Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
6.4.92779.1 | $x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - x^{2} - 2 x + 1$ | $-\,92779$ | $S_6$ (as 6T16) | trivial |
6.4.94363.1 | $x^{6} - 2 x^{4} - 2 x^{3} + 3 x + 1$ | $-\,197\cdot 479$ | $S_6$ (as 6T16) | trivial |
6.4.103243.1 | $x^{6} - x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x - 1$ | $-\,7^{4}\cdot 43$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.104483.1 | $x^{6} - x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - x + 1$ | $-\,163\cdot 641$ | $S_6$ (as 6T16) | trivial |
6.4.104875.1 | $x^{6} - 2 x^{5} - x^{4} + x^{3} + 2 x^{2} + x - 1$ | $-\,5^{3}\cdot 839$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.118987.1 | $x^{6} - x^{5} + 4 x^{3} - 2 x^{2} - 2 x + 1$ | $-\,11\cdot 29\cdot 373$ | $S_6$ (as 6T16) | trivial |
6.4.124659.1 | $x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,3^{8}\cdot 19$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.133787.1 | $x^{6} - 3 x^{5} + 2 x^{4} - x^{2} + 3 x - 1$ | $-\,353\cdot 379$ | $S_6$ (as 6T16) | trivial |
6.4.144875.1 | $x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - 3 x + 1$ | $-\,5^{3}\cdot 19\cdot 61$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.149875.1 | $x^{6} - 3 x^{4} - 2 x^{3} + x^{2} + 3 x + 1$ | $-\,5^{3}\cdot 11\cdot 109$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.153664.1 | $x^{6} - x^{4} - 2 x^{2} + 1$ | $-\,2^{6}\cdot 7^{4}$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.158875.1 | $x^{6} - 2 x^{3} - 5 x^{2} + 1$ | $-\,5^{3}\cdot 31\cdot 41$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.161939.1 | $x^{6} - 2 x^{5} + x^{4} - 2 x^{3} - x^{2} + 3 x - 1$ | $-\,67\cdot 2417$ | $S_6$ (as 6T16) | trivial |
6.4.170471.1 | $x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 3 x^{2} + x + 1$ | $-\,7^{4}\cdot 71$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.174875.1 | $x^{6} - x^{5} - 2 x^{4} + 4 x^{3} + x^{2} - 3 x - 1$ | $-\,5^{3}\cdot 1399$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.187904.1 | $x^{6} - 4 x^{4} - 2 x^{3} + 3 x^{2} + 2 x - 1$ | $-\,2^{9}\cdot 367$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.188875.1 | $x^{6} - x^{5} - 4 x^{3} + 2 x^{2} + 2 x - 1$ | $-\,5^{3}\cdot 1511$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.195379.1 | $x^{6} + x^{4} - 2 x^{3} - 3 x^{2} + x + 1$ | $-\,47\cdot 4157$ | $S_6$ (as 6T16) | trivial |
6.4.199283.1 | $x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,7^{4}\cdot 83$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.202375.1 | $x^{6} - 2 x^{5} - 2 x^{4} + 5 x^{3} - x^{2} - 3 x + 1$ | $-\,5^{3}\cdot 1619$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.209107.1 | $x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 2 x + 1$ | $-\,67\cdot 3121$ | $S_6$ (as 6T16) | trivial |
6.4.214747.1 | $x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x + 1$ | $-\,13\cdot 16519$ | $S_6$ (as 6T16) | trivial |
6.4.214875.1 | $x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x^{2} + 2 x + 1$ | $-\,3^{2}\cdot 5^{3}\cdot 191$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.215811.1 | $x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + x^{2} + 3 x + 1$ | $-\,3^{3}\cdot 7993$ | $S_6$ (as 6T16) | trivial |
