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 |
---|---|---|---|---|
14.0.9095120158391.1 | $x^{14} - 7 x^{13} + 25 x^{12} - 59 x^{11} + 103 x^{10} - 141 x^{9} + 159 x^{8} - 153 x^{7} + 129 x^{6} - 95 x^{5} + 58 x^{4} - 27 x^{3} + 10 x^{2} - 3 x + 1$ | $-\,71^{7}$ | $D_{7}$ (as 14T2) | trivial |
14.0.9669040949311.1 | $x^{14} - x^{13} + 3 x^{12} - 6 x^{11} + 5 x^{10} - 9 x^{9} + 11 x^{8} - 7 x^{7} + 11 x^{6} - 9 x^{5} + 5 x^{4} - 6 x^{3} + 3 x^{2} - x + 1$ | $-\,19^{2}\cdot 79\cdot 18413^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.0.9745585291264.1 | $x^{14} - 4 x^{13} + 7 x^{12} - 4 x^{11} - 8 x^{10} + 24 x^{9} - 30 x^{8} + 16 x^{7} + 13 x^{6} - 38 x^{5} + 46 x^{4} - 36 x^{3} + 19 x^{2} - 6 x + 1$ | $-\,2^{14}\cdot 29^{6}$ | $C_7 \wr C_2$ (as 14T8) | trivial |
14.0.9866941650479.1 | $x^{14} - 3 x^{13} + 6 x^{12} - 11 x^{11} + 16 x^{10} - 21 x^{9} + 25 x^{8} - 25 x^{7} + 25 x^{6} - 21 x^{5} + 16 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ | $-\,167^{2}\cdot 191\cdot 1361^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.0.11856232199187.1 | $x^{14} - x^{13} + x^{12} - x^{10} - x^{9} + x^{8} - x^{7} - x^{6} + 3 x^{5} - 2 x^{4} + x^{3} + x^{2} - x + 1$ | $-\,3^{7}\cdot 5421231001$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.0.12985240103739.1 | $x^{14} - x^{13} + x^{12} - 4 x^{11} + 4 x^{10} - 2 x^{9} + 5 x^{8} - 6 x^{7} + 2 x^{6} - 2 x^{5} + 5 x^{4} - 2 x^{3} - x + 1$ | $-\,3^{7}\cdot 5937466897$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.0.13048447346663.1 | $x^{14} - x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + x^{8} - x^{7} + x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} - x + 1$ | $-\,23\cdot 37^{2}\cdot 20357^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.0.13824820988163.1 | $x^{14} - 3 x^{13} + 8 x^{12} - 18 x^{11} + 32 x^{10} - 52 x^{9} + 70 x^{8} - 81 x^{7} + 82 x^{6} - 70 x^{5} + 52 x^{4} - 31 x^{3} + 16 x^{2} - 6 x + 1$ | $-\,3^{7}\cdot 43^{6}$ | $C_7 \wr C_2$ (as 14T8) | trivial |
14.0.16973485041483.1 | $x^{14} - 2 x^{13} + 2 x^{12} - 6 x^{11} + 8 x^{10} - 4 x^{9} + 9 x^{8} - 11 x^{7} + 6 x^{6} - 6 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} + 1$ | $-\,3^{7}\cdot 37^{2}\cdot 2381^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.0.22139206005899.1 | $x^{14} - 3 x^{13} + 4 x^{12} - 2 x^{11} + x^{10} - 4 x^{9} + 9 x^{8} - 11 x^{7} + 9 x^{6} - 4 x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ | $-\,59\cdot 593^{2}\cdot 1033^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.0.28466647927227.1 | $x^{14} - x^{13} + 2 x^{12} + 3 x^{11} - x^{10} + 4 x^{9} + 3 x^{8} + 2 x^{7} + 2 x^{4} - 2 x^{3} - x^{2} + 1$ | $-\,3^{7}\cdot 114089^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.0.30270895108587.1 | $x^{14} - 4 x^{13} + 6 x^{12} - 3 x^{11} - 6 x^{10} + 14 x^{9} - 12 x^{8} + 2 x^{7} + 10 x^{6} - 8 x^{5} - 3 x^{4} + x^{3} + 7 x^{2} - 5 x + 1$ | $-\,3^{7}\cdot 7^{12}$ | $C_7 \wr C_2$ (as 14T8) | trivial |
14.0.51902598731283.1 | $x^{14} - 2 x^{13} + 3 x^{12} - 6 x^{11} + 6 x^{10} - 4 x^{9} + 3 x^{8} + x^{7} - x^{5} + 3 x^{4} + 3 x^{2} + x + 1$ | $-\,3^{11}\cdot 17117^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
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 |
14.0.56316949686099.1 | $x^{14} - 2 x^{13} + 6 x^{12} - 11 x^{11} + 19 x^{10} - 26 x^{9} + 33 x^{8} - 35 x^{7} + 33 x^{6} - 26 x^{5} + 19 x^{4} - 10 x^{3} + 6 x^{2} - x + 1$ | $-\,3^{7}\cdot 2953^{3}$ | $D_7 \wr C_2$ (as 14T20) | 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 |
