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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
9.1.404197705.1 | $x^{9} + x - 1$ | $5\cdot 197\cdot 410353$ | $S_9$ (as 9T34) | trivial |
9.1.3279991040.1 | $x^{9} - 4 x - 4$ | $2^{8}\cdot 5\cdot 223\cdot 11491$ | $S_9$ (as 9T34) | trivial |
9.1.396450145280.1 | $x^{9} - 4 x - 8$ | $2^{10}\cdot 5\cdot 7\cdot 19\cdot 577\cdot 1009$ | $S_9$ (as 9T34) | trivial |
9.1.1551188000745.1 | $x^{9} - 9 x - 9$ | $3^{10}\cdot 5\cdot 17\cdot 29\cdot 10657$ | $S_9$ (as 9T34) | trivial |
9.1.2541882605545.1 | $x^{9} + x - 3$ | $5\cdot 73\cdot 6964061933$ | $S_9$ (as 9T34) | trivial |
9.3.4298866865920.1 | $x^{9} - 4 x - 2$ | $-\,2^{8}\cdot 5\cdot 11\cdot 23\cdot 29\cdot 167\cdot 2741$ | $S_9$ (as 9T34) | trivial |
9.3.4397659090615.1 | $x^{9} - 4 x - 1$ | $-\,5\cdot 7\cdot 31\cdot 67\cdot 101\cdot 307\cdot 1951$ | $S_9$ (as 9T34) | trivial |
9.1.5950778711040.1 | $x^{9} - 18 x^{5} + 81 x - 128$ | $2^{10}\cdot 3^{19}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.6604518850560.1 | $x^{9} - 3 x^{8} + 8 x^{6} - 12 x^{5} + 12 x^{4} - 24 x^{2} + 30 x - 10$ | $-\,2^{26}\cdot 3^{9}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.8916099916815.1 | $x^{9} - 9 x - 1$ | $-\,3^{14}\cdot 5\cdot 7\cdot 13\cdot 17\cdot 241$ | $S_9$ (as 9T34) | trivial |
9.1.18797206913280.1 | $x^{9} + 6 x - 2$ | $2^{8}\cdot 3^{7}\cdot 5\cdot 6714823$ | $S_9$ (as 9T34) | trivial |
9.3.23803114844160.1 | $x^{9} - 18 x^{5} + 81 x - 32$ | $-\,2^{12}\cdot 3^{19}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.25290809521920.1 | $x^{9} - 9 x - 4$ | $-\,2^{8}\cdot 3^{19}\cdot 5\cdot 17$ | $S_9$ (as 9T34) | trivial |
9.1.25390005944320.1 | $x^{9} + x - 4$ | $2^{16}\cdot 5\cdot 77484149$ | $S_9$ (as 9T34) | trivial |
9.1.48616417935360.1 | $x^{9} + 6 x - 4$ | $2^{14}\cdot 3^{9}\cdot 5\cdot 11\cdot 2741$ | $S_9$ (as 9T34) | trivial |
9.1.162679417207360.1 | $x^{9} + x - 6$ | $2^{6}\cdot 5\cdot 508373178773$ | $S_9$ (as 9T34) | trivial |
9.1.171617548402665.1 | $x^{9} + 6 x - 3$ | $3^{9}\cdot 5\cdot 653\cdot 2670467$ | $S_9$ (as 9T34) | trivial |
9.3.252934582763520.1 | $x^{9} - 2 x^{8} - 12 x^{7} + 50 x^{6} - 22 x^{5} - 84 x^{4} + 64 x^{3} + 100 x^{2} - 144 x + 48$ | $-\,2^{16}\cdot 3^{8}\cdot 5\cdot 7^{6}$ | $S_9$ (as 9T34) | $[3]$ |
9.1.507799783342080.1 | $x^{9} + 576 x - 1024$ | $2^{18}\cdot 3^{18}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.507799783342080.2 | $x^{9} + 36 x - 32$ | $2^{18}\cdot 3^{18}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.642684100792320.1 | $x^{9} - 18 x^{5} + 81 x - 192$ | $2^{12}\cdot 3^{22}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.646319605541120.1 | $x^{9} - 4 x - 6$ | $2^{8}\cdot 5\cdot 7\cdot 47\cdot 163\cdot 191\cdot 49297$ | $S_9$ (as 9T34) | trivial |
9.1.819793334626560.1 | $x^{9} + 6 x - 6$ | $2^{8}\cdot 3^{9}\cdot 5\cdot 7\cdot 4648417$ | $S_9$ (as 9T34) | trivial |
9.1.1667228227338240.1 | $x^{9} + 6 x - 8$ | $2^{22}\cdot 3^{9}\cdot 5\cdot 7\cdot 577$ | $S_9$ (as 9T34) | trivial |
9.1.1871806375804545.1 | $x^{9} + 6 x - 9$ | $3^{7}\cdot 5\cdot 557\cdot 307317251$ | $S_9$ (as 9T34) | trivial |
9.1.2229003975896585.1 | $x^{9} - 4 x - 7$ | $5\cdot 173\cdot 2309\cdot 19559\cdot 57059$ | $S_9$ (as 9T34) | trivial |
