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 |
---|---|---|---|---|
12.2.167630295667.1 | $x^{12} - 3 x^{11} + 4 x^{10} - x^{9} - 6 x^{8} + 15 x^{7} - 19 x^{6} + 15 x^{5} - 6 x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ | $-\,29^{2}\cdot 43\cdot 2153^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.2.168661105243.1 | $x^{12} - 5 x^{11} + 12 x^{10} - 16 x^{9} + 12 x^{8} - 4 x^{7} + x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$ | $-\,67\cdot 131^{2}\cdot 383^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.2.173809422763.1 | $x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{7} - 2 x^{5} + 4 x^{3} - 3 x^{2} - x + 1$ | $-\,31^{4}\cdot 53^{2}\cdot 67$ | $C_2\wr (C_2\times S_4)$ (as 12T250) | trivial |
12.2.175113024319.1 | $x^{12} - 4 x^{11} + 8 x^{10} - 9 x^{9} + 4 x^{8} + 5 x^{7} - 16 x^{6} + 23 x^{5} - 24 x^{4} + 19 x^{3} - 12 x^{2} + 5 x - 1$ | $-\,23^{4}\cdot 79\cdot 89^{2}$ | $C_2\wr (C_2\times S_4)$ (as 12T250) | trivial |
12.2.175122415616.1 | $x^{12} - 4 x^{11} + 10 x^{10} - 16 x^{9} + 17 x^{8} - 6 x^{7} - 12 x^{6} + 30 x^{5} - 37 x^{4} + 30 x^{3} - 17 x^{2} + 6 x - 1$ | $-\,2^{18}\cdot 71\cdot 97^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.2.177788874752.1 | $x^{12} - 4 x^{9} + 3 x^{8} - 4 x^{7} + 11 x^{6} - 8 x^{5} + 8 x^{4} - 14 x^{3} + 13 x^{2} - 6 x + 1$ | $-\,2^{12}\cdot 31^{4}\cdot 47$ | $C_2\wr S_4$ (as 12T227) | trivial |
12.2.204800642687.1 | $x^{12} - 3 x^{11} + 5 x^{10} - 3 x^{9} - 4 x^{8} + 12 x^{7} - 15 x^{6} + 12 x^{5} - 4 x^{4} - 3 x^{3} + 5 x^{2} - 3 x + 1$ | $-\,23\cdot 197^{2}\cdot 479^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.2.205567038859.1 | $x^{12} - x^{11} + 2 x^{10} + x^{8} + 4 x^{7} - 5 x^{6} + 4 x^{5} - 8 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $-\,7^{8}\cdot 13^{2}\cdot 211$ | $D_4\wr C_3$ (as 12T222) | trivial |
12.2.206487484375.1 | $x^{12} - x^{11} + 2 x^{10} + x^{9} - 3 x^{8} + 8 x^{7} - 13 x^{6} + 16 x^{5} - 17 x^{4} + 13 x^{3} - 8 x^{2} + 3 x - 1$ | $-\,5^{6}\cdot 79\cdot 409^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.2.208976546875.1 | $x^{12} - 2 x^{11} + 4 x^{10} - 5 x^{9} + 4 x^{8} + x^{7} - 9 x^{6} + 18 x^{5} - 22 x^{4} + 19 x^{3} - 12 x^{2} + 5 x - 1$ | $-\,5^{6}\cdot 19\cdot 839^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.2.225117671875.1 | $x^{12} - x^{10} - x^{9} - x^{8} + 3 x^{7} + 3 x^{6} - 2 x^{4} - 2 x^{3} - 1$ | $-\,5^{6}\cdot 179\cdot 80489$ | $S_6\wr C_2$ (as 12T299) | trivial |
12.2.233544944483.1 | $x^{12} - 3 x^{11} + 2 x^{10} + 5 x^{9} - 9 x^{8} + 3 x^{7} + 6 x^{6} - 7 x^{5} + 3 x^{4} + x^{3} - x^{2} + x - 1$ | $-\,23^{4}\cdot 101\cdot 8263$ | $A_4^3.(C_2\times S_4)$ (as 12T294) | trivial |
