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 |
---|---|---|---|---|
13.1.1325925503633.1 | $x^{13} - x^{12} - x^{11} + x^{10} + 3 x^{8} - x^{7} - 5 x^{6} + x^{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} - x + 1$ | $97\cdot 13669335089$ | $S_{13}$ (as 13T9) | trivial |
13.1.1346252740661.1 | $x^{13} - 4 x^{11} + 5 x^{9} - x^{7} - x^{6} - x^{5} + 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1$ | $1346252740661$ | $S_{13}$ (as 13T9) | trivial |
13.1.1452927822421.1 | $x^{13} - 4 x^{12} + 6 x^{11} - x^{10} - 10 x^{9} + 17 x^{8} - 9 x^{7} - 9 x^{6} + 19 x^{5} - 11 x^{4} - 2 x^{3} + 7 x^{2} - 4 x + 1$ | $83\cdot 17505154487$ | $S_{13}$ (as 13T9) | trivial |
13.1.3518110599125.1 | $x^{13} + x^{11} - 2 x^{10} + x^{9} - x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 2 x - 1$ | $5^{3}\cdot 5351\cdot 5259743$ | $S_{13}$ (as 13T9) | trivial |
13.1.4082190012125.1 | $x^{13} - x^{12} - 2 x^{11} + x^{10} + 2 x^{8} + 2 x^{7} - x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$ | $5^{3}\cdot 73\cdot 447363289$ | $S_{13}$ (as 13T9) | trivial |
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 |
13.1.10905397816000.1 | $x^{13} - 3 x^{12} + 8 x^{11} - 12 x^{10} + 15 x^{9} - 12 x^{8} + 6 x^{7} + x^{6} - 6 x^{5} + 8 x^{4} - 6 x^{3} + 5 x^{2} - x + 1$ | $2^{6}\cdot 5^{3}\cdot 26141\cdot 52147$ | $S_{13}$ (as 13T9) | trivial |
13.1.12359517706496.1 | $x^{13} - 3 x^{12} + 5 x^{11} - 4 x^{10} + 5 x^{8} - 7 x^{7} + 6 x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x^{2} + 1$ | $2^{8}\cdot 71\cdot 5197\cdot 130843$ | $S_{13}$ (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 |
13.1.24777340928000.1 | $x^{13} - 2 x^{12} + 4 x^{11} - 5 x^{10} + 2 x^{9} + x^{8} - 6 x^{7} + 8 x^{6} - 3 x^{5} + 4 x^{4} + 4 x^{3} - x^{2} + 4 x - 1$ | $2^{14}\cdot 5^{3}\cdot 12098311$ | $S_{13}$ (as 13T9) | trivial |
13.5.28261626739249.1 | $x^{13} - 3 x^{12} + 3 x^{11} + 3 x^{10} - 13 x^{9} + 14 x^{8} + 2 x^{7} - 20 x^{6} + 18 x^{5} + x^{4} - 11 x^{3} + 6 x^{2} + x - 1$ | $2161\cdot 13078031809$ | $S_{13}$ (as 13T9) | trivial |
13.5.28318356165577.1 | $x^{13} - 3 x^{11} - 4 x^{10} + 2 x^{9} + 9 x^{8} + 6 x^{7} - 4 x^{6} - 10 x^{5} - 3 x^{4} + 4 x^{3} + 4 x^{2} - 1$ | $1721\cdot 16454593937$ | $S_{13}$ (as 13T9) | trivial |
13.1.29747917088000.1 | $x^{13} - 4 x^{12} + 10 x^{11} - 20 x^{10} + 30 x^{9} - 40 x^{8} + 44 x^{7} - 43 x^{6} + 38 x^{5} - 31 x^{4} + 24 x^{3} - 16 x^{2} + 8 x - 2$ | $2^{8}\cdot 5^{3}\cdot 139\cdot 6687931$ | $S_{13}$ (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 |
13.1.36713824791125.1 | $x^{13} - x^{12} + x^{10} - x^{8} + 4 x^{5} - 9 x^{4} + 12 x^{3} - 8 x^{2} + 4 x - 1$ | $5^{3}\cdot 374321\cdot 784649$ | $S_{13}$ (as 13T9) | trivial |
13.1.48103150106125.1 | $x^{13} - 2 x^{12} + 4 x^{10} - 3 x^{9} - 5 x^{8} + 7 x^{7} + x^{6} - 8 x^{5} + 3 x^{4} + 5 x^{3} - 3 x^{2} - x + 2$ | $5^{3}\cdot 83\cdot 4636448203$ | $S_{13}$ (as 13T9) | trivial |
13.1.48551226272641.1 | $x^{13} - 2 x^{12} + 4 x^{10} - 5 x^{9} + x^{8} + 5 x^{7} - 11 x^{6} + 19 x^{5} - 22 x^{4} + 16 x^{3} - 10 x^{2} + 6 x - 1$ | $191^{6}$ | $D_{13}$ (as 13T2) | 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 |