6.4.216587.1 | $x^{6} - x^{5} - x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 1$ | $-\,7\cdot 30941$ | $S_6$ (as 6T16) | trivial |
6.4.217024.1 | $x^{6} - 2 x^{3} - 3 x^{2} + 4 x - 1$ | $-\,2^{6}\cdot 3391$ | $S_6$ (as 6T16) | trivial |
6.4.218491.1 | $x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + 2 x + 1$ | $-\,7^{5}\cdot 13$ | $A_4\times C_2$ (as 6T6) | trivial |
6.4.221875.1 | $x^{6} - 2 x^{5} + 3 x - 1$ | $-\,5^{5}\cdot 71$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.225403.1 | $x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,17\cdot 13259$ | $S_6$ (as 6T16) | trivial |
6.4.228544.1 | $x^{6} - 2 x^{5} + 4 x^{3} - 3 x^{2} - 2 x + 1$ | $-\,2^{6}\cdot 3571$ | $S_6$ (as 6T16) | trivial |
6.4.233003.1 | $x^{6} - 3 x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ | $-\,41\cdot 5683$ | $S_6$ (as 6T16) | trivial |
6.4.237179.1 | $x^{6} - x^{5} - 3 x^{4} + 2 x^{2} + 3 x + 1$ | $-\,237179$ | $S_6$ (as 6T16) | trivial |
6.4.238507.1 | $x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 4 x^{2} - 2 x - 1$ | $-\,19\cdot 12553$ | $S_6$ (as 6T16) | trivial |
6.4.242467.1 | $x^{6} - x^{4} - x^{3} - 2 x^{2} + x + 1$ | $-\,242467$ | $S_6$ (as 6T16) | trivial |
6.4.254875.1 | $x^{6} - x^{5} - 4 x^{4} + 5 x^{3} + 3 x^{2} - 4 x - 1$ | $-\,5^{3}\cdot 2039$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.255179.1 | $x^{6} - 2 x^{5} - x^{4} + 3 x^{2} + 3 x - 1$ | $-\,255179$ | $S_6$ (as 6T16) | trivial |
6.4.255823.1 | $x^{6} - x^{5} - x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$ | $-\,109\cdot 2347$ | $S_6$ (as 6T16) | trivial |
6.4.257339.1 | $x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} - x + 1$ | $-\,257339$ | $S_6$ (as 6T16) | trivial |
6.4.257344.1 | $x^{6} - 2 x^{5} + 2 x^{3} - 3 x^{2} + 1$ | $-\,2^{6}\cdot 4021$ | $S_6$ (as 6T16) | trivial |
6.4.259283.1 | $x^{6} - 2 x^{5} - x^{4} + 3 x^{3} - 2 x^{2} + x + 1$ | $-\,251\cdot 1033$ | $S_6$ (as 6T16) | trivial |
6.4.262375.1 | $x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 1$ | $-\,5^{3}\cdot 2099$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.264931.1 | $x^{6} - x^{5} - 3 x^{4} + 2 x^{3} + x^{2} + 2 x - 1$ | $-\,264931$ | $S_6$ (as 6T16) | trivial |
6.4.269395.1 | $x^{6} - x^{5} - 2 x^{4} + 2 x + 1$ | $-\,5\cdot 7\cdot 43\cdot 179$ | $S_6$ (as 6T16) | trivial |
6.4.288576.1 | $x^{6} - 2 x^{5} - x^{2} + 2 x + 1$ | $-\,2^{6}\cdot 3^{3}\cdot 167$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.295643.1 | $x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 2 x^{2} - 4 x + 1$ | $-\,239\cdot 1237$ | $S_6$ (as 6T16) | trivial |
6.4.302123.1 | $x^{6} - x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ | $-\,302123$ | $S_6$ (as 6T16) | trivial |
6.4.302375.1 | $x^{6} - x^{4} - 3 x^{3} - x^{2} + 4 x + 1$ | $-\,5^{3}\cdot 41\cdot 59$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.4.303619.1 | $x^{6} - x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + 2 x - 1$ | $-\,303619$ | $S_6$ (as 6T16) | trivial |
6.4.304859.1 | $x^{6} - x^{4} - 3 x^{3} + 3 x - 1$ | $-\,83\cdot 3673$ | $S_6$ (as 6T16) | trivial |
6.4.304927.1 | $x^{6} - 2 x^{5} + 2 x^{3} - 7 x^{2} + 6 x - 1$ | $-\,7^{4}\cdot 127$ | $A_4\times C_2$ (as 6T6) | trivial |