Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
Results (47 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
14.8.9324056974004327.1 | $x^{14} - x^{13} - 4 x^{12} + 8 x^{11} + 2 x^{10} - 33 x^{9} + 7 x^{8} + 70 x^{7} - 2 x^{6} - 72 x^{5} - 9 x^{4} + 32 x^{3} + 6 x^{2} - 5 x - 1$ | $-\,23\cdot 71^{2}\cdot 283583^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.8.11012732926484375.1 | $x^{14} - 2 x^{13} - 2 x^{12} + 10 x^{11} - 8 x^{10} - 12 x^{9} + 23 x^{8} - 7 x^{7} - 16 x^{6} + 18 x^{5} - 8 x^{3} + 4 x^{2} + x - 1$ | $-\,5^{7}\cdot 41\cdot 229\cdot 349\cdot 43019$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.8.16266899635859375.1 | $x^{14} - 5 x^{13} + 7 x^{12} - 4 x^{11} + 15 x^{10} - 22 x^{9} - 11 x^{8} + 23 x^{7} - 9 x^{6} + 16 x^{5} - 6 x^{3} - 2 x^{2} - 3 x - 1$ | $-\,5^{7}\cdot 5011\cdot 41551849$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.8.17381743359198867.1 | $x^{14} - 2 x^{13} - 5 x^{12} + 4 x^{11} + 18 x^{10} + 4 x^{9} - 30 x^{8} - 24 x^{7} + 22 x^{6} + 30 x^{5} - 16 x^{4} - 10 x^{3} + 11 x^{2} - x - 1$ | $-\,3^{3}\cdot 11^{2}\cdot 107^{2}\cdot 21557^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.8.28782958484969879.1 | $x^{14} - 4 x^{13} + 4 x^{12} + 8 x^{11} - 30 x^{10} + 43 x^{9} - 35 x^{8} - 7 x^{7} + 56 x^{6} - 54 x^{5} - 4 x^{4} + 32 x^{3} - 8 x^{2} - 4 x + 1$ | $-\,71^{3}\cdot 283583^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.8.87169416344387584.1 | $x^{14} - 2 x^{12} - 3 x^{10} + 6 x^{8} - 9 x^{6} + 14 x^{4} - 7 x^{2} + 1$ | $-\,2^{14}\cdot 107^{2}\cdot 21557^{2}$ | $C_2^7.S_7$ (as 14T57) | trivial |
14.8.258316958750207623.1 | $x^{14} - 5 x^{13} + 6 x^{12} + 4 x^{11} - 19 x^{10} + 42 x^{9} - 40 x^{8} - 31 x^{7} + 79 x^{6} + 36 x^{5} - 175 x^{4} + 117 x^{3} - 19 x^{2} - 4 x + 1$ | $-\,7\cdot 577^{6}$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.8.417195690175859375.1 | $x^{14} - 3 x^{13} - 5 x^{12} + 18 x^{11} + 14 x^{10} - 52 x^{9} - 27 x^{8} + 91 x^{7} + 31 x^{6} - 86 x^{5} - 11 x^{4} + 40 x^{3} - 3 x^{2} - 8 x + 1$ | $-\,5^{7}\cdot 11\cdot 2939\cdot 5351\cdot 30869$ | $S_7\wr C_2$ (as 14T61) | trivial |
14.8.158...827.1 | $x^{14} - 7 x^{13} + 24 x^{12} - 53 x^{11} + 53 x^{10} + 54 x^{9} - 293 x^{8} + 551 x^{7} - 576 x^{6} + 309 x^{5} - x^{4} - 118 x^{3} + 58 x^{2} - 2 x - 1$ | $-\,43\cdot 577^{6}$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.8.173...183.1 | $x^{14} - 4 x^{13} - 2 x^{12} + 17 x^{11} + 12 x^{10} - 48 x^{9} - 31 x^{8} + 80 x^{7} + 30 x^{6} - 65 x^{5} - 11 x^{4} + 26 x^{3} + 2 x^{2} - 5 x - 1$ | $-\,47\cdot 577^{6}$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.8.182...375.1 | $x^{14} - 5 x^{13} + 5 x^{12} + 11 x^{11} - 26 x^{10} + 17 x^{9} - 4 x^{8} - x^{7} + 50 x^{6} - 95 x^{5} + x^{4} + 76 x^{3} + 3 x^{2} - 18 x - 4$ | $-\,5^{7}\cdot 28579^{3}$ | $D_7 \wr C_2$ (as 14T20) | trivial |
