Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (7 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
17.5.362...901.1 | $x^{17} - 5 x^{15} - x^{14} + 5 x^{13} + 6 x^{12} + 9 x^{11} - 16 x^{10} - 21 x^{9} + 19 x^{8} + 13 x^{7} - 5 x^{6} - 4 x^{5} - 5 x^{4} + 3 x^{3} - x + 1$ | $55954279\cdot 64715583419$ | $S_{17}$ (as 17T10) | trivial |
17.5.475...701.1 | $x^{17} - 6 x^{15} - 2 x^{14} + 17 x^{13} + 13 x^{12} - 27 x^{11} - 34 x^{10} + 20 x^{9} + 47 x^{8} - 38 x^{6} - 13 x^{5} + 17 x^{4} + 12 x^{3} - 2 x^{2} - 3 x - 1$ | $97\cdot 2927\cdot 2315407\cdot 7234597$ | $S_{17}$ (as 17T10) | trivial |
17.5.145...793.1 | $x^{17} - 2 x^{16} + 4 x^{15} - 2 x^{14} + 6 x^{12} - 5 x^{11} + x^{10} + 3 x^{9} - 6 x^{8} - 7 x^{7} - x^{6} - 5 x^{5} - 9 x^{4} - 3 x^{3} - 2 x^{2} - 3 x - 1$ | $10170343\cdot 1427427651151$ | $S_{17}$ (as 17T10) | trivial |
17.5.890...861.1 | $x^{17} - 2 x^{16} - 5 x^{15} + 8 x^{14} + 14 x^{13} - 6 x^{12} - 34 x^{11} - 12 x^{10} + 42 x^{9} + 47 x^{8} - 33 x^{7} - 52 x^{6} + 13 x^{5} + 21 x^{4} + 3 x^{3} - 5 x^{2} - 2 x + 1$ | $946391\cdot 3063653\cdot 30715207$ | $S_{17}$ (as 17T10) | trivial |
17.5.374...388.1 | $x^{17} - x^{16} - 4 x^{15} + 4 x^{14} + 6 x^{13} - 6 x^{12} - 8 x^{11} + 8 x^{10} + 9 x^{9} - 7 x^{8} - 9 x^{7} + 3 x^{6} + 9 x^{5} - 2 x^{4} - 6 x^{3} + 4 x^{2} + 2 x - 1$ | $2^{2}\cdot 9368869340728638677625097$ | $S_{17}$ (as 17T10) | trivial |
17.5.478...988.1 | $x^{17} - 2 x^{16} - 2 x^{15} + 9 x^{14} - 8 x^{13} - 6 x^{12} + 22 x^{11} - 20 x^{10} - 4 x^{9} + 23 x^{8} - 20 x^{7} + 7 x^{6} + x^{5} - 11 x^{4} + 11 x^{3} - x^{2} - 3 x + 1$ | $2^{2}\cdot 71\cdot 113\cdot 398023\cdot 3743302227733793$ | $S_{17}$ (as 17T10) | trivial |
17.5.878...000.1 | $x^{17} - 8 x^{16} - 17 x^{15} + 376 x^{14} - 1517 x^{13} + 2374 x^{12} - 258 x^{11} - 2424 x^{10} - 507 x^{9} - 2266 x^{8} + 26723 x^{7} - 46312 x^{6} + 33731 x^{5} - 13660 x^{4} + 980 x^{3} + 10560 x^{2} - 10440 x + 2880$ | $2^{18}\cdot 3^{28}\cdot 5^{14}\cdot 7^{4}$ | $A_{17}$ (as 17T9) | trivial |
17.5.353...000.1 | $x^{17} - 6 x^{16} + 36 x^{15} + 16 x^{14} - 159 x^{13} + 1746 x^{12} - 1916 x^{11} + 3324 x^{10} + 11532 x^{9} - 36888 x^{8} + 40500 x^{7} - 24420 x^{6} - 123199 x^{5} + 197142 x^{4} - 110508 x^{3} + 40728 x^{2} - 3663 x + 1494$ | $2^{32}\cdot 3^{16}\cdot 5^{12}\cdot 23^{8}$ | $\PSL(2,16):C_2$ (as 17T7) | trivial |