## Results (20 matches)

displayed columns for results
Label Polynomial Discriminant Galois group Class group
15.5.35351257235385344.1 $x^{15} - 3 x^{13} - 5 x^{12} + 8 x^{11} + x^{10} + 14 x^{9} - 13 x^{8} - 17 x^{7} + 4 x^{6} + x^{5} + 22 x^{4} - 2 x^{3} - 8 x^{2} - 3 x - 1$ $-\,2^{10}\cdot 11^{13}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.388863829589238784.1 $x^{15} - 3 x^{14} + 2 x^{13} - x^{12} + 5 x^{11} - 22 x^{9} + 33 x^{8} - 22 x^{7} + 22 x^{6} - 22 x^{5} - 9 x^{4} + 38 x^{3} - 29 x^{2} + 9 x - 1$ $-\,2^{10}\cdot 11^{14}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.202...303.1 $x^{15} - x^{14} - 4 x^{13} + 7 x^{12} + 24 x^{11} - 26 x^{10} - 57 x^{9} + 76 x^{8} + 79 x^{7} - 88 x^{6} - 97 x^{5} + 35 x^{4} + 42 x^{3} - 15 x^{2} + 1$ $-\,11^{12}\cdot 23^{5}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.244...591.1 $x^{15} - 4 x^{14} + 7 x^{13} - 17 x^{12} + 51 x^{11} - 87 x^{10} - 7 x^{9} + 172 x^{8} - 100 x^{7} - 69 x^{6} - 17 x^{5} + 62 x^{4} + 50 x^{3} - 22 x^{2} - 18 x - 1$ $-\,31^{13}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.898...871.1 $x^{15} + 9 x^{13} - 4 x^{12} + 28 x^{11} - 20 x^{10} + 4 x^{9} - 32 x^{8} - 71 x^{7} + 48 x^{6} - 57 x^{5} + 28 x^{4} + 38 x^{3} + 3 x^{2} + 3 x - 1$ $-\,11^{12}\cdot 31^{5}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.944...512.1 $x^{15} - 5 x^{14} + 8 x^{13} + 8 x^{12} - 52 x^{11} + 77 x^{10} - 22 x^{9} + 11 x^{8} - 121 x^{7} - 44 x^{6} + 275 x^{5} - 26 x^{4} - 101 x^{3} - 43 x^{2} - 10 x + 43$ $-\,2^{10}\cdot 3^{5}\cdot 11^{14}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.140...031.1 $x^{15} - 4 x^{14} + 2 x^{13} + 25 x^{12} - 77 x^{11} + 56 x^{10} + 46 x^{9} + 26 x^{8} - 157 x^{7} + 71 x^{6} - 67 x^{5} + 95 x^{4} + 26 x^{3} - 34 x^{2} - 11 x + 1$ $-\,3^{5}\cdot 7^{5}\cdot 11^{13}$ $S_3 \times C_5$ (as 15T4) trivial
15.15.140...613.1 $x^{15} - 6 x^{14} - 3 x^{13} + 80 x^{12} - 96 x^{11} - 330 x^{10} + 715 x^{9} + 308 x^{8} - 1694 x^{7} + 715 x^{6} + 1287 x^{5} - 1217 x^{4} + 53 x^{3} + 263 x^{2} - 76 x + 1$ $11^{14}\cdot 13^{5}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.288...375.1 $x^{15} - 3 x^{14} + 2 x^{13} - x^{12} - 17 x^{11} + 22 x^{10} + 99 x^{7} + 154 x^{6} + 132 x^{5} + 321 x^{4} + 643 x^{3} - 84 x^{2} - 343 x + 197$ $-\,3^{5}\cdot 5^{5}\cdot 11^{14}$ $S_3 \times C_5$ (as 15T4) trivial
15.15.539...537.1 $x^{15} - x^{14} - 23 x^{13} + 2 x^{12} + 169 x^{11} + 66 x^{10} - 473 x^{9} - 264 x^{8} + 572 x^{7} + 341 x^{6} - 297 x^{5} - 157 x^{4} + 69 x^{3} + 25 x^{2} - 6 x - 1$ $11^{14}\cdot 17^{5}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.121...000.1 $x^{15} - 6 x^{14} + 19 x^{13} - 52 x^{12} + 91 x^{11} - 165 x^{10} + 209 x^{9} - 396 x^{8} + 1034 x^{7} - 1397 x^{6} + 1749 x^{5} - 1998 x^{4} + 1109 x^{3} - 826 x^{2} + 848 x - 197$ $-\,2^{10}\cdot 5^{5}\cdot 11^{14}$ $S_3 \times C_5$ (as 15T4) trivial
15.5.544...587.1 $x^{15} - 22 x^{12} + 66 x^{9} - 33 x^{6} - 22 x^{3} + 11$ $-\,3^{15}\cdot 11^{14}$ $S_3 \times C_5$ (as 15T4) $[2]$
15.5.120...331.1 $x^{15} + 6 x^{13} - 19 x^{12} - 45 x^{11} + 87 x^{10} - 123 x^{9} + 117 x^{8} - 228 x^{7} - 555 x^{6} + 2619 x^{5} + 2145 x^{4} - 4231 x^{3} - 3645 x^{2} + 1209 x + 2069$ $-\,3^{20}\cdot 11^{13}$ $S_3 \times C_5$ (as 15T4) $[3]$
15.5.282...731.1 $x^{15} - 5 x^{14} - 23 x^{13} - 164 x^{12} + 654 x^{11} + 2155 x^{10} + 7876 x^{9} - 2893 x^{8} - 35937 x^{7} - 601975 x^{6} - 709885 x^{5} + 3344264 x^{4} + 11561561 x^{3} - 1175603 x^{2} - 34755534 x - 26797639$ $-\,11^{13}\cdot 31^{10}$ $S_3 \times C_5$ (as 15T4) $[33]$
15.5.337...000.1 $x^{15} - 110 x^{13} - 330 x^{12} + 6050 x^{11} + 25674 x^{10} - 442200 x^{9} - 2425610 x^{8} + 6912345 x^{7} + 36375350 x^{6} - 70930618 x^{5} - 40668100 x^{4} + 762404060 x^{3} - 1733605720 x^{2} - 2315335000 x + 7384846832$ $-\,2^{15}\cdot 5^{25}\cdot 11^{13}$ $S_3 \times C_5$ (as 15T4) $[5, 5]$
15.15.183...648.1 $x^{15} - 676 x^{13} - 2038 x^{12} + 154340 x^{11} + 777118 x^{10} - 13426470 x^{9} - 81228726 x^{8} + 443602723 x^{7} + 3071208794 x^{6} - 3528834550 x^{5} - 35037744764 x^{4} - 10574547144 x^{3} + 113736612400 x^{2} + 132200896640 x + 34747476224$ $2^{15}\cdot 11^{13}\cdot 61^{13}$ $S_3 \times C_5$ (as 15T4) $[5]$
15.5.330...999.1 $x^{15} - 2 x^{14} - 5995 x^{13} + 37278 x^{12} + 12591603 x^{11} - 125770086 x^{10} - 9981552889 x^{9} + 127789199194 x^{8} + 1679913052736 x^{7} - 14585961566768 x^{6} - 215344958988368 x^{5} + 7140439214752 x^{4} + 11110764946271360 x^{3} + 74237750960369664 x^{2} + 322453908130652160 x + 543122152076214272$ $-\,11^{12}\cdot 19^{5}\cdot 461^{13}$ $S_3 \times C_5$ (as 15T4) $[2, 2, 10, 8125610]$
15.15.236...000.1 $x^{15} - 11275 x^{13} - 124025 x^{12} + 45081960 x^{11} + 891723965 x^{10} - 76578988200 x^{9} - 2216106307965 x^{8} + 44485161759555 x^{7} + 2079870790777010 x^{6} + 8195553887899983 x^{5} - 457716480374582000 x^{4} - 5640651315561778120 x^{3} + 1700941616424112590 x^{2} + 316610688507343605265 x + 1257096395450004601701$ $2^{10}\cdot 3^{5}\cdot 5^{25}\cdot 11^{13}\cdot 41^{13}$ $S_3 \times C_5$ (as 15T4) $[5, 5, 55]$
15.5.218...792.1 $x^{15} - 2 x^{14} - 5518 x^{13} + 145177 x^{12} + 10337726 x^{11} - 586917623 x^{10} + 3771529909 x^{9} + 531822012342 x^{8} - 23558245878420 x^{7} + 579004818046875 x^{6} - 10215903964721319 x^{5} + 131630106918356613 x^{4} - 1205008059400695846 x^{3} + 5950390757960217555 x^{2} + 20744208523450960470 x - 156585180055842346293$ $-\,2^{10}\cdot 3^{5}\cdot 11^{5}\cdot 31^{13}\cdot 181^{13}$ $S_3 \times C_5$ (as 15T4) not computed
15.5.411...944.1 $x^{15} - 2 x^{14} - 32683 x^{13} + 474556 x^{12} + 398483171 x^{11} - 9448930490 x^{10} - 2149890958601 x^{9} + 60044615624016 x^{8} + 4866594417860856 x^{7} - 97851943474667568 x^{6} - 5825118141734624712 x^{5} + 17888510070027150336 x^{4} + 3008732613506684865072 x^{3} + 35886037118520058343136 x^{2} + 505655319767204772863856 x + 5751424233849962588258304$ $-\,2^{15}\cdot 3^{5}\cdot 11^{13}\cdot 41^{13}\cdot 61^{13}$ $S_3 \times C_5$ (as 15T4) not computed
displayed columns for results