Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
12.0.41223887921.1 | $x^{12} - 2 x^{11} + 2 x^{10} - x^{9} + 2 x^{8} - 5 x^{7} + 8 x^{6} - 7 x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ | $37^{2}\cdot 41\cdot 857^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.0.41479432225.1 | $x^{12} - 4 x^{11} + 8 x^{10} - 11 x^{9} + 12 x^{8} - 9 x^{7} + 3 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{3} - x + 1$ | $5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 23^{4}$ | $C_2^2\wr S_3$ (as 12T139) | trivial |
12.0.42058512657.1 | $x^{12} + 2 x^{10} - x^{9} + x^{8} - 5 x^{7} + 6 x^{6} - 10 x^{5} + 13 x^{4} - 10 x^{3} + 7 x^{2} - 4 x + 1$ | $3^{6}\cdot 7^{2}\cdot 73\cdot 127^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.0.42194001221.1 | $x^{12} - 3 x^{11} + 7 x^{10} - 12 x^{9} + 17 x^{8} - 21 x^{7} + 24 x^{6} - 24 x^{5} + 22 x^{4} - 17 x^{3} + 10 x^{2} - 4 x + 1$ | $41\cdot 1029121981$ | $S_{12}$ (as 12T301) | trivial |
12.0.42553255797.1 | $x^{12} - x^{9} + 5 x^{8} - 2 x^{7} - x^{6} - 7 x^{5} + 8 x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 1$ | $3^{6}\cdot 13^{3}\cdot 163^{2}$ | $C_3\wr D_4$ (as 12T167) | trivial |
12.0.42925852301.1 | $x^{12} - x^{11} - 2 x^{10} + 3 x^{9} + x^{8} - x^{7} - x^{6} - 2 x^{5} + 3 x^{4} + 2 x^{3} - 2 x^{2} - x + 1$ | $79\cdot 543365219$ | $S_{12}$ (as 12T301) | trivial |
12.0.44223092609.1 | $x^{12} - x^{11} + x^{9} - 2 x^{8} + x^{7} + 3 x^{4} - x^{3} - 2 x^{2} + 1$ | $89\cdot 22291^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.0.44533203125.1 | $x^{12} - 2 x^{11} + 7 x^{10} - 7 x^{9} + 14 x^{8} - 6 x^{7} + 13 x^{6} - 2 x^{5} + 10 x^{4} - 2 x^{3} + 5 x^{2} - x + 1$ | $5^{9}\cdot 151^{2}$ | $C_3\wr C_4$ (as 12T131) | trivial |
12.0.45425463296.1 | $x^{12} - 2 x^{11} + 2 x^{9} - 2 x^{8} + 3 x^{6} - 2 x^{4} - 2 x^{3} + 2 x + 1$ | $2^{12}\cdot 89\cdot 353^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.0.45539379833.1 | $x^{12} - x^{11} - x^{9} + 3 x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 3 x^{4} - x^{3} - x + 1$ | $17\cdot 73^{2}\cdot 709^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.0.46060985097.1 | $x^{12} - 5 x^{11} + 12 x^{10} - 19 x^{9} + 24 x^{8} - 27 x^{7} + 28 x^{6} - 24 x^{5} + 15 x^{4} - 5 x^{3} + x^{2} - x + 1$ | $3^{6}\cdot 337\cdot 433^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.0.46110822453.1 | $x^{12} - 2 x^{11} + x^{10} + x^{9} + x^{8} - 5 x^{7} + 6 x^{6} - 4 x^{5} + 4 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$ | $3^{6}\cdot 63252157$ | $S_6\wr C_2$ (as 12T299) | trivial |
