Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (13 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
15.13.150...219.1 | $x^{15} - 20 x^{13} - 9 x^{12} + 160 x^{11} + 144 x^{10} - 612 x^{9} - 864 x^{8} + 944 x^{7} + 2269 x^{6} + 320 x^{5} - 2024 x^{4} - 1777 x^{3} - 560 x^{2} - 60 x - 1$ | $-\,11^{13}\cdot 23\cdot 109\cdot 1738307$ | $S_3\wr C_5$ (as 15T81) | trivial |
15.13.105...011.1 | $x^{15} - 20 x^{13} - 10 x^{12} + 160 x^{11} + 160 x^{10} - 607 x^{9} - 960 x^{8} + 884 x^{7} + 2520 x^{6} + 560 x^{5} - 2240 x^{4} - 2100 x^{3} - 640 x^{2} - 48 x - 1$ | $-\,61^{3}\cdot 107\cdot 397^{3}\cdot 601\cdot 1158121$ | $S_3^5.S_5$ (as 15T93) | trivial |
15.13.557...088.1 | $x^{15} - 33 x^{13} - 22 x^{12} + 396 x^{11} + 528 x^{10} - 1903 x^{9} - 4158 x^{8} + 1683 x^{7} + 11264 x^{6} + 9207 x^{5} - 3630 x^{4} - 11000 x^{3} - 7920 x^{2} - 2640 x - 352$ | $-\,2^{10}\cdot 3^{15}\cdot 11^{14}$ | $S_3\wr C_5$ (as 15T81) | trivial |
15.13.264...643.1 | $x^{15} - 20 x^{13} - 14 x^{12} + 160 x^{11} + 224 x^{10} - 589 x^{9} - 1344 x^{8} + 668 x^{7} + 3521 x^{6} + 1424 x^{5} - 3080 x^{4} - 3241 x^{3} - 1008 x^{2} - 92 x - 1$ | $-\,401^{6}\cdot 6369171443$ | $S_3\wr D_5$ (as 15T86) | trivial |
15.13.274...699.1 | $x^{15} - 20 x^{13} - 10 x^{12} + 160 x^{11} + 160 x^{10} - 609 x^{9} - 960 x^{8} + 908 x^{7} + 2525 x^{6} + 464 x^{5} - 2280 x^{4} - 1973 x^{3} - 560 x^{2} - 44 x - 1$ | $-\,13\cdot 59\cdot 1451\cdot 36497^{3}\cdot 507839$ | $S_3^5.S_5$ (as 15T93) | trivial |
15.13.284...239.1 | $x^{15} - 15 x^{13} - 17 x^{12} + 90 x^{11} + 204 x^{10} - 264 x^{9} - 918 x^{8} + 351 x^{7} + 1885 x^{6} - 81 x^{5} - 1671 x^{4} - 209 x^{3} + 441 x^{2} + 141 x + 9$ | $-\,3^{17}\cdot 53\cdot 401^{6}$ | $S_3\wr D_5$ (as 15T86) | trivial |
15.13.171...952.1 | $x^{15} - 45 x^{13} - 30 x^{12} + 711 x^{11} + 948 x^{10} - 4436 x^{9} - 9504 x^{8} + 6300 x^{7} + 32288 x^{6} + 24948 x^{5} - 14184 x^{4} - 36384 x^{3} - 25920 x^{2} - 8640 x - 1152$ | $-\,2^{8}\cdot 3^{15}\cdot 881^{6}$ | $S_3\wr A_5$ (as 15T90) | trivial |
15.13.310...216.1 | $x^{15} - 15 x^{13} - 3 x^{12} + 90 x^{11} + 36 x^{10} - 278 x^{9} - 162 x^{8} + 477 x^{7} + 338 x^{6} - 459 x^{5} - 327 x^{4} + 232 x^{3} + 126 x^{2} - 48 x - 12$ | $-\,2^{16}\cdot 3^{15}\cdot 53^{9}$ | $S_3\wr F_5$ (as 15T87) | trivial |
15.13.806...032.1 | $x^{15} - 46 x^{13} - 14 x^{12} + 744 x^{11} + 183 x^{10} - 5430 x^{9} + 2554 x^{8} + 27217 x^{7} - 28396 x^{6} - 115050 x^{5} + 36504 x^{4} + 215190 x^{3} + 47709 x^{2} - 118098 x - 55404$ | $-\,2^{8}\cdot 3^{3}\cdot 11^{6}\cdot 19^{4}\cdot 131^{6}$ | $S_3\wr A_5$ (as 15T90) | trivial |
15.13.172...000.1 | $x^{15} - 45 x^{13} - 75 x^{12} + 450 x^{11} + 1320 x^{10} + 1230 x^{9} - 90 x^{8} - 15165 x^{7} - 30560 x^{6} + 41355 x^{5} + 89985 x^{4} - 65975 x^{3} - 74970 x^{2} + 62925 x - 9587$ | $-\,2^{12}\cdot 3^{19}\cdot 5^{15}\cdot 7^{6}\cdot 101$ | $S_3\wr F_5$ (as 15T87) | trivial |
15.13.315...951.1 | $x^{15} - 2 x^{14} - 23 x^{13} + 42 x^{12} + 182 x^{11} - 300 x^{10} - 614 x^{9} + 885 x^{8} + 918 x^{7} - 1113 x^{6} - 525 x^{5} + 508 x^{4} + 60 x^{3} - 65 x^{2} + x + 1$ | $-\,13\cdot 17\cdot 23585458327\cdot 60\!\cdots\!53$ | $S_{15}$ (as 15T104) | trivial |
15.13.686...679.1 | $x^{15} - 2 x^{14} - 23 x^{13} + 42 x^{12} + 182 x^{11} - 300 x^{10} - 614 x^{9} + 885 x^{8} + 918 x^{7} - 1112 x^{6} - 525 x^{5} + 508 x^{4} + 60 x^{3} - 66 x^{2} + x + 1$ | $-\,277\cdot 140891\cdot 1754444023\cdot 100190895611918899269402449839$ | $S_{15}$ (as 15T104) | trivial |
15.13.771...000.1 | $x^{15} - 1628 x^{13} - 5920 x^{12} + 1105179 x^{11} + 7903120 x^{10} - 388843381 x^{9} - 4223348520 x^{8} + 69563456700 x^{7} + 1121721226000 x^{6} - 4146108150000 x^{5} - 145380612000000 x^{4} - 422827275000000 x^{3} + 6657280500000000 x^{2} + 53977950000000000 x + 119951000000000000$ | $-\,2^{15}\cdot 5^{3}\cdot 7^{10}\cdot 13^{4}\cdot 1973^{2}\cdot 9227^{4}\cdot 9097717^{2}$ | $S_5\wr C_3$ (as 15T101) | trivial |