Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (50 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
13.3.5570916369223.1 | $x^{13} - x^{12} + x^{11} - 4 x^{10} + 5 x^{9} - 5 x^{8} + 6 x^{7} - 2 x^{6} - 5 x^{5} + 5 x^{4} - 7 x^{3} + 5 x^{2} - x + 1$ | $-\,5570916369223$ | $S_{13}$ (as 13T9) | trivial |
13.3.5717814639679.1 | $x^{13} - 2 x^{12} - 3 x^{11} + 7 x^{10} + 3 x^{9} - 7 x^{8} - 6 x^{7} + 4 x^{6} + 8 x^{5} - 3 x^{4} - 4 x^{3} + 2 x^{2} - 1$ | $-\,89\cdot 107\cdot 283\cdot 2121631$ | $S_{13}$ (as 13T9) | trivial |
13.3.6855574490939.1 | $x^{13} - x^{12} + 2 x^{11} + 2 x^{10} - 3 x^{9} + x^{8} - x^{7} - 8 x^{6} - 7 x^{5} - 6 x^{4} - 6 x^{3} - 6 x^{2} - 4 x - 1$ | $-\,1798333\cdot 3812183$ | $S_{13}$ (as 13T9) | trivial |
13.3.7805208559959.1 | $x^{13} - 4 x^{12} + 6 x^{11} - 6 x^{10} + 7 x^{9} - 5 x^{8} - x^{7} + x^{6} + 5 x^{5} - 2 x^{4} - 3 x^{3} - x^{2} + 1$ | $-\,3^{3}\cdot 31\cdot 71\cdot 821\cdot 159977$ | $S_{13}$ (as 13T9) | trivial |
13.3.9197165262683.1 | $x^{13} - 2 x^{10} + 2 x^{9} - x^{8} - 3 x^{7} - 3 x^{6} + 9 x^{5} - 10 x^{4} + 7 x^{3} + 1$ | $-\,82163\cdot 111938041$ | $S_{13}$ (as 13T9) | trivial |
13.3.14047799762079.1 | $x^{13} - 2 x^{12} + 2 x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 3 x^{4} - 2 x^{3} + 3 x^{2} - x - 1$ | $-\,3^{3}\cdot 16103\cdot 32310059$ | $S_{13}$ (as 13T9) | trivial |
13.3.18597951501632.1 | $x^{13} - 2 x^{12} + x^{11} + x^{10} - 6 x^{9} + 3 x^{8} + 7 x^{7} - 4 x^{6} + 4 x^{4} - 4 x^{3} - 4 x^{2} + x + 1$ | $-\,2^{6}\cdot 67\cdot 43517\cdot 99667$ | $S_{13}$ (as 13T9) | trivial |
13.3.21982001088443.1 | $x^{13} - x^{12} + x^{11} + 3 x^{10} - 8 x^{9} + 10 x^{8} - 6 x^{7} - 5 x^{6} + 15 x^{5} - 19 x^{4} + 15 x^{3} - 9 x^{2} + 3 x - 1$ | $-\,11^{2}\cdot 71\cdot 2558724373$ | $S_{13}$ (as 13T9) | trivial |
13.3.21990353102339.1 | $x^{13} - 2 x^{12} + 4 x^{11} - 5 x^{10} + 3 x^{9} + x^{8} - 4 x^{7} + 9 x^{6} - 7 x^{5} + 2 x^{4} - 4 x^{2} + 4 x - 1$ | $-\,157\cdot 3169\cdot 44198783$ | $S_{13}$ (as 13T9) | trivial |
13.3.34372007159104.1 | $x^{13} - x^{12} - 2 x^{11} + 5 x^{10} + x^{9} - 8 x^{8} + 5 x^{7} + 7 x^{6} - 2 x^{4} - 4 x - 1$ | $-\,2^{6}\cdot 29\cdot 239\cdot 77487031$ | $S_{13}$ (as 13T9) | trivial |
13.3.49047631346319.1 | $x^{13} - 2 x^{12} + 3 x^{11} + 2 x^{10} - 9 x^{9} + 12 x^{8} - 2 x^{7} - 19 x^{6} + 27 x^{5} - 19 x^{4} - x^{3} + 11 x^{2} - 6 x + 1$ | $-\,3\cdot 16349210448773$ | $S_{13}$ (as 13T9) | trivial |
13.3.53877019237375.1 | $x^{13} - 2 x^{12} - 4 x^{11} + 7 x^{10} + 6 x^{9} - 6 x^{8} - 6 x^{7} - 8 x^{6} + 8 x^{5} + 15 x^{4} - 7 x^{3} - 7 x^{2} + x + 1$ | $-\,5^{3}\cdot 204793\cdot 2104643$ | $S_{13}$ (as 13T9) | trivial |
13.3.60464861374756.1 | $x^{13} - x^{11} - 3 x^{10} - x^{9} + 4 x^{8} + 5 x^{7} - x^{6} - 6 x^{5} - 5 x^{4} + x^{3} + 4 x^{2} + 3 x + 1$ | $-\,2^{2}\cdot 15116215343689$ | $S_{13}$ (as 13T9) | trivial |