12.2.238362687139.1 | $x^{12} - 2 x^{11} + 4 x^{10} - 4 x^{9} + x^{8} + 3 x^{7} - 8 x^{6} + 7 x^{5} - 3 x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ | $-\,23^{4}\cdot 317\cdot 2687$ | $A_4^3.(C_2\times S_4)$ (as 12T294) | trivial |
12.2.239557046875.1 | $x^{12} - x^{10} - x^{9} + 2 x^{7} - 2 x^{6} + x^{4} + x^{3} - x + 1$ | $-\,5^{6}\cdot 19\cdot 806929$ | $S_6\wr C_2$ (as 12T299) | trivial |
12.2.247087671875.1 | $x^{12} - x^{11} - 3 x^{9} + x^{7} + 3 x^{6} + x^{5} - 3 x^{3} - x + 1$ | $-\,5^{6}\cdot 11^{3}\cdot 109^{2}$ | $D_6\wr C_2$ (as 12T125) | trivial |
12.2.255609008128.1 | $x^{12} - 2 x^{11} + 3 x^{10} - 4 x^{9} + 7 x^{8} - 8 x^{7} - 2 x^{6} + 18 x^{5} - 28 x^{4} + 22 x^{3} - 11 x^{2} + 4 x - 1$ | $-\,2^{12}\cdot 23^{4}\cdot 223$ | $C_2\wr S_4$ (as 12T227) | trivial |
12.2.257978421875.1 | $x^{12} - 2 x^{11} + 2 x^{9} - 5 x^{7} + 10 x^{6} - 16 x^{5} + 20 x^{4} - 19 x^{3} + 12 x^{2} - 5 x + 1$ | $-\,5^{6}\cdot 23^{4}\cdot 59$ | $C_2\wr D_6$ (as 12T193) | trivial |
12.2.266846228071.1 | $x^{12} - x^{11} + 2 x^{10} - 3 x^{9} + 3 x^{8} - 4 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ | $-\,31\cdot 92779^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.2.273636802651.1 | $x^{12} - x^{11} + 5 x^{10} - 4 x^{9} + 12 x^{8} - 6 x^{7} + 15 x^{6} - 6 x^{5} + 9 x^{4} - 5 x^{3} + x^{2} - 3 x - 1$ | $-\,283^{3}\cdot 12073$ | $S_3\wr S_4$ (as 12T289) | trivial |
12.2.279198105664.1 | $x^{12} - 5 x^{10} + 9 x^{8} - 7 x^{6} + x^{4} + 3 x^{2} - 1$ | $-\,2^{6}\cdot 257^{4}$ | $C_2\wr S_4$ (as 12T227) | trivial |
12.2.288323843827.1 | $x^{12} - 3 x^{11} + 8 x^{9} - 6 x^{8} - 7 x^{7} + 10 x^{6} + x^{5} - 7 x^{4} + x^{3} + 4 x^{2} - 1$ | $-\,283^{3}\cdot 12721$ | $S_3\wr S_4$ (as 12T289) | trivial |
12.2.293890894259.1 | $x^{12} - x^{9} - x^{4} + x + 1$ | $-\,103\cdot 2853309653$ | $S_{12}$ (as 12T301) | trivial |
12.2.299095170283.1 | $x^{12} - 2 x^{11} + 4 x^{10} - x^{9} - 2 x^{8} + 6 x^{7} - 4 x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 1$ | $-\,7^{8}\cdot 13^{2}\cdot 307$ | $D_4\wr C_3$ (as 12T222) | trivial |
12.2.307980921875.1 | $x^{12} - 2 x^{11} + 3 x^{10} - 7 x^{9} + 12 x^{8} - 12 x^{7} + 13 x^{6} - 12 x^{5} + 5 x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1$ | $-\,5^{6}\cdot 11^{3}\cdot 59\cdot 251$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.2.314972378176.1 | $x^{12} - x^{10} - 3 x^{8} + x^{6} + 3 x^{4} - x^{2} - 1$ | $-\,2^{6}\cdot 31^{4}\cdot 73^{2}$ | $C_2\wr D_6$ (as 12T186) | trivial |
