Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (36 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
17.3.158...023.1 | $x^{17} - x^{15} - x^{14} - 5 x^{13} + 4 x^{12} + x^{11} + 15 x^{9} - 13 x^{8} - 2 x^{7} + 7 x^{6} - 18 x^{5} + 20 x^{4} - 10 x^{3} + 6 x^{2} - 4 x + 1$ | $-\,2131\cdot 546781\cdot 1361451193$ | $S_{17}$ (as 17T10) | trivial |
17.3.191...491.1 | $x^{17} - 3 x^{16} + 4 x^{15} - 3 x^{14} + x^{13} + 4 x^{12} - 8 x^{11} + 9 x^{10} - 2 x^{9} - 9 x^{8} + 12 x^{7} - x^{6} - 4 x^{5} + 2 x^{4} - 3 x^{3} + x^{2} - x - 1$ | $-\,227\cdot 2411\cdot 3533\cdot 988994191$ | $S_{17}$ (as 17T10) | trivial |
17.3.215...383.1 | $x^{17} - 2 x^{15} - 4 x^{14} + 4 x^{13} + 7 x^{12} - 3 x^{11} - 3 x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} - 4 x^{6} + 14 x^{5} - 2 x^{4} - 7 x^{3} + 2 x + 1$ | $-\,37^{5}\cdot 433\cdot 5531\cdot 12953$ | $S_{17}$ (as 17T10) | trivial |
17.3.231...203.1 | $x^{17} - x^{16} + x^{15} - 3 x^{14} + 4 x^{13} - 4 x^{12} - x^{11} + 4 x^{10} - 5 x^{9} + 17 x^{8} - 42 x^{7} + 59 x^{6} - 45 x^{5} + 9 x^{4} + 15 x^{3} - 15 x^{2} + 6 x - 1$ | $-\,16843\cdot 137239279050521$ | $S_{17}$ (as 17T10) | trivial |
17.3.275...423.1 | $x^{17} - 3 x^{16} + 7 x^{15} - 10 x^{14} + 12 x^{13} - 11 x^{12} + 10 x^{11} - 7 x^{10} + 2 x^{9} + 5 x^{8} - 13 x^{7} + 11 x^{6} - 5 x^{5} - 6 x^{4} + 11 x^{3} - 9 x^{2} + 5 x - 1$ | $-\,75653\cdot 3119681\cdot 11682611$ | $S_{17}$ (as 17T10) | trivial |
17.3.377...359.1 | $x^{17} - 4 x^{16} + 12 x^{15} - 26 x^{14} + 48 x^{13} - 75 x^{12} + 105 x^{11} - 126 x^{10} + 136 x^{9} - 129 x^{8} + 107 x^{7} - 80 x^{6} + 47 x^{5} - 23 x^{4} + 11 x^{3} - 2 x^{2} - 2 x + 1$ | $-\,137\cdot 1926157\cdot 14323744651$ | $S_{17}$ (as 17T10) | trivial |
17.3.207...144.1 | $x^{17} - 2 x^{16} + x^{15} + 2 x^{14} - 3 x^{13} + 3 x^{11} - 3 x^{10} - x^{9} + 6 x^{8} - 5 x^{7} - 4 x^{6} + 8 x^{5} - 3 x^{4} - 4 x^{3} + 3 x^{2} - 1$ | $-\,2^{3}\cdot 17\cdot 20759\cdot 9318913\cdot 78851137$ | $S_{17}$ (as 17T10) | trivial |
17.3.855...476.1 | $x^{17} - 3 x^{16} + 4 x^{15} + x^{14} - 13 x^{13} + 26 x^{12} - 25 x^{11} + 2 x^{10} + 35 x^{9} - 62 x^{8} + 59 x^{7} - 25 x^{6} - 13 x^{5} + 33 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$ | $-\,2^{2}\cdot 11\cdot 53\cdot 34759\cdot 105529138935877$ | $S_{17}$ (as 17T10) | trivial |
17.3.725...168.1 | $x^{17} - 3 x^{16} + 3 x^{15} - 17 x^{14} + 27 x^{13} + 27 x^{12} + 85 x^{11} - 303 x^{10} + 141 x^{9} - 35 x^{8} + 609 x^{7} - 1599 x^{6} + 985 x^{5} + 513 x^{4} + 1935 x^{3} - 3869 x^{2} + 1272 x - 48$ | $-\,2^{29}\cdot 3^{38}$ | $S_{17}$ (as 17T10) | trivial |
17.3.238...231.1 | $x^{17} - 3 x - 1$ | $-\,17987\cdot 132440913396223585034213$ | $S_{17}$ (as 17T10) | trivial |
17.3.253...408.1 | $x^{17} - 9 x - 4$ | $-\,2^{16}\cdot 38738303271636409747303$ | $S_{17}$ (as 17T10) | trivial |
17.3.316...472.1 | $x^{17} - 4 x - 2$ | $-\,2^{16}\cdot 13\cdot 371913541399740797081579$ | $S_{17}$ (as 17T10) | trivial |
17.3.316...167.1 | $x^{17} - 4 x - 1$ | $-\,19\cdot 67\cdot 2269\cdot 109717694805120239246291$ | $S_{17}$ (as 17T10) | trivial |