14.0.74532401109963.1 | $x^{14} - x^{13} + 2 x^{12} - x^{11} + 2 x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - 3 x^{5} - x^{3} + 2 x^{2} + x + 1$ | $-\,3^{7}\cdot 184607^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.0.76600746490099.1 | $x^{14} - 2 x^{13} + 6 x^{12} - 8 x^{11} + 16 x^{10} - 17 x^{9} + 24 x^{8} - 21 x^{7} + 24 x^{6} - 17 x^{5} + 16 x^{4} - 8 x^{3} + 6 x^{2} - 2 x + 1$ | $-\,13^{4}\cdot 19\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (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 |
14.0.118236562059083.1 | $x^{14} - 3 x^{13} + 2 x^{12} + 3 x^{11} - 5 x^{10} - x^{9} + x^{8} + 2 x^{7} + 11 x^{6} - 13 x^{5} + 6 x^{4} - 8 x^{3} + 4 x^{2} + 1$ | $-\,13\cdot 71^{7}$ | $C_2\wr D_7$ (as 14T38) | 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 |
14.0.172575877556547.1 | $x^{14} - x^{13} - x^{12} + 2 x^{10} + x^{9} - x^{8} - x^{7} - x^{6} + x^{5} + 2 x^{4} - x^{2} - x + 1$ | $-\,3^{7}\cdot 280909^{2}$ | $S_7\times C_2$ (as 14T49) | 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 |
14.4.250058750499647.1 | $x^{14} - 2 x^{13} + x^{12} - x^{11} + x^{10} - 4 x^{9} + 9 x^{8} - 9 x^{7} + 9 x^{6} - 4 x^{5} + x^{4} - x^{3} + x^{2} - 2 x + 1$ | $-\,47\cdot 107^{2}\cdot 21557^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.0.263657868936003.1 | $x^{14} + x^{12} - 2 x^{11} - x^{10} + 3 x^{7} - x^{4} - 2 x^{3} + x^{2} + 1$ | $-\,3^{7}\cdot 103^{2}\cdot 3371^{2}$ | $S_7\times C_2$ (as 14T49) | trivial |
14.4.270118421833507.1 | $x^{14} - x^{13} - 3 x^{12} - x^{11} + x^{10} + 2 x^{8} + 7 x^{7} + 3 x^{6} + 4 x^{5} + 9 x^{4} + 7 x^{3} + x^{2} + 1$ | $-\,13^{4}\cdot 67\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.0.280155320935227.1 | $x^{14} - x^{13} + 2 x^{12} - x^{11} + 3 x^{10} - 4 x^{9} + 3 x^{8} - 4 x^{7} + 2 x^{6} - 4 x^{5} + 2 x^{4} + 5 x^{2} + 2 x + 1$ | $-\,3^{7}\cdot 71^{6}$ | $D_{14}$ (as 14T3) | trivial |
14.4.297261105546875.1 | $x^{14} - 3 x^{12} - x^{11} + 5 x^{10} + 3 x^{9} - 6 x^{8} - 6 x^{7} + 3 x^{6} + 7 x^{5} - 4 x^{3} - 2 x^{2} + x + 1$ | $-\,5^{7}\cdot 89\cdot 971\cdot 44029$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.0.318497840669359.1 | $x^{14} - 4 x^{13} + 8 x^{12} - 10 x^{11} + 15 x^{10} - 28 x^{9} + 42 x^{8} - 41 x^{7} + 32 x^{6} - 31 x^{5} + 37 x^{4} - 35 x^{3} + 21 x^{2} - 7 x + 1$ | $-\,13^{4}\cdot 79\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (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 |
14.4.334624313614643.1 | $x^{14} - x^{13} - 4 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 2 x^{8} - 12 x^{7} + x^{5} + 2 x^{4} + 6 x^{3} - 3 x^{2} + x - 1$ | $-\,13^{4}\cdot 83\cdot 109^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | 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 |
14.0.407483719072587.1 | $x^{14} - x^{13} + 4 x^{12} - x^{11} + 4 x^{10} + 2 x^{9} - 6 x^{8} + 3 x^{7} - 6 x^{6} + 2 x^{5} + 4 x^{4} - x^{3} + 4 x^{2} - x + 1$ | $-\,3^{15}\cdot 73^{4}$ | $A_7\times C_2$ (as 14T47) | trivial |
14.4.411650990546875.1 | $x^{14} - 3 x^{12} - 2 x^{11} + 5 x^{10} + 4 x^{9} - 6 x^{8} - 7 x^{7} + 7 x^{6} + 9 x^{5} - 4 x^{4} - 6 x^{3} + 2 x^{2} + 2 x - 1$ | $-\,5^{7}\cdot 24851\cdot 212029$ | $S_7\wr C_2$ (as 14T61) | 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 |
14.0.445660887761159.1 | $x^{14} - x^{13} + 6 x^{12} - 4 x^{11} + 12 x^{10} - 2 x^{9} + 11 x^{8} + 3 x^{7} + 11 x^{6} - 2 x^{5} + 12 x^{4} - 4 x^{3} + 6 x^{2} - x + 1$ | $-\,7^{2}\cdot 71^{7}$ | $C_2^6:D_7$ (as 14T27) | trivial |
14.0.489862582246303.1 | $x^{14} - 5 x^{13} + 18 x^{12} - 44 x^{11} + 89 x^{10} - 140 x^{9} + 190 x^{8} - 209 x^{7} + 201 x^{6} - 156 x^{5} + 104 x^{4} - 55 x^{3} + 23 x^{2} - 7 x + 1$ | $-\,7^{7}\cdot 29^{6}$ | $C_7 \wr C_2$ (as 14T8) | 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 |
14.4.498897726810659.1 | $x^{14} - 2 x^{13} + 3 x^{11} - 7 x^{10} + x^{9} + 14 x^{8} - 2 x^{7} - 13 x^{6} + 2 x^{5} + 4 x^{4} - 4 x^{3} + 3 x + 1$ | $-\,11^{3}\cdot 71^{2}\cdot 8623^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |