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 |
---|---|---|---|---|
14.2.52058057626129.1 | $x^{14} - 2 x^{13} + 3 x^{12} - 4 x^{11} + 4 x^{10} - 4 x^{9} + 4 x^{8} - 5 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$ | $7215127^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.54815765790289.1 | $x^{14} + x^{12} - 2 x^{8} - x^{7} - 2 x^{6} + x^{2} + 1$ | $7^{2}\cdot 1057681^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.55059380046329.1 | $x^{14} - 4 x^{13} + 6 x^{12} - x^{11} - 10 x^{10} + 18 x^{9} - 18 x^{8} + 15 x^{7} - 13 x^{6} + 11 x^{5} - 8 x^{4} + 6 x^{3} - 3 x^{2} + 1$ | $277^{2}\cdot 569\cdot 1123^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.62662828387597.1 | $x^{14} - x^{13} - 3 x^{12} + 5 x^{11} + 2 x^{10} - 11 x^{9} + 4 x^{8} + 11 x^{7} - 11 x^{6} - 2 x^{5} + 10 x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$ | $167^{2}\cdot 1213\cdot 1361^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.63097400703125.1 | $x^{14} - 3 x^{13} + 2 x^{12} + 4 x^{11} - 8 x^{10} + 2 x^{9} + 8 x^{8} - 10 x^{7} + x^{6} + 7 x^{5} - 6 x^{4} + x^{3} + 2 x^{2} - x + 1$ | $5^{7}\cdot 807646729$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.2.68537510017457.1 | $x^{14} - 4 x^{13} + 10 x^{12} - 15 x^{11} + 11 x^{10} + 6 x^{9} - 26 x^{8} + 35 x^{7} - 26 x^{6} + 6 x^{5} + 11 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$ | $13^{4}\cdot 17\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.78352380449344.1 | $x^{14} - 2 x^{12} + x^{10} + 2 x^{8} - 3 x^{6} + x^{4} - 1$ | $2^{6}\cdot 23^{2}\cdot 73^{2}\cdot 659^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.94241555580481.1 | $x^{14} - x^{12} - 2 x^{9} + 3 x^{7} - 2 x^{5} - x^{2} + 1$ | $43^{2}\cdot 401^{2}\cdot 563^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.94724481953125.1 | $x^{14} - x^{13} - 2 x^{12} + 5 x^{11} + 2 x^{10} - 9 x^{9} + 2 x^{8} + 10 x^{7} - 6 x^{6} - 6 x^{5} + 7 x^{4} + x^{3} - 4 x^{2} + 1$ | $5^{7}\cdot 199\cdot 6092831$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.2.103886084489093.1 | $x^{14} - 3 x^{12} - 3 x^{11} + 6 x^{10} + 7 x^{9} - 5 x^{8} - 12 x^{7} + 2 x^{6} + 11 x^{5} + x^{4} - 7 x^{3} - 2 x^{2} + 4 x - 1$ | $53\cdot 977^{2}\cdot 1433^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.116768679686993.1 | $x^{14} - 3 x^{13} + 7 x^{12} - 14 x^{11} + 21 x^{10} - 29 x^{9} + 35 x^{8} - 37 x^{7} + 35 x^{6} - 29 x^{5} + 21 x^{4} - 14 x^{3} + 7 x^{2} - 3 x + 1$ | $257\cdot 674057^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.154291569457229.1 | $x^{14} - x^{13} + x^{12} - 2 x^{11} + 2 x^{10} - 3 x^{9} + 3 x^{8} - 3 x^{7} + 3 x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} - x + 1$ | $29\cdot 107^{2}\cdot 21557^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.160805685121205.1 | $x^{14} + x^{12} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} + x^{2} + 1$ | $5\cdot 41^{2}\cdot 138319^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.2.212764932023296.1 | $x^{14} - x^{10} + x^{8} + x^{2} - 1$ | $2^{10}\cdot 455827^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.245928712415581.1 | $x^{14} - x^{13} + 4 x^{12} - x^{11} + 3 x^{10} + 3 x^{9} - 4 x^{8} + 9 x^{7} - 16 x^{6} + 14 x^{5} - 21 x^{4} + 10 x^{3} - 9 x^{2} + 2 x - 1$ | $13^{4}\cdot 61\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.321952970703125.1 | $x^{14} - 3 x^{13} + 2 x^{12} + 3 x^{11} - 7 x^{10} + 11 x^{9} - 25 x^{8} + 33 x^{7} - 4 x^{6} - 56 x^{5} + 93 x^{4} - 78 x^{3} + 38 x^{2} - 10 x + 1$ | $5^{9}\cdot 37^{2}\cdot 347^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.2.386441371953125.1 | $x^{14} - x^{13} - 2 x^{12} + 4 x^{11} - 2 x^{10} - 3 x^{9} + x^{8} + 6 x^{6} - 11 x^{5} + 5 x^{4} - 12 x^{3} + 24 x^{2} - 20 x + 5$ | $5^{7}\cdot 53^{2}\cdot 1327^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.2.391066968923137.1 | $x^{14} - 4 x^{13} + 5 x^{12} + 4 x^{11} - 14 x^{10} + 5 x^{9} + 13 x^{8} - 9 x^{7} - 9 x^{6} + 8 x^{5} + 4 x^{4} - 5 x^{3} + x - 1$ | $13^{4}\cdot 97\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.422859037223221.1 | $x^{14} - 2 x^{13} - 4 x^{12} + 6 x^{11} + 10 x^{10} - 3 x^{9} - 19 x^{8} - 6 x^{7} + 27 x^{6} - x^{5} - 20 x^{4} + 9 x^{3} + 4 x^{2} - 4 x + 1$ | $71^{6}\cdot 3301$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.2.493856488203125.1 | $x^{14} - 2 x^{13} + 6 x^{11} - 3 x^{10} - 8 x^{9} + 13 x^{8} + 4 x^{7} - 16 x^{6} + 7 x^{5} + 13 x^{4} - 11 x^{3} - 4 x^{2} + 6 x - 1$ | $5^{7}\cdot 43^{6}$ | $D_{14}$ (as 14T3) | trivial |
14.2.508017475013049.1 | $x^{14} - x^{11} - x^{10} - 4 x^{9} + x^{7} - 4 x^{5} - x^{4} - x^{3} + 1$ | $3^{2}\cdot 2741^{4}$ | $C_2^6:\GL(3,2)$ (as 14T50) | trivial |
14.2.511335829405696.1 | $x^{14} + x^{12} - 3 x^{10} - 2 x^{8} + 5 x^{6} + 2 x^{4} - 2 x^{2} - 1$ | $2^{16}\cdot 19^{2}\cdot 4649^{2}$ | $C_2^6.S_7$ (as 14T55) | trivial |
14.2.552331698375977.1 | $x^{14} - 4 x^{13} + 8 x^{12} - 10 x^{11} + 5 x^{10} + 3 x^{9} - 10 x^{8} + 7 x^{7} - x^{6} - 2 x^{5} + 5 x^{4} + x^{2} + 3 x + 1$ | $13^{4}\cdot 109^{4}\cdot 137$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.729722900774101.1 | $x^{14} - 3 x^{12} - x^{11} + 10 x^{10} - x^{9} - 10 x^{8} + 2 x^{7} + 10 x^{6} + 5 x^{5} - 4 x^{4} - 2 x^{3} + 3 x^{2} + 2 x - 1$ | $13^{4}\cdot 109^{4}\cdot 181$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.788759961620480.1 | $x^{14} - x^{13} - x^{11} + x^{10} + 2 x^{9} - 3 x^{8} + 3 x^{7} - 3 x^{6} + 2 x^{5} + x^{4} - x^{3} - x + 1$ | $2^{12}\cdot 5\cdot 443^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.842608211391089.1 | $x^{14} - 