12.2.327779546875.1 | $x^{12} - 2 x^{11} + 2 x^{10} - 3 x^{9} + x^{8} + x^{7} + x^{4} - x^{3} + x^{2} + x - 1$ | $-\,5^{6}\cdot 11^{3}\cdot 15761$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.2.336393921875.1 | $x^{12} - x^{11} - x^{10} - x^{9} + 3 x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - x^{3} - x^{2} - x + 1$ | $-\,5^{6}\cdot 11\cdot 1399^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.2.341962230519.1 | $x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 31 x^{8} - 43 x^{7} + 52 x^{6} - 56 x^{5} + 52 x^{4} - 39 x^{3} + 21 x^{2} - 7 x + 1$ | $-\,3^{3}\cdot 7^{8}\cdot 13^{3}$ | $C_4^3:C_6$ (as 12T141) | trivial |
12.2.349257427087.1 | $x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 9 x^{8} - 12 x^{7} + 18 x^{6} - 18 x^{5} + 14 x^{4} - 9 x^{3} + 5 x^{2} - 2 x - 1$ | $-\,127\cdot 229^{4}$ | $C_2\wr S_4$ (as 12T227) | trivial |
12.2.353996898304.1 | $x^{12} - 2 x^{11} + x^{10} + 4 x^{7} - 4 x^{6} + 2 x^{5} - 2 x^{4} + 4 x^{2} - 4 x + 1$ | $-\,2^{18}\cdot 7^{3}\cdot 31\cdot 127$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.2.362031460339.1 | $x^{12} - x^{7} + x^{6} + 2 x^{5} - 2 x^{4} + x^{3} - x^{2} - x + 1$ | $-\,362031460339$ | $S_{12}$ (as 12T301) | trivial |
12.2.373065296875.1 | $x^{12} - 2 x^{11} - 2 x^{10} + 8 x^{9} - 12 x^{7} + 3 x^{6} + 11 x^{5} - 5 x^{4} - 6 x^{3} + 3 x^{2} + x - 1$ | $-\,5^{6}\cdot 19^{3}\cdot 59^{2}$ | $D_6\wr C_2$ (as 12T125) | trivial |
12.2.396228830787.1 | $x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 3 x^{7} - x^{6} + 3 x^{4} + x^{3} - 3 x^{2} - x + 1$ | $-\,3^{3}\cdot 23^{4}\cdot 229^{2}$ | $C_2\wr D_6$ (as 12T186) | trivial |
12.2.398786546875.1 | $x^{12} - 3 x^{11} + 4 x^{10} - 3 x^{9} + 4 x^{8} - 7 x^{7} + 7 x^{6} - x^{5} - 4 x^{4} + 4 x^{3} - x^{2} + x - 1$ | $-\,5^{6}\cdot 19^{3}\cdot 61^{2}$ | $D_6\wr C_2$ (as 12T125) | trivial |
12.2.417344000000.1 | $x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + x^{8} - 4 x^{7} + 4 x^{6} + 5 x^{4} - 6 x^{3} + x^{2} + 1$ | $-\,2^{12}\cdot 5^{6}\cdot 6521$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.2.419159399791.1 | $x^{12} - 2 x^{11} + 3 x^{9} - 2 x^{8} - x^{7} + x^{6} - x^{5} + x^{4} + 2 x^{3} - 2 x^{2} + 1$ | $-\,11^{4}\cdot 31^{5}$ | $C_2 \times S_4$ (as 12T22) | trivial |
12.2.438976000000.1 | $x^{12} - x^{11} + 2 x^{10} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 6 x^{5} - 3 x^{4} + 2 x^{2} - x + 1$ | $-\,2^{12}\cdot 5^{6}\cdot 19^{3}$ | $D_6\wr C_2$ (as 12T125) | trivial |
12.2.447330484375.1 | $x^{12} - 2 x^{11} + x^{10} - 3 x^{9} + 8 x^{8} - 3 x^{7} - 2 x^{6} - 4 x^{5} + 2 x^{4} + 9 x^{3} - 9 x^{2} + 4 x - 1$ | $-\,5^{6}\cdot 31^{5}$ | $(C_6\times C_2):C_2$ (as 12T13) | trivial |
