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 |
---|---|---|---|---|
7.3.612233.1 | $x^{7} - x^{6} + x^{5} - x^{3} + x^{2} - x - 1$ | $71\cdot 8623$ | $S_7$ (as 7T7) | trivial |
7.3.612569.1 | $x^{7} - 3 x^{5} - x^{4} + 3 x^{3} + 1$ | $593\cdot 1033$ | $S_7$ (as 7T7) | trivial |
7.3.640681.1 | $x^{7} - 2 x^{6} + 2 x^{5} - 3 x^{3} + 2 x^{2} - 1$ | $59\cdot 10859$ | $S_7$ (as 7T7) | trivial |
7.3.649177.1 | $x^{7} - x^{6} - x^{4} + 3 x^{2} - 1$ | $59\cdot 11003$ | $S_7$ (as 7T7) | trivial |
7.3.661033.1 | $x^{7} - x^{6} - x^{5} + 2 x^{3} + x^{2} - 2 x - 1$ | $173\cdot 3821$ | $S_7$ (as 7T7) | trivial |
7.3.674057.1 | $x^{7} - 3 x^{6} + 5 x^{5} - 6 x^{4} + 3 x^{3} - x^{2} - x + 1$ | $674057$ | $S_7$ (as 7T7) | trivial |
7.3.689033.1 | $x^{7} - x^{5} - 3 x^{4} - x^{3} + 2 x^{2} + 2 x + 1$ | $689033$ | $S_7$ (as 7T7) | trivial |
7.3.696401.1 | $x^{7} - x^{6} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 1$ | $109\cdot 6389$ | $S_7$ (as 7T7) | trivial |
7.3.724873.1 | $x^{7} - x^{6} + x^{4} - 2 x^{3} + x^{2} - 1$ | $31\cdot 67\cdot 349$ | $S_7$ (as 7T7) | trivial |
7.3.726721.1 | $x^{7} - x^{6} + 2 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$ | $79\cdot 9199$ | $S_7$ (as 7T7) | trivial |
7.3.746633.1 | $x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 4 x^{3} - 2 x^{2} + x + 1$ | $127\cdot 5879$ | $S_7$ (as 7T7) | trivial |
7.3.753209.1 | $x^{7} - x^{6} - x^{5} + 4 x^{4} - 3 x^{3} - x^{2} + 3 x - 1$ | $37\cdot 20357$ | $S_7$ (as 7T7) | trivial |
7.3.763993.1 | $x^{7} - x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x + 1$ | $113\cdot 6761$ | $S_7$ (as 7T7) | trivial |
7.3.765529.1 | $x^{7} - 2 x^{6} + 3 x^{4} - 4 x^{3} + 2 x - 1$ | $19\cdot 43\cdot 937$ | $S_7$ (as 7T7) | trivial |
7.3.780401.1 | $x^{7} - 2 x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$ | $780401$ | $S_7$ (as 7T7) | trivial |
7.3.788857.1 | $x^{7} - x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + 2 x - 1$ | $31\cdot 25447$ | $S_7$ (as 7T7) | trivial |
7.3.789289.1 | $x^{7} - x^{4} - 2 x^{3} + 1$ | $79\cdot 97\cdot 103$ | $S_7$ (as 7T7) | trivial |
7.3.792873.1 | $x^{7} - 2 x^{6} + 2 x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - 1$ | $3^{2}\cdot 37\cdot 2381$ | $S_7$ (as 7T7) | trivial |
7.3.794233.1 | $x^{7} - x^{5} - 3 x^{4} - x^{3} + 3 x^{2} + x - 1$ | $11\cdot 103\cdot 701$ | $S_7$ (as 7T7) | trivial |
7.3.796753.1 | $x^{7} - x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - x - 1$ | $41\cdot 19433$ | $S_7$ (as 7T7) | trivial |
7.3.819713.1 | $x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{3} + 3 x^{2} - 1$ | $41\cdot 19993$ | $S_7$ (as 7T7) | trivial |
7.3.830801.1 | $x^{7} - 2 x^{6} + x^{5} + x^{4} - 3 x^{3} + 2 x^{2} - 1$ | $830801$ | $S_7$ (as 7T7) | trivial |
7.3.838289.1 | $x^{7} - 3 x^{5} - x^{4} + 3 x^{3} - 2 x + 1$ | $521\cdot 1609$ | $S_7$ (as 7T7) | trivial |
7.3.877193.1 | $x^{7} - x^{6} - 2 x^{5} + x^{4} + 2 x^{3} + x^{2} - 2 x - 1$ | $739\cdot 1187$ | $S_7$ (as 7T7) | trivial |
7.3.891169.1 | $x^{7} - x^{6} - x^{5} + 2 x^{4} - 3 x^{2} + 1$ | $149\cdot 5981$ | $S_7$ (as 7T7) | trivial |