2 x^{13} - x^{12} + 3 x^{11} - 3 x^{10} + 4 x^{9} + x^{8} + 5 x^{7} + x^{6} + 4 x^{5} - 3 x^{4} + 3 x^{3} - x^{2} - 2 x + 1$ | $11\cdot 13^{4}\cdot 19\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.890987630226941.1 | $x^{14} - 2 x^{13} + 2 x^{12} - 6 x^{10} + x^{9} + 4 x^{8} - 13 x^{7} + 4 x^{6} + x^{5} - 6 x^{4} + 2 x^{2} - 2 x + 1$ | $13^{5}\cdot 17\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.923240576117509.1 | $x^{14} - 5 x^{13} + 11 x^{12} - 16 x^{11} + 18 x^{10} - 21 x^{9} + 27 x^{8} - 31 x^{7} + 27 x^{6} - 21 x^{5} + 18 x^{4} - 16 x^{3} + 11 x^{2} - 5 x + 1$ | $13^{4}\cdot 109^{4}\cdot 229$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.923240576117509.2 | $x^{14} - x^{13} + 3 x^{12} - 3 x^{11} + 3 x^{10} - 10 x^{9} + 16 x^{8} - 27 x^{7} + 33 x^{6} - 21 x^{5} + 10 x^{4} + 3 x^{3} - 10 x^{2} + 3 x + 1$ | $13^{4}\cdot 109^{4}\cdot 229$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.959588563913537.1 | $x^{14} - 6 x^{13} + 15 x^{12} - 18 x^{11} - x^{10} + 52 x^{9} - 125 x^{8} + 189 x^{7} - 217 x^{6} + 198 x^{5} - 146 x^{4} + 83 x^{3} - 33 x^{2} + 8 x - 1$ | $17\cdot 2741^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.971619994953361.1 | $x^{14} - 6 x^{13} + 15 x^{12} - 22 x^{11} + 26 x^{10} - 41 x^{9} + 81 x^{8} - 135 x^{7} + 173 x^{6} - 172 x^{5} + 130 x^{4} - 75 x^{3} + 32 x^{2} - 9 x + 1$ | $13^{4}\cdot 109^{4}\cdot 241$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.973177856947837.1 | $x^{14} - 3 x^{13} + 3 x^{12} - 13 x^{10} + 27 x^{9} - 4 x^{8} - 31 x^{7} + 36 x^{6} - 14 x^{5} - 13 x^{4} + 22 x^{3} - 15 x^{2} + 6 x - 1$ | $71^{7}\cdot 107$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.2.1068249673759921.1 | $x^{14} + x^{12} - x^{10} + 2 x^{8} - 7 x^{6} + x^{4} + 3 x^{2} - 1$ | $5717^{4}$ | $C_2^3:\GL(3,2)$ (as 14T34) | trivial |
14.2.1116758251460917.1 | $x^{14} - 3 x^{13} + 5 x^{12} - 2 x^{11} - 5 x^{10} + 12 x^{9} - 3 x^{8} - 3 x^{7} + 11 x^{6} - 4 x^{4} - x^{3} - 3 x^{2} - 3 x - 1$ | $13^{4}\cdot 109^{4}\cdot 277$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.1261896507968473.1 | $x^{14} - 5 x^{13} + 12 x^{12} - 21 x^{11} + 29 x^{10} - 34 x^{9} + 36 x^{8} - 37 x^{7} + 36 x^{6} - 34 x^{5} + 29 x^{4} - 21 x^{3} + 12 x^{2} - 5 x + 1$ | $13^{4}\cdot 109^{4}\cdot 313$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.1261896507968473.2 | $x^{14} - 3 x^{13} + 7 x^{12} - 15 x^{11} + 25 x^{10} - 36 x^{9} + 45 x^{8} - 49 x^{7} + 45 x^{6} - 36 x^{5} + 25 x^{4} - 15 x^{3} + 7 x^{2} - 3 x + 1$ | $13^{4}\cdot 109^{4}\cdot 313$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.1278022980913757.1 | $x^{14} - 3 x^{13} + 8 x^{12} - 17 x^{11} + 29 x^{10} - 36 x^{9} + 38 x^{8} - 23 x^{7} - 3 x^{6} + 35 x^{5} - 46 x^{4} + 42 x^{3} - 21 x^{2} + 8 x - 1$ | $13^{4}\cdot 109^{4}\cdot 317$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.2.1328264921546161.1 | $x^{14} - 2 x^{12} - 3 x^{10} + 10 x^{8} - 6 x^{6} - 5 x^{4} + 7 x^{2} - 1$ | $6037^{4}$ | $C_2^3:\GL(3,2)$ (as 14T34) | trivial |
