Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (31 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 19.3.146...972.1 | $x^{19} - 2 x^{18} + 7 x^{16} - 10 x^{15} - x^{14} + 19 x^{13} - 19 x^{12} - 9 x^{11} + 33 x^{10} - 19 x^{9} - 20 x^{8} + 32 x^{7} - 9 x^{6} - 17 x^{5} + 17 x^{4} - 3 x^{3} - 5 x^{2} + 4 x - 1$ | $2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.787...824.1 | $x^{19} - 2 x^{18} + 7 x^{16} - 10 x^{15} - x^{14} + 19 x^{13} - 19 x^{12} - 9 x^{11} + 33 x^{10} - 19 x^{9} - 20 x^{8} + 33 x^{7} - 9 x^{6} - 18 x^{5} + 17 x^{4} - 3 x^{3} - 5 x^{2} + 4 x - 1$ | $2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.457...029.1 | $x^{19} - 3 x - 1$ | $15451\cdot 1192721\cdot 1892107519\cdot 1311498030721$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.792...893.1 | $x^{19} - 6 x - 1$ | $1811\cdot 26072749799\cdot 167860372602034140737$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.108...280.1 | $x^{19} - 4 x - 2$ | $2^{18}\cdot 5\cdot 61\cdot 121171\cdot 1116312139673805569479$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.108...277.1 | $x^{19} - 4 x - 1$ | $277\cdot 1033\cdot 13915748550233\cdot 2716178228054209$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.216...536.1 | $x^{19} - 8 x - 4$ | $2^{18}\cdot 11\cdot 53\cdot 421\cdot 2482463\cdot 135422601683162041$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.202...793.1 | $x^{19} - 9 x - 4$ | $629113\cdot 661588211623\cdot 487141714838860007$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.749...269.1 | $x^{19} - 5 x - 3$ | $3^{18}\cdot 7\cdot 1193402926633\cdot 231645392486891$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.750...024.1 | $x^{19} - 5 x - 2$ | $2^{19}\cdot 7\cdot 4397\cdot 86323\cdot 197123\cdot 2733044013891403$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.750...021.1 | $x^{19} - 5 x - 1$ | $7\cdot 229\cdot 46\!\cdots\!07$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.596...440.1 | $x^{19} - 6 x - 4$ | $2^{34}\cdot 5\cdot 41\cdot 2819\cdot 847901\cdot 708003258176033$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.239...573.1 | $x^{19} - 6 x - 3$ | $3^{18}\cdot 5526979\cdot 11347703\cdot 986703355583761$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.239...328.1 | $x^{19} - 6 x - 2$ | $2^{18}\cdot 13\cdot 653\cdot 10774134287092701706273089133$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.498...989.1 | $x^{19} - 7 x - 3$ | $3^{16}\cdot 13\cdot 89051486359588962351884125193$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.112...664.1 | $x^{19} - 7 x - 2$ | $2^{18}\cdot 42\!\cdots\!31$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.440...757.1 | $x^{19} - 7 x - 5$ | $11\cdot 21881\cdot 1229121979\cdot 1490537448908633894245613$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.448...088.1 | $x^{19} - 7 x - 4$ | $2^{18}\cdot 13\cdot 23\cdot 31\cdot 942847\cdot 195714118629896492875189$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.448...653.1 | $x^{19} - 7 x - 1$ | $13\cdot 34\!\cdots\!81$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.546...464.1 | $x^{19} - 8 x - 6$ | $2^{18}\cdot 3^{18}\cdot 1626601603931\cdot 33108756840559$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.566...853.1 | $x^{19} - 8 x - 5$ | $10771\cdot 2100606749\cdot 14133445561\cdot 17708737489650787$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.567...997.1 | $x^{19} - 8 x - 3$ | $3^{18}\cdot 4967\cdot 151598782807\cdot 19437585947910517$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.567...752.1 | $x^{19} - 8 x - 2$ | $2^{18}\cdot 269879\cdot 934176914887\cdot 85797908177168821$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.567...749.1 | $x^{19} - 8 x - 1$ | $29\cdot 6080707\cdot 32\!\cdots\!83$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.499...165.1 | $x^{19} - 9 x - 7$ | $5\cdot 99\!\cdots\!33$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.529...472.1 | $x^{19} - 9 x - 6$ | $2^{19}\cdot 3^{18}\cdot 107\cdot 122029\cdot 19964965175341736357$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.531...861.1 | $x^{19} - 9 x - 5$ | $6219297888079\cdot 8544954240347693873940241859$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.531...005.1 | $x^{19} - 9 x - 3$ | $3^{18}\cdot 5\cdot 71\cdot 1069\cdot 2542879\cdot 142166878031666904029$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.531...760.1 | $x^{19} - 9 x - 2$ | $2^{19}\cdot 5\cdot 17\cdot 11\!\cdots\!87$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.531...757.1 | $x^{19} - 9 x - 1$ | $101\cdot 9221\cdot 1141909\cdot 263051581967\cdot 189994470465354439$ | $S_{19}$ (as 19T8) | trivial |
| 19.3.361...000.1 | $x^{19} - 380 x - 360$ | $2^{24}\cdot 3^{36}\cdot 5^{18}\cdot 19^{20}$ | $A_{19}$ (as 19T7) | trivial |