9.1.2233402039184905.1 | $x^{9} + x - 7$ | $5\cdot 73\cdot 55373\cdot 110503489$ | $S_9$ (as 9T34) | trivial |
9.3.4266435204370935.1 | $x^{9} - 9 x - 7$ | $-\,3^{19}\cdot 5\cdot 73\cdot 89\cdot 113$ | $S_9$ (as 9T34) | trivial |
9.3.6497295360950295.1 | $x^{9} - 9 x - 3$ | $-\,3^{18}\cdot 5\cdot 11\cdot 73\cdot 4177$ | $S_9$ (as 9T34) | trivial |
9.3.6499738047133440.1 | $x^{9} - 9 x - 2$ | $-\,2^{8}\cdot 3^{19}\cdot 5\cdot 17\cdot 257$ | $S_9$ (as 9T34) | trivial |
9.1.6499837243555840.1 | $x^{9} + x - 8$ | $2^{25}\cdot 5\cdot 73\cdot 530713$ | $S_9$ (as 9T34) | trivial |
9.1.16672783653155465.1 | $x^{9} - 4 x - 9$ | $5\cdot 11\cdot 6553\cdot 19387\cdot 2386133$ | $S_9$ (as 9T34) | $[2, 2]$ |
9.1.16677181716443785.1 | $x^{9} + x - 9$ | $5\cdot 43133\cdot 77329106329$ | $S_9$ (as 9T34) | trivial |
9.3.109267739753840640.1 | $x^{9} - 3 x^{8} + 18 x^{7} - 70 x^{6} - 252 x^{5} - 420 x^{4} - 420 x^{3} - 180 x^{2} + 36 x + 36$ | $-\,2^{20}\cdot 3^{11}\cdot 5\cdot 7^{6}$ | $S_9$ (as 9T34) | trivial |
9.3.208229648656711680.1 | $x^{9} - 729 x - 648$ | $-\,2^{14}\cdot 3^{26}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.462210647237591040.1 | $x^{9} - 1944 x - 3456$ | $2^{31}\cdot 3^{16}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.1480744168225505280.1 | $x^{9} - 36 x^{7} + 486 x^{5} - 2916 x^{3} + 6561 x - 6144$ | $2^{20}\cdot 3^{24}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.132...440.2 | $x^{9} - 3 x^{8} - 60 x^{7} + 116 x^{6} + 906 x^{5} - 894 x^{4} - 5428 x^{3} + 2268 x^{2} + 24057 x + 34869$ | $-\,2^{20}\cdot 3^{11}\cdot 5\cdot 7^{6}\cdot 11^{2}$ | $S_9$ (as 9T34) | trivial |
9.1.368...760.1 | $x^{9} - 36 x^{7} + 486 x^{5} - 2916 x^{3} + 6561 x - 77824$ | $2^{15}\cdot 3^{14}\cdot 5\cdot 19^{6}$ | $S_9$ (as 9T34) | trivial |
9.1.473...960.1 | $x^{9} + 6561 x - 17496$ | $2^{25}\cdot 3^{24}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.533...080.1 | $x^{9} - 5184 x - 9216$ | $-\,2^{22}\cdot 3^{26}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.561...360.1 | $x^{9} + 486 x - 1296$ | $2^{30}\cdot 3^{21}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.710...440.1 | $x^{9} - 36 x^{7} - 168 x^{6} - 378 x^{5} - 504 x^{4} - 420 x^{3} - 216 x^{2} - 63 x + 393208$ | $-\,2^{24}\cdot 3^{25}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.414...920.1 | $x^{9} - 12 x^{7} - 16 x^{6} + 288 x^{5} - 648 x^{3} - 7344 x^{2} + 29160 x - 17280$ | $2^{18}\cdot 3^{12}\cdot 5\cdot 29^{6}$ | $S_9$ (as 9T34) | trivial |
9.1.426...640.1 | $x^{9} + 81 x - 72$ | $2^{25}\cdot 3^{26}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.113...040.1 | $x^{9} - 157464 x - 419904$ | $-\,2^{28}\cdot 3^{25}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.454...160.1 | $x^{9} + 39366 x - 104976$ | $2^{30}\cdot 3^{25}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.909...320.1 | $x^{9} - 2519424 x - 13436928$ | $2^{31}\cdot 3^{25}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.3.136...480.1 | $x^{9} - 54 x - 48$ | $-\,2^{30}\cdot 3^{26}\cdot 5$ | $S_9$ (as 9T34) | trivial |
9.1.180...760.1 | $x^{9} - 3 x^{8} - 111 x^{7} + 389 x^{6} + 4173 x^{5} - 9219 x^{4} - 87209 x^{3} + 50283 x^{2} + 2781882 x - 9576858$ | $2^{15}\cdot 3^{16}\cdot 5\cdot 37^{6}$ | $S_9$ (as 9T34) | trivial |