12.0.46574387721.1 | $x^{12} - x^{11} - x^{10} + x^{9} + 2 x^{8} - 3 x^{6} + 2 x^{4} + x^{3} - x^{2} - x + 1$ | $3^{6}\cdot 7993^{2}$ | $S_6\times C_2$ (as 12T219) | trivial |
12.0.46580196393.1 | $x^{12} - 3 x^{10} - x^{9} + 5 x^{8} + x^{7} - 7 x^{6} - x^{5} + 8 x^{4} + 2 x^{3} - 4 x^{2} - x + 1$ | $3^{6}\cdot 157\cdot 406981$ | $S_6\wr C_2$ (as 12T299) | trivial |
12.0.46716936381.1 | $x^{12} - 4 x^{11} + 9 x^{10} - 15 x^{9} + 23 x^{8} - 33 x^{7} + 44 x^{6} - 50 x^{5} + 45 x^{4} - 29 x^{3} + 13 x^{2} - 4 x + 1$ | $3^{6}\cdot 23^{4}\cdot 229$ | $C_2\wr D_6$ (as 12T193) | trivial |
12.0.46779109213.1 | $x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 8 x^{8} - 3 x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - x^{3} + 2 x^{2} - x + 1$ | $31^{4}\cdot 37^{3}$ | $C_4\wr S_3$ (as 12T150) | trivial |
12.0.46911328256.1 | $x^{12} - 2 x^{9} + 4 x^{8} - 4 x^{7} + x^{6} + 4 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$ | $2^{12}\cdot 13^{4}\cdot 401$ | $A_4^2:D_4$ (as 12T208) | trivial |
12.0.47724987301.1 | $x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 16 x^{8} - 19 x^{7} + 20 x^{6} - 18 x^{5} + 15 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ | $61\cdot 83^{2}\cdot 337^{2}$ | $C_2^6.S_6$ (as 12T293) | trivial |
12.0.47738317081.1 | $x^{12} - 3 x^{11} + x^{10} + 7 x^{9} - 8 x^{8} - 4 x^{7} + 13 x^{6} - 4 x^{5} - 8 x^{4} + 7 x^{3} + x^{2} - 3 x + 1$ | $7^{10}\cdot 13^{2}$ | $C_2^2 \times A_4$ (as 12T25) | trivial |
12.0.48737056617.1 | $x^{12} - 2 x^{11} + 5 x^{10} - 10 x^{9} + 16 x^{8} - 22 x^{7} + 30 x^{6} - 31 x^{5} + 28 x^{4} - 27 x^{3} + 19 x^{2} - 7 x + 1$ | $3^{9}\cdot 19^{5}$ | $C_6\wr C_2$ (as 12T42) | trivial |
12.0.50551744653.1 | $x^{12} - 4 x^{11} + 11 x^{10} - 21 x^{9} + 32 x^{8} - 40 x^{7} + 45 x^{6} - 46 x^{5} + 40 x^{4} - 26 x^{3} + 12 x^{2} - 4 x + 1$ | $3^{6}\cdot 37^{5}$ | $C_6\wr C_2$ (as 12T42) | trivial |
12.0.51067940737.1 | $x^{12} - 3 x^{11} + 6 x^{10} - 10 x^{9} + 15 x^{8} - 18 x^{7} + 20 x^{6} - 19 x^{5} + 16 x^{4} - 12 x^{3} + 7 x^{2} - 3 x + 1$ | $11^{2}\cdot 31^{4}\cdot 457$ | $C_2\wr (C_2\times S_4)$ (as 12T250) | trivial |
12.0.51514924901.1 | $x^{12} - 2 x^{11} - x^{10} + 2 x^{9} + 4 x^{8} - x^{7} - 7 x^{6} + x^{5} + 4 x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ | $11^{2}\cdot 31^{4}\cdot 461$ | $C_2\wr (C_2\times S_4)$ (as 12T250) | trivial |
12.0.53440955929.1 | $x^{12} - x^{11} + x^{10} - 3 x^{9} + 4 x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - x + 1$ | $19^{2}\cdot 23^{6}$ | $C_2\times S_4$ (as 12T21) | trivial |