13.3.69188908404875.1 | $x^{13} - 3 x^{12} + 3 x^{11} - 3 x^{10} + 5 x^{9} + 2 x^{8} - 17 x^{7} + 10 x^{6} + 16 x^{5} - 16 x^{4} - 5 x^{3} + 7 x^{2} - 1$ | $-\,5^{3}\cdot 7^{5}\cdot 31\cdot 1062367$ | $S_{13}$ (as 13T9) | trivial |
13.3.96082590998375.1 | $x^{13} - 4 x^{11} - 3 x^{10} + 9 x^{9} + 10 x^{8} - 4 x^{7} - 12 x^{6} - 13 x^{5} + 5 x^{4} + 12 x^{3} - x + 1$ | $-\,5^{3}\cdot 768660727987$ | $S_{13}$ (as 13T9) | trivial |
13.3.105628246955776.1 | $x^{13} - x^{12} + 3 x^{11} - x^{10} + 3 x^{9} + 6 x^{8} - 6 x^{7} + x^{6} + 6 x^{5} - 8 x^{4} - 9 x^{3} + 2 x^{2} + 4 x + 1$ | $-\,2^{8}\cdot 257\cdot 1605487703$ | $S_{13}$ (as 13T9) | trivial |
13.3.114312593686528.1 | $x^{13} - x^{12} - 5 x^{11} + 15 x^{9} + 9 x^{8} - 28 x^{7} - 20 x^{6} + 26 x^{5} + 20 x^{4} - 12 x^{3} - 10 x^{2} + 2 x + 2$ | $-\,2^{14}\cdot 6977087017$ | $S_{13}$ (as 13T9) | trivial |
13.3.134713017952000.1 | $x^{13} - 5 x^{12} + 15 x^{11} - 34 x^{10} + 56 x^{9} - 79 x^{8} + 85 x^{7} - 78 x^{6} + 53 x^{5} - 25 x^{4} + 6 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,2^{8}\cdot 5^{3}\cdot 4209781811$ | $S_{13}$ (as 13T9) | trivial |
13.3.156408138976000.1 | $x^{13} - 3 x^{12} + 3 x^{11} - 4 x^{10} + 4 x^{9} + 7 x^{8} - 20 x^{7} + 27 x^{6} - 35 x^{5} + 41 x^{4} - 36 x^{3} + 24 x^{2} - 12 x + 4$ | $-\,2^{8}\cdot 5^{3}\cdot 137\cdot 599\cdot 59561$ | $S_{13}$ (as 13T9) | trivial |
13.3.215762905145828.1 | $x^{13} - 2 x^{12} + x^{11} + 5 x^{10} - 10 x^{9} + 4 x^{8} + 8 x^{7} - 13 x^{6} + 5 x^{5} + 10 x^{4} - 9 x^{3} - 3 x^{2} + 4 x + 1$ | $-\,2^{2}\cdot 953\cdot 10313\cdot 5488313$ | $S_{13}$ (as 13T9) | trivial |
13.3.509211272757248.1 | $x^{13} - x^{12} - 2 x^{11} - 2 x^{10} + 3 x^{9} + 4 x^{8} + 8 x^{7} - 4 x^{6} - 13 x^{5} + 3 x^{4} + 2 x^{3} - 6 x^{2} + x + 2$ | $-\,2^{14}\cdot 31079789597$ | $S_{13}$ (as 13T9) | trivial |
13.3.1990387975424000.1 | $x^{13} - x^{12} - 4 x^{11} - 2 x^{10} + 6 x^{9} + 3 x^{8} - x^{7} - 6 x^{6} + x^{4} + x^{3} - 12 x^{2} - 3 x + 1$ | $-\,2^{11}\cdot 5^{3}\cdot 84089\cdot 92461$ | $S_{13}$ (as 13T9) | trivial |
13.3.71106764206294000.1 | $x^{13} - 2 x^{12} - x^{11} + 4 x^{10} + 4 x^{9} + 5 x^{8} - 27 x^{7} - 6 x^{6} - 16 x^{5} + 80 x^{4} + 27 x^{3} - 13 x^{2} - 84 x - 36$ | $-\,2^{4}\cdot 5^{3}\cdot 241\cdot 147524407067$ | $S_{13}$ (as 13T9) | trivial |
13.3.142...435.1 | $x^{13} - 3 x - 1$ | $-\,5\cdot 226169\cdot 12570105664223$ | $S_{13}$ (as 13T9) | trivial |
13.3.597...896.1 | $x^{13} - 4 x - 2$ | $-\,2^{12}\cdot 11546071\cdot 12625811381$ | $S_{13}$ (as 13T9) | trivial |
13.3.598...931.1 | $x^{13} - 4 x - 1$ | $-\,23\cdot 17579\cdot 1479900843934943$ | $S_{13}$ (as 13T9) | trivial |
13.3.119...080.1 | $x^{13} - 8 x - 4$ | $-\,2^{12}\cdot 5\cdot 23\cdot 1993\cdot 1273413051689$ | $S_{13}$ (as 13T9) | trivial |
