{3} + 765535945 x^{2} - 725385798 x + 5718892873$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 53^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 14, 5460]$ |
| 12.0.186...064.6 | $x^{12} - 2 x^{11} + 307 x^{10} - 506 x^{9} + 40532 x^{8} - 53740 x^{7} + 2941140 x^{6} - 2980318 x^{5} + 123571099 x^{4} - 86207266 x^{3} + 2848609153 x^{2} - 1041821864 x + 28128047641$ | $2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 53^{6}$ | $C_6\times C_2$ (as 12T2) | $[26, 6552]$ |
| 12.0.188...125.1 | $x^{12} - x^{11} + 398 x^{10} - 126 x^{9} + 64553 x^{8} + 12398 x^{7} + 5445884 x^{6} + 2549904 x^{5} + 252526341 x^{4} + 119660013 x^{3} + 6155914968 x^{2} + 1786052977 x + 62174703641$ | $5^{9}\cdot 7^{8}\cdot 109^{6}$ | $C_{12}$ (as 12T1) | $[2, 92410]$ |
| 12.0.193...496.10 | $x^{12} - 2 x^{11} + 333 x^{10} - 552 x^{9} + 47339 x^{8} - 62758 x^{7} + 3673382 x^{6} - 3667870 x^{5} + 163992613 x^{4} - 110101244 x^{3} + 3992362134 x^{2} - 1357569336 x + 41405864761$ | $2^{12}\cdot 3^{6}\cdot 13^{10}\cdot 19^{6}$ | $C_6\times C_2$ (as 12T2) | $[2, 2, 81468]$ |
| 12.0.196...237.1 | $x^{12} - x^{11} + 482 x^{10} - 482 x^{9} + 89467 x^{8} - 89467 x^{7} + 7991335 x^{6} - 7991335 x^{5} + 349088637 x^{4} - 349088637 x^{3} + 6659388724 x^{2} - 6659388724 x + 40013832041$ | $13^{11}\cdot 149^{6}$ | $C_{12}$ (as 12T1) | $[35, 5110]$ |
| 12.0.221...968.1 | $x^{12} + 494 x^{10} + 93860 x^{8} + 8560032 x^{6} + 379494752 x^{4} + 7210400288 x^{2} + 39142172992$ | $2^{18}\cdot 13^{11}\cdot 19^{6}$ | $C_{12}$ (as 12T1) | $[2, 122954]$ |