17.3.633...816.1 | $x^{17} - 8 x - 4$ | $-\,2^{16}\cdot 3\cdot 11\cdot 37\cdot 3121561\cdot 13503587\cdot 187895273$ | $S_{17}$ (as 17T10) | trivial |
17.3.140...383.1 | $x^{17} - 5 x - 3$ | $-\,7\cdot 618079271321299\cdot 3244645955426531$ | $S_{17}$ (as 17T10) | trivial |
17.3.140...128.1 | $x^{17} - 5 x - 2$ | $-\,2^{16}\cdot 3\cdot 3131923046309\cdot 22855769909249$ | $S_{17}$ (as 17T10) | trivial |
17.3.140...823.1 | $x^{17} - 5 x - 1$ | $-\,3\cdot 89\cdot 1699\cdot 507289\cdot 2211365603\cdot 27655986893$ | $S_{17}$ (as 17T10) | trivial |
17.3.771...496.1 | $x^{17} - 6 x - 4$ | $-\,2^{30}\cdot 2329417133\cdot 30854159809163$ | $S_{17}$ (as 17T10) | trivial |
17.3.312...759.1 | $x^{17} - 6 x - 3$ | $-\,3^{16}\cdot 41\cdot 487\cdot 363235722813937432337$ | $S_{17}$ (as 17T10) | trivial |
17.3.312...504.1 | $x^{17} - 6 x - 2$ | $-\,2^{16}\cdot 2791\cdot 724723\cdot 2355478215670018723$ | $S_{17}$ (as 17T10) | trivial |
17.3.312...199.1 | $x^{17} - 6 x - 1$ | $-\,7\cdot 41\cdot 40841\cdot 6864777739\cdot 3880487013052123$ | $S_{17}$ (as 17T10) | trivial |
17.3.107...160.1 | $x^{17} - 7 x - 2$ | $-\,2^{14}\cdot 5\cdot 3251\cdot 9473\cdot 425237890924282842001$ | $S_{17}$ (as 17T10) | trivial |
17.3.416...887.1 | $x^{17} - 7 x - 5$ | $-\,59\cdot 912539\cdot 77360031636376385786613287$ | $S_{17}$ (as 17T10) | trivial |
17.3.428...120.1 | $x^{17} - 7 x - 4$ | $-\,2^{32}\cdot 5\cdot 19\cdot 223\cdot 29611\cdot 18565699\cdot 85718383$ | $S_{17}$ (as 17T10) | trivial |
17.3.429...895.1 | $x^{17} - 7 x - 3$ | $-\,5\cdot 47\cdot 421\cdot 43374336132579615850126292617$ | $S_{17}$ (as 17T10) | trivial |
17.3.429...335.1 | $x^{17} - 7 x - 1$ | $-\,5\cdot 11\cdot 78\!\cdots\!97$ | $S_{17}$ (as 17T10) | trivial |
17.3.461...544.1 | $x^{17} - 8 x - 2$ | $-\,2^{16}\cdot 977\cdot 143572109\cdot 502067855635349603$ | $S_{17}$ (as 17T10) | trivial |
17.3.392...056.1 | $x^{17} - 8 x - 6$ | $-\,2^{16}\cdot 598215319360726628348781489071$ | $S_{17}$ (as 17T10) | trivial |
17.3.414...143.1 | $x^{17} - 8 x - 5$ | $-\,3\cdot 2186209\cdot 164061345157\cdot 38486512346763137$ | $S_{17}$ (as 17T10) | trivial |
17.3.415...151.1 | $x^{17} - 8 x - 3$ | $-\,61\cdot 3533\cdot 163481\cdot 1178985247918158460303967$ | $S_{17}$ (as 17T10) | trivial |
17.3.415...591.1 | $x^{17} - 8 x - 1$ | $-\,3\cdot 2555684029\cdot 99995675629\cdot 54180108271117$ | $S_{17}$ (as 17T10) | trivial |
17.3.280...127.1 | $x^{17} - 9 x - 7$ | $-\,67\cdot 542797\cdot 80951558783101\cdot 95159072441773$ | $S_{17}$ (as 17T10) | trivial |
17.3.305...792.1 | $x^{17} - 9 x - 6$ | $-\,2^{16}\cdot 3^{16}\cdot 268235867903\cdot 403458097169$ | $S_{17}$ (as 17T10) | trivial |
17.3.307...879.1 | $x^{17} - 9 x - 5$ | $-\,536705537\cdot 572964977325919334221374767$ | $S_{17}$ (as 17T10) | trivial |
17.3.307...887.1 | $x^{17} - 9 x - 3$ | $-\,3^{16}\cdot 593\cdot 33641\cdot 95413\cdot 3754664319237163$ | $S_{17}$ (as 17T10) | trivial |
17.3.307...632.1 | $x^{17} - 9 x - 2$ | $-\,2^{16}\cdot 46\!\cdots\!87$ | $S_{17}$ (as 17T10) | trivial |
17.3.307...327.1 | $x^{17} - 9 x - 1$ | $-\,101\cdot 374761\cdot 21841751\cdot 372116706329069072557$ | $S_{17}$ (as 17T10) | trivial |