13.3.237...827.1 | $x^{13} - 6 x - 3$ | $-\,3^{12}\cdot 24749\cdot 180439539103$ | $S_{13}$ (as 13T9) | trivial |
13.3.553...256.1 | $x^{13} - 9 x - 4$ | $-\,2^{14}\cdot 43\cdot 7852028154455813$ | $S_{13}$ (as 13T9) | trivial |
13.3.107...427.1 | $x^{13} - 5 x - 3$ | $-\,3^{12}\cdot 37\cdot 1033\cdot 527906776207$ | $S_{13}$ (as 13T9) | trivial |
13.3.108...712.1 | $x^{13} - 5 x - 2$ | $-\,2^{12}\cdot 1373\cdot 4079\cdot 93893\cdot 5052637$ | $S_{13}$ (as 13T9) | trivial |
13.3.108...747.1 | $x^{13} - 5 x - 1$ | $-\,97\cdot 7489\cdot 14982677517575459$ | $S_{13}$ (as 13T9) | trivial |
13.3.278...112.1 | $x^{13} - 6 x - 4$ | $-\,2^{22}\cdot 7\cdot 11\cdot 86209262103439$ | $S_{13}$ (as 13T9) | trivial |
13.3.959...291.1 | $x^{13} - 7 x - 3$ | $-\,3^{11}\cdot 71\cdot 8627573\cdot 884392891$ | $S_{13}$ (as 13T9) | trivial |
13.3.116...808.1 | $x^{13} - 6 x - 2$ | $-\,2^{12}\cdot 7\cdot 29\cdot 1601\cdot 10211\cdot 8566846531$ | $S_{13}$ (as 13T9) | trivial |
13.3.116...843.1 | $x^{13} - 6 x - 1$ | $-\,7\cdot 106123\cdot 474647\cdot 330265270729$ | $S_{13}$ (as 13T9) | trivial |
13.3.196...483.1 | $x^{13} - 8 x - 1$ | $-\,196067122333410552143483$ | $S_{13}$ (as 13T9) | trivial |
13.3.215...976.1 | $x^{13} - 7 x - 2$ | $-\,2^{10}\cdot 6311\cdot 33418789974864709$ | $S_{13}$ (as 13T9) | trivial |
13.3.789...067.1 | $x^{13} - 7 x - 5$ | $-\,11\cdot 6389\cdot 11239887182523352373$ | $S_{13}$ (as 13T9) | trivial |
13.3.858...544.1 | $x^{13} - 7 x - 4$ | $-\,2^{25}\cdot 397\cdot 64468409915761$ | $S_{13}$ (as 13T9) | trivial |
13.3.863...939.1 | $x^{13} - 7 x - 1$ | $-\,1951\cdot 442784289501823599389$ | $S_{13}$ (as 13T9) | trivial |
13.3.424...320.1 | $x^{13} - 8 x - 6$ | $-\,2^{12}\cdot 3^{12}\cdot 5\cdot 11943947\cdot 32634517$ | $S_{13}$ (as 13T9) | trivial |
13.3.482...203.1 | $x^{13} - 8 x - 5$ | $-\,521\cdot 1231\cdot 7527444318037649653$ | $S_{13}$ (as 13T9) | trivial |
13.3.490...755.1 | $x^{13} - 8 x - 3$ | $-\,3^{12}\cdot 5\cdot 11\cdot 59\cdot 103\cdot 27594564189113$ | $S_{13}$ (as 13T9) | trivial |
13.3.490...040.1 | $x^{13} - 8 x - 2$ | $-\,2^{12}\cdot 5\cdot 239339688381919058023$ | $S_{13}$ (as 13T9) | trivial |
13.3.184...371.1 | $x^{13} - 9 x - 7$ | $-\,1531661\cdot 12059685344860216111$ | $S_{13}$ (as 13T9) | trivial |
13.3.220...216.1 | $x^{13} - 9 x - 6$ | $-\,2^{12}\cdot 3^{12}\cdot 182029\cdot 55532949839$ | $S_{13}$ (as 13T9) | trivial |
13.3.225...099.1 | $x^{13} - 9 x - 5$ | $-\,23\cdot 101\cdot 9724316372600271793313$ | $S_{13}$ (as 13T9) | trivial |
13.3.226...651.1 | $x^{13} - 9 x - 3$ | $-\,3^{12}\cdot 54469\cdot 16734163\cdot 46786013$ | $S_{13}$ (as 13T9) | trivial |
13.3.226...936.1 | $x^{13} - 9 x - 2$ | $-\,2^{12}\cdot 16519\cdot 334952983395693989$ | $S_{13}$ (as 13T9) | trivial |