13.1.57655000561921.1 | $x^{13} - 3 x^{12} + 7 x^{11} - 10 x^{10} + 15 x^{9} - 17 x^{8} + 19 x^{7} - 18 x^{6} + 15 x^{5} - 12 x^{4} + 6 x^{3} - 3 x^{2} + 2 x - 1$ | $7^{4}\cdot 83^{2}\cdot 1867^{2}$ | $A_{13}$ (as 13T8) | 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 |
13.5.132939170094109.1 | $x^{13} - x^{12} - x^{11} - 3 x^{10} + x^{9} + 5 x^{8} + 5 x^{7} + 3 x^{6} - 7 x^{5} - 7 x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1$ | $132939170094109$ | $S_{13}$ (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 |
13.7.137400291790087.1 | $x^{13} - 4 x^{12} + x^{11} + 15 x^{10} - 18 x^{9} - 15 x^{8} + 38 x^{7} - 5 x^{6} - 32 x^{5} + 17 x^{4} + 11 x^{3} - 10 x^{2} - x + 1$ | $-\,137400291790087$ | $S_{13}$ (as 13T9) | trivial |
13.7.146839998625007.1 | $x^{13} - 2 x^{11} - 3 x^{10} - 4 x^{9} + 7 x^{8} + 6 x^{7} - 4 x^{6} - 2 x^{5} - 5 x^{4} + 5 x^{3} + 3 x^{2} - 4 x + 1$ | $-\,146839998625007$ | $S_{13}$ (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 |
13.5.197683647463424.1 | $x^{13} - 2 x^{12} + x^{11} - 3 x^{10} - 5 x^{9} + 7 x^{8} + 2 x^{7} + 6 x^{6} + 4 x^{5} - 6 x^{4} - 8 x^{3} + 6 x - 2$ | $2^{14}\cdot 12065652311$ | $S_{13}$ (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 |
13.1.293959006143997.1 | $x^{13} - x - 1$ | $28201\cdot 10423708597$ | $S_{13}$ (as 13T9) | trivial |
13.1.311791207040509.1 | $x^{13} + x - 1$ | $7\cdot 17\cdot 47\cdot 277\cdot 1723\cdot 116803$ | $S_{13}$ (as 13T9) | trivial |
13.1.330928743953809.1 | $x^{13} - 6 x^{12} + 15 x^{11} - 21 x^{10} + 19 x^{9} - 13 x^{8} + 12 x^{7} - 22 x^{6} + 36 x^{5} - 38 x^{4} + 27 x^{3} - 16 x^{2} + 8 x - 1$ | $263^{6}$ | $D_{13}$ (as 13T2) | 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 |
13.9.737652920184769.1 | $x^{13} - 2 x^{12} - 8 x^{11} + 17 x^{10} + 21 x^{9} - 53 x^{8} - 19 x^{7} + 75 x^{6} - 48 x^{4} + 5 x^{3} + 12 x^{2} - x - 1$ | $737652920184769$ | $S_{13}$ (as 13T9) | trivial |
13.9.748906923760081.1 | $x^{13} - x^{12} - 8 x^{11} + 3 x^{10} + 28 x^{9} - 50 x^{7} - 3 x^{6} + 44 x^{5} - 4 x^{4} - 17 x^{3} + 5 x^{2} + 2 x - 1$ | $364027\cdot 2057284003$ | $S_{13}$ (as 13T9) | trivial |
13.5.1204994394291500.1 | $x^{13} - 3 x^{12} + 2 x^{10} + 6 x^{9} - 9 x^{7} - 3 x^{6} + x^{5} + 4 x^{4} - 8 x^{3} - 3 x^{2} + 3 x + 1$ | $2^{2}\cdot 5^{3}\cdot 83\cdot 11171\cdot 2599231$ | $S_{13}$ (as 13T9) | trivial |
13.1.1414971204906609.1 | $x^{13} - x^{12} + x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + 4 x^{5} - 5 x^{4} + 4 x^{3} - 2 x + 1$ | $3^{6}\cdot 7^{2}\cdot 29^{2}\cdot 6863^{2}$ | $A_{13}$ (as 13T8) | 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 |
13.11.4161299413431551.1 | $x^{13} - x^{12} - 9 x^{11} + 5 x^{10} + 27 x^{9} - 6 x^{8} - 29 x^{7} - 3 x^{6} + x^{5} + 6 x^{4} + 12 x^{3} - 4 x - 1$ | $-\,137\cdot 14653\cdot 29411\cdot 70481$ | $S_{13}$ (as 13T9) | trivial |
13.11.4712558875285687.1 | $x^{13} - 6 x^{11} - 3 x^{10} + 9 x^{9} + 19 x^{8} + 7 x^{7} - 42 x^{6} - 25 x^{5} + 39 x^{4} + 15 x^{3} - 14 x^{2} - 2 x + 1$ | $-\,4712558875285687$ | $S_{13}$ (as 13T9) | trivial |