14.2.2098795051761664.1 | $x^{14} - 2 x^{12} + 2 x^{10} + x^{6} - 3 x^{4} + x^{2} - 1$ | $2^{14}\cdot 71^{6}$ | $C_2^6:D_7$ (as 14T28) | trivial |
14.2.2098795051761664.2 | $x^{14} + x^{12} - x^{10} - x^{8} - x^{6} + x^{4} + 2 x^{2} - 1$ | $2^{14}\cdot 71^{6}$ | $C_2^6:D_7$ (as 14T28) | trivial |
14.2.2647140367335424.1 | $x^{14} - 3 x^{12} + x^{10} + x^{8} - x^{6} + 7 x^{4} - x^{2} - 1$ | $2^{18}\cdot 317^{4}$ | $C_2^6:\GL(3,2)$ (as 14T50) | trivial |
14.2.3329851404800000.1 | $x^{14} - 3 x^{13} + 4 x^{12} - 5 x^{11} + 5 x^{10} + 2 x^{9} - 9 x^{8} + 7 x^{7} - 3 x^{6} + 2 x^{5} - 7 x^{4} + 5 x^{3} - 4 x^{2} + x - 1$ | $2^{12}\cdot 5^{5}\cdot 127^{4}$ | $C_2^4:\GL(3,2)$ (as 14T43) | trivial |
14.2.3405373945327868.1 | $x^{14} - 2 x^{13} + x^{12} + x^{11} - 3 x^{10} + 2 x^{9} + x^{8} - 3 x^{7} + 3 x^{6} + x^{5} - 3 x^{4} + x^{3} + x^{2} - 2 x - 1$ | $2^{2}\cdot 571\cdot 1490969328077$ | $S_{14}$ (as 14T63) | trivial |
14.2.4396746947664269.1 | $x^{14} - x^{13} - x^{12} + 2 x^{11} + 2 x^{10} - 9 x^{9} + 5 x^{8} + x^{7} + 5 x^{6} - 9 x^{5} + 2 x^{4} + 2 x^{3} - x^{2} - x + 1$ | $11^{8}\cdot 29^{5}$ | $C_2^7.A_7$ (as 14T56) | trivial |
14.2.5712803040866857.1 | $x^{14} - 3 x^{13} + 8 x^{12} - 15 x^{11} + 24 x^{10} - 26 x^{9} + 23 x^{8} - 22 x^{7} + 23 x^{6} - 22 x^{5} + 9 x^{4} - 7 x^{3} + 3 x^{2} - 6 x - 1$ | $13^{5}\cdot 109^{5}$ | $C_2\times \GL(3,2)$ (as 14T17) | trivial |
14.2.5712803040866857.2 | $x^{14} - 3 x^{13} + 8 x^{12} - 13 x^{11} + 15 x^{10} - 14 x^{9} - x^{7} - 14 x^{5} + 15 x^{4} - 13 x^{3} + 8 x^{2} - 3 x + 1$ | $13^{5}\cdot 109^{5}$ | $C_2\times \GL(3,2)$ (as 14T17) | trivial |
14.2.7108512163632049.1 | $x^{14} - 2 x^{13} - 5 x^{12} + 15 x^{11} + 5 x^{10} - 44 x^{9} + 17 x^{8} + 66 x^{7} - 51 x^{6} - 56 x^{5} + 54 x^{4} + 33 x^{3} - 14 x^{2} + x + 5$ | $17^{6}\cdot 131^{4}$ | $C_2^6:A_7$ (as 14T53) | trivial |
14.2.7729847623880704.1 | $x^{14} - 5 x^{13} + 7 x^{12} + x^{11} - x^{10} - 9 x^{9} - 23 x^{8} + 61 x^{7} - 38 x^{6} + 22 x^{5} - 24 x^{4} + 10 x^{3} - 4 x^{2} + 2 x - 2$ | $2^{12}\cdot 7^{2}\cdot 443^{4}$ | $C_2^6:\GL(3,2)$ (as 14T50) | trivial |
14.2.9242067299140625.1 | $x^{14} - 2 x^{13} + 5 x^{12} - 5 x^{11} + 8 x^{10} - 10 x^{9} + x^{8} - 2 x^{7} - 5 x^{6} + 8 x^{5} + 10 x^{4} + 2 x^{3} - 6 x^{2} - x + 1$ | $5^{7}\cdot 4909^{3}$ | $D_7 \wr C_2$ (as 14T20) | trivial |
14.2.9604489472586752.1 | $x^{14} - 2 x^{13} + x^{12} + x^{11} - 3 x^{10} + 2 x^{9} + x^{8} - 4 x^{7} + 3 x^{6} + 2 x^{5} - 3 x^{4} + x^{3} + x^{2} - 2 x - 1$ | $2^{10}\cdot 2109097\cdot 4447109$ | $S_{14}$ (as 14T63) | trivial |