7.3.909673.1 | $x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 2 x^{3} - x^{2} - x + 1$ | $23\cdot 39551$ | $S_7$ (as 7T7) | trivial |
7.3.909929.1 | $x^{7} - 2 x^{5} - x^{4} + 4 x^{3} + 2 x^{2} - 2 x - 1$ | $19\cdot 83\cdot 577$ | $S_7$ (as 7T7) | trivial |
7.3.919969.1 | $x^{7} - 2 x^{6} - x^{5} + 3 x^{4} + x^{3} - 3 x^{2} - x + 1$ | $919969$ | $S_7$ (as 7T7) | trivial |
7.3.941177.1 | $x^{7} - 2 x^{5} + x^{3} - x^{2} - x + 1$ | $113\cdot 8329$ | $S_7$ (as 7T7) | trivial |
7.3.970129.1 | $x^{7} - x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - 2 x^{2} - x + 1$ | $571\cdot 1699$ | $S_7$ (as 7T7) | trivial |
7.3.983441.1 | $x^{7} - 2 x^{5} - x^{4} - x^{3} + x^{2} + 2 x + 1$ | $983441$ | $S_7$ (as 7T7) | trivial |
7.3.995173.1 | $x^{7} - 3 x^{5} - x^{4} + 2 x^{3} + 3 x^{2} - 1$ | $995173$ | $S_7$ (as 7T7) | trivial |
7.3.1011913.1 | $x^{7} - x^{6} - x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ | $7\cdot 37\cdot 3907$ | $S_7$ (as 7T7) | trivial |
7.3.1016777.1 | $x^{7} - x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 3 x^{2} + x + 1$ | $1016777$ | $S_7$ (as 7T7) | trivial |
7.3.1018217.1 | $x^{7} - x^{6} + x^{5} - 3 x^{4} - x^{2} + x + 1$ | $1018217$ | $S_7$ (as 7T7) | trivial |
7.3.1026801.1 | $x^{7} - x^{6} - x^{5} - x^{4} + x^{3} + x^{2} + 1$ | $3^{2}\cdot 114089$ | $S_7$ (as 7T7) | trivial |
7.3.1033441.1 | $x^{7} - x^{6} + x^{4} - x^{2} - 2 x + 1$ | $1033441$ | $S_7$ (as 7T7) | trivial |
7.3.1045573.1 | $x^{7} - x^{6} - x^{5} + 2 x^{4} + x^{3} - 2 x^{2} - 2 x + 1$ | $1045573$ | $S_7$ (as 7T7) | trivial |
7.3.1047017.1 | $x^{7} - 2 x^{5} - 2 x^{4} + x^{3} + x^{2} + x + 1$ | $41\cdot 25537$ | $S_7$ (as 7T7) | trivial |
7.3.1048193.1 | $x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1$ | $1048193$ | $S_7$ (as 7T7) | trivial |
7.3.1063369.1 | $x^{7} - x^{6} - x^{5} - x^{3} + x^{2} + x + 1$ | $499\cdot 2131$ | $S_7$ (as 7T7) | trivial |
7.3.1069193.1 | $x^{7} - 2 x^{5} - 2 x^{4} + 3 x^{3} + 2 x^{2} - 2 x - 1$ | $1069193$ | $S_7$ (as 7T7) | trivial |
7.3.1072033.1 | $x^{7} - x^{5} - x^{4} - x^{3} - x^{2} + x + 1$ | $43\cdot 107\cdot 233$ | $S_7$ (as 7T7) | trivial |
7.3.1078193.1 | $x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + x - 1$ | $19\cdot 56747$ | $S_7$ (as 7T7) | trivial |
7.3.1084313.1 | $x^{7} - x^{6} + 2 x^{4} - 2 x^{3} - 1$ | $1084313$ | $S_7$ (as 7T7) | trivial |
7.3.1087369.1 | $x^{7} - x^{6} - x^{5} + 3 x^{4} - 2 x^{3} - x^{2} + x - 1$ | $137\cdot 7937$ | $S_7$ (as 7T7) | trivial |
7.3.1104217.1 | $x^{7} - 3 x^{6} + 6 x^{5} - 7 x^{4} + 4 x^{3} - 3 x + 1$ | $1104217$ | $S_7$ (as 7T7) | trivial |
7.3.1106461.1 | $x^{7} - 2 x^{6} + x^{5} + 2 x^{4} - 3 x^{3} + x^{2} - 1$ | $23\cdot 73\cdot 659$ | $S_7$ (as 7T7) | trivial |
7.3.1121929.1 | $x^{7} - x^{6} - x^{5} - x^{4} + 2 x^{3} - 2 x^{2} + 1$ | $163\cdot 6883$ | $S_7$ (as 7T7) | trivial |
7.3.1123273.1 | $x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{3} + 2 x^{2} - x - 1$ | $263\cdot 4271$ | $S_7$ (as 7T7) | trivial |