12.0.54507773961.1 | $x^{12} - x^{11} - 2 x^{10} + 5 x^{9} - x^{8} - 4 x^{7} + 5 x^{6} - 4 x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - x + 1$ | $3^{6}\cdot 8647^{2}$ | $S_6\times C_2$ (as 12T219) | trivial |
12.0.55358453125.1 | $x^{12} - 4 x^{11} + 11 x^{10} - 22 x^{9} + 35 x^{8} - 45 x^{7} + 49 x^{6} - 44 x^{5} + 33 x^{4} - 21 x^{3} + 11 x^{2} - 4 x + 1$ | $5^{6}\cdot 61\cdot 241^{2}$ | $S_4^2:D_4$ (as 12T260) | trivial |
12.0.56689952000.1 | $x^{12} - 5 x^{11} + 13 x^{10} - 25 x^{9} + 39 x^{8} - 50 x^{7} + 53 x^{6} - 48 x^{5} + 37 x^{4} - 23 x^{3} + 12 x^{2} - 4 x + 1$ | $2^{8}\cdot 5^{3}\cdot 11^{6}$ | $(C_6\times C_2):C_2$ (as 12T15) | trivial |
12.0.58300115053.1 | $x^{12} - x^{11} + 4 x^{10} - 4 x^{9} + 9 x^{8} - 6 x^{7} + 11 x^{6} - 6 x^{5} + 8 x^{4} - 3 x^{3} + 4 x^{2} - x + 1$ | $23^{4}\cdot 208333$ | $A_4^3.(C_2\times S_4)$ (as 12T294) | trivial |
12.0.59081901957.1 | $x^{12} - 3 x^{11} + 5 x^{10} - 6 x^{9} + 5 x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 4 x^{4} + 2 x^{3} - x + 1$ | $3^{6}\cdot 13^{3}\cdot 37\cdot 997$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.0.59182215273.1 | $x^{12} - 5 x^{11} + 14 x^{10} - 31 x^{9} + 53 x^{8} - 72 x^{7} + 81 x^{6} - 72 x^{5} + 53 x^{4} - 31 x^{3} + 14 x^{2} - 5 x + 1$ | $3^{6}\cdot 433^{3}$ | $\SOPlus(4,2)$ (as 12T35) | trivial |
12.0.59767578125.1 | $x^{12} - 5 x^{11} + 13 x^{10} - 21 x^{9} + 24 x^{8} - 21 x^{7} + 18 x^{6} - 17 x^{5} + 15 x^{4} - 9 x^{3} + 4 x^{2} - 2 x + 1$ | $5^{9}\cdot 71\cdot 431$ | $S_3\wr C_4$ (as 12T264) | trivial |
12.0.60454515625.1 | $x^{12} - x^{11} - 2 x^{10} + 2 x^{9} + 4 x^{8} - 3 x^{7} - 5 x^{6} + 3 x^{5} + 5 x^{4} - x^{3} - 3 x^{2} + 1$ | $5^{6}\cdot 7^{2}\cdot 281^{2}$ | $S_4^2:C_2^2$ (as 12T236) | trivial |
12.0.63518590021.1 | $x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{5} - x^{4} + 2 x^{2} - x + 1$ | $23^{4}\cdot 61^{3}$ | $C_4\wr S_3$ (as 12T150) | trivial |
12.0.63568613376.1 | $x^{12} - 4 x^{11} + 9 x^{10} - 14 x^{9} + 16 x^{8} - 14 x^{7} + 10 x^{6} - 6 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ | $2^{12}\cdot 3^{6}\cdot 61\cdot 349$ | $S_3\wr C_2^2$ (as 12T261) | trivial |
12.0.63853279857.1 | $x^{12} - 4 x^{11} + 9 x^{10} - 13 x^{9} + 17 x^{8} - 21 x^{7} + 25 x^{6} - 27 x^{5} + 26 x^{4} - 20 x^{3} + 12 x^{2} - 5 x + 1$ | $3^{6}\cdot 23^{4}\cdot 313$ | $C_2\wr D_6$ (as 12T193) | trivial |
12.0.63995902381.1 | $x^{12} - x^{11} + 2 x^{9} - x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ | $73^{2}\cdot 229^{3}$ | $C_3\wr S_4$ (as 12T231) | trivial |
12.0.66468114161.1 | $x^{12} - x^{11} - 2 x^{10} + 4 x^{9} + x^{8} - 5 x^{7} + x^{6} + 5 x^{5} + x^{4} - 4 x^{3} - 2 x^{2} + x + 1$ | $23^{6}\cdot 449$ | $C_2\wr S_3$ (as 12T135) | trivial |