12.2.451992187175.1 | $x^{12} - x^{11} + 4 x^{10} + x^{9} - x^{8} + 12 x^{7} - 9 x^{6} + 12 x^{5} - x^{4} + x^{3} + 4 x^{2} - x + 1$ | $-\,5^{2}\cdot 23^{5}\cdot 53^{2}$ | $C_2\wr S_4$ (as 12T223) | trivial |
12.2.458342033107.1 | $x^{12} - 3 x^{11} + 2 x^{10} + 3 x^{9} - 6 x^{8} + 3 x^{7} + 4 x^{6} - 10 x^{5} + 8 x^{4} - x^{3} - 2 x^{2} + x - 1$ | $-\,7^{8}\cdot 43^{3}$ | $C_2^3.(C_2\times A_4)$ (as 12T104) | trivial |
12.2.458342033107.2 | $x^{12} - 4 x^{11} + 6 x^{10} - 4 x^{9} + x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$ | $-\,7^{8}\cdot 43^{3}$ | $C_2^3.(C_2\times A_4)$ (as 12T104) | trivial |
12.2.530569362483.1 | $x^{12} - x^{11} + x^{10} - 3 x^{9} + 6 x^{8} - 7 x^{7} + 4 x^{6} - 6 x^{5} + 10 x^{4} - 11 x^{3} + 5 x^{2} + x - 1$ | $-\,3^{4}\cdot 17^{2}\cdot 283^{3}$ | $C_3^3:(S_3\times S_4)$ (as 12T258) | trivial |
12.2.533806460928.1 | $x^{12} - 5 x^{11} + 13 x^{10} - 23 x^{9} + 31 x^{8} - 32 x^{7} + 27 x^{6} - 17 x^{5} + 8 x^{4} - 2 x^{3} + x - 1$ | $-\,2^{12}\cdot 3^{3}\cdot 13^{6}$ | $S_3\times D_4$ (as 12T28) | trivial |
12.2.562523516779.1 | $x^{12} - 2 x^{11} - x^{10} + 7 x^{9} - 5 x^{8} - 6 x^{7} + 11 x^{6} - 3 x^{5} - 5 x^{4} + 6 x^{3} - 2 x^{2} - x + 1$ | $-\,7^{8}\cdot 97579$ | $S_4\wr C_3$ (as 12T292) | trivial |
12.2.566636000000.1 | $x^{12} - 4 x^{10} - x^{9} + 7 x^{8} + 4 x^{7} - 5 x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - x^{2} - 3 x + 1$ | $-\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 59$ | $C_2\wr D_6$ (as 12T193) | trivial |
12.2.620200350784.1 | $x^{12} + 3 x^{10} + 5 x^{8} + 5 x^{6} + x^{4} - x^{2} - 1$ | $-\,2^{6}\cdot 7^{8}\cdot 41^{2}$ | $D_4\wr C_3$ (as 12T222) | trivial |
12.2.644204000000.1 | $x^{12} - 3 x^{11} + 3 x^{10} - x^{9} - 3 x^{8} + 4 x^{7} - x^{6} + 8 x^{5} - 7 x^{4} - 3 x^{3} - 2 x^{2} + 4 x - 1$ | $-\,2^{8}\cdot 5^{6}\cdot 11^{5}$ | $(C_6\times C_2):C_2$ (as 12T13) | trivial |
12.2.644204000000.2 | $x^{12} - 3 x^{11} + 2 x^{10} + 4 x^{9} - 7 x^{8} + 2 x^{7} + 3 x^{6} + 2 x^{5} - 7 x^{4} + 4 x^{3} + 2 x^{2} - 3 x + 1$ | $-\,2^{8}\cdot 5^{6}\cdot 11^{5}$ | $D_6:D_6$ (as 12T81) | trivial |
12.2.659081523200.1 | $x^{12} - 2 x^{11} + 5 x^{10} - 2 x^{9} + 6 x^{8} - 2 x^{7} + 11 x^{6} + 2 x^{5} - x^{4} + 2 x^{3} + 4 x - 1$ | $-\,2^{12}\cdot 5^{2}\cdot 23^{5}$ | $C_2^3:S_4$ (as 12T100) | trivial |
12.2.713607421387.1 | $x^{12} - 4 x^{10} - 2 x^{9} + 6 x^{8} + 10 x^{7} - x^{6} - 13 x^{5} - 9 x^{4} + 4 x^{3} + 9 x^{2} + 5 x + 1$ | $-\,7^{8}\cdot 123787$ | $S_4\wr C_3$ (as 12T292) | trivial |