12.0.66699927001.1 | $x^{12} - x^{9} + x^{7} - x^{4} - x^{3} + x + 1$ | $47\cdot 1117\cdot 1270499$ | $S_{12}$ (as 12T301) | trivial |
12.0.67030763409.1 | $x^{12} - x^{11} - 2 x^{10} + 6 x^{8} - x^{7} - 5 x^{6} - x^{5} + 6 x^{4} - 2 x^{2} - x + 1$ | $3^{6}\cdot 43^{2}\cdot 223^{2}$ | $S_6\times C_2$ (as 12T219) | trivial |
12.0.69637938597.1 | $x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} + 4 x^{6} - 11 x^{5} + 17 x^{4} - 16 x^{3} + 11 x^{2} - 5 x + 1$ | $3^{6}\cdot 19^{4}\cdot 733$ | $A_4^2:D_4$ (as 12T208) | trivial |
12.0.70127513856.1 | $x^{12} + x^{10} - 3 x^{8} - 3 x^{6} + 2 x^{4} + 2 x^{2} + 1$ | $2^{8}\cdot 3^{6}\cdot 613^{2}$ | $S_4^2:C_2^2$ (as 12T236) | trivial |
12.0.70516271401.1 | $x^{12} - 3 x^{11} + 4 x^{10} - x^{9} - 3 x^{8} + 4 x^{7} - 3 x^{6} + 4 x^{5} - 3 x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ | $37^{2}\cdot 7177^{2}$ | $C_2^5:S_6$ (as 12T285) | trivial |
12.0.71939651121.1 | $x^{12} - x^{11} - 3 x^{10} + x^{9} + 5 x^{8} + 3 x^{7} - 3 x^{6} - 7 x^{5} - 2 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ | $3^{6}\cdot 13^{3}\cdot 44917$ | $S_3\wr D_4$ (as 12T274) | trivial |
12.0.72509192309.1 | $x^{12} - x^{10} - x^{9} + x^{7} + x^{6} + x^{5} - 2 x^{3} - x^{2} + x + 1$ | $72509192309$ | $S_{12}$ (as 12T301) | trivial |
12.0.73358639104.1 | $x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + 6 x^{8} - 10 x^{7} + 10 x^{6} - 12 x^{5} + 17 x^{4} - 14 x^{3} + 8 x^{2} - 4 x + 1$ | $2^{18}\cdot 23^{4}$ | $C_2 \times S_4$ (as 12T23) | trivial |
12.0.73645476129.1 | $x^{12} - x^{11} - x^{10} + 2 x^{9} - 2 x^{7} + 3 x^{5} - 2 x^{4} + 2 x^{2} - 2 x + 1$ | $3^{6}\cdot 19^{2}\cdot 23^{4}$ | $C_2^2\times S_4$ (as 12T48) | trivial |
12.0.74733890625.1 | $x^{12} - 6 x^{11} + 21 x^{10} - 50 x^{9} + 93 x^{8} - 138 x^{7} + 164 x^{6} - 153 x^{5} + 111 x^{4} - 61 x^{3} + 24 x^{2} - 6 x + 1$ | $3^{14}\cdot 5^{6}$ | $D_6$ (as 12T3) | trivial |
12.0.74880094208.1 | $x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + 5 x^{8} - 10 x^{7} + 14 x^{6} - 16 x^{5} + 17 x^{4} - 14 x^{3} + 9 x^{2} - 4 x + 1$ | $2^{12}\cdot 17^{3}\cdot 61^{2}$ | $C_3\wr D_4$ (as 12T167) | trivial |
12.0.74948100349.1 | $x^{12} - x^{11} - x^{10} + 2 x^{9} + 2 x^{8} - 5 x^{7} + 3 x^{6} + 2 x^{4} - 6 x^{3} + 7 x^{2} - 4 x + 1$ | $79^{2}\cdot 229^{3}$ | $C_3\wr S_4$ (as 12T231) | trivial |
12.0.75794375168.1 | $x^{12} - 4 x^{11} + 9 x^{10} - 12 x^{9} + 14 x^{8} - 19 x^{7} + 30 x^{6} - 39 x^{5} + 37 x^{4} - 26 x^{3} + 14 x^{2} - 5 x + 1$ | $2^{9}\cdot 23^{6}$ | $(C_6\times C_2):C_2$ (as 12T15) | trivial |