14.8.476...304.1 | $x^{14} - 4 x^{13} - 2 x^{12} + 8 x^{11} + x^{10} + 18 x^{9} - 25 x^{8} + 4 x^{7} - 25 x^{6} + 18 x^{5} + x^{4} + 8 x^{3} - 2 x^{2} - 4 x + 1$ | $-\,2^{14}\cdot 4129^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.8.476...304.2 | $x^{14} - x^{12} - 31 x^{10} + 55 x^{8} + 23 x^{6} - 43 x^{4} - 13 x^{2} + 1$ | $-\,2^{14}\cdot 4129^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.8.645...575.1 | $x^{14} - 6 x^{13} + 8 x^{12} + 19 x^{11} - 70 x^{10} + 78 x^{9} + 3 x^{8} - 110 x^{7} + 64 x^{6} + 123 x^{5} - 81 x^{4} - 136 x^{3} + 88 x^{2} + 45 x - 25$ | $-\,5^{2}\cdot 7\cdot 577^{6}$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.8.853...784.1 | $x^{14} - 3 x^{13} - 5 x^{12} + 18 x^{11} - 7 x^{10} + x^{9} + 3 x^{8} + 71 x^{6} - 193 x^{5} - 59 x^{4} + 34 x^{3} + 35 x^{2} + 11 x + 1$ | $-\,2^{20}\cdot 19\cdot 809^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.8.122...799.1 | $x^{14} - 7 x^{13} + 17 x^{12} + 5 x^{11} - 129 x^{10} + 279 x^{9} - 59 x^{8} - 741 x^{7} + 1251 x^{6} - 237 x^{5} - 1340 x^{4} + 1237 x^{3} + 252 x^{2} - 733 x - 109$ | $-\,107^{3}\cdot 21557^{3}$ | $C_2^6.S_7$ (as 14T54) | trivial |
14.8.179...719.1 | $x^{14} - 5 x^{13} + 46 x^{11} - 104 x^{10} - 9 x^{9} + 425 x^{8} - 655 x^{7} - 81 x^{6} + 1100 x^{5} - 778 x^{4} - 378 x^{3} + 416 x^{2} + 130 x + 43$ | $-\,61^{3}\cdot 42899^{3}$ | $C_2^6.S_7$ (as 14T54) | trivial |
14.8.185...979.1 | $x^{14} - 3 x^{13} - 5 x^{12} + 36 x^{11} - 38 x^{10} - 102 x^{9} + 268 x^{8} - 69 x^{7} - 438 x^{6} + 421 x^{5} + 114 x^{4} - 244 x^{3} + 46 x^{2} + 29 x - 8$ | $-\,19\cdot 149^{4}\cdot 211^{4}$ | $C_2^7.A_7$ (as 14T56) | trivial |
14.8.190...216.1 | $x^{14} + 4 x^{12} - 50 x^{10} + 72 x^{8} + 73 x^{6} - 104 x^{4} - 16 x^{2} + 4$ | $-\,2^{16}\cdot 4129^{4}$ | $C_2^4:\GL(3,2)$ (as 14T43) | trivial |
14.8.190...216.2 | $x^{14} + 4 x^{12} - 18 x^{10} - 20 x^{8} + 105 x^{6} - 76 x^{4} - 16 x^{2} + 16$ | $-\,2^{16}\cdot 4129^{4}$ | $C_2^4:\GL(3,2)$ (as 14T43) | trivial |
14.8.192...904.1 | $x^{14} - 4 x^{13} - 7 x^{12} + 30 x^{11} + 6 x^{10} + 6 x^{9} - 35 x^{8} - 70 x^{7} - 35 x^{6} + 6 x^{5} + 6 x^{4} + 30 x^{3} - 7 x^{2} - 4 x + 1$ | $-\,2^{12}\cdot 19\cdot 3967^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | trivial |
14.8.224...343.1 | $x^{14} - 3 x^{12} - 21 x^{10} + 75 x^{8} + 12 x^{6} - 173 x^{4} + 21 x^{2} + 92$ | $-\,23\cdot 149^{4}\cdot 211^{4}$ | $C_2^7.A_7$ (as 14T56) | trivial |
14.8.287...904.1 | $x^{14} - 3 x^{12} - 32 x^{10} + 32 x^{8} + 104 x^{6} - 148 x^{4} + 44 x^{2} + 4$ | $-\,2^{26}\cdot 809^{4}$ | $C_2^4:\GL(3,2)$ (as 14T43) | trivial |
14.8.287...904.2 | $x^{14} - 12 x^{12} + 30 x^{10} + 92 x^{8} - 295 x^{6} - 216 x^{4} + 80 x^{2} + 16$ | $-\,2^{26}\cdot 809^{4}$ | $C_2^4:\GL(3,2)$ (as 14T43) | trivial |
14.8.374...303.1 | $x^{14} - 4 x^{13} - 7 x^{12} + 41 x^{11} + 11 x^{10} - 166 x^{9} + 25 x^{8} + 337 x^{7} - 98 x^{6} - 358 x^{5} + 113 x^{4} + 186 x^{3} - 54 x^{2} - 37 x + 11$ | $-\,218599\cdot 171431488499897$ | $S_{14}$ (as 14T63) | trivial |
14.8.429...591.1 | $x^{14} - 5 x^{13} - 2 x^{12} + 41 x^{11} - 23 x^{10} - 132 x^{9} + 106 x^{8} + 211 x^{7} - 172 x^{6} - 172 x^{5} + 121 x^{4} + 65 x^{3} - 34 x^{2} - 9 x + 1$ | $-\,23\cdot 49081\cdot 4208629\cdot 9037933$ | $S_{14}$ (as 14T63) | trivial |
14.8.627...744.1 | $x^{14} + x^{12} - 20 x^{11} + 5 x^{10} + 22 x^{9} + 67 x^{8} - 30 x^{7} - 163 x^{6} + 38 x^{5} + 129 x^{4} - 2 x^{3} - 39 x^{2} - 12 x - 1$ | $-\,2^{12}\cdot 19\cdot 73^{8}$ | $C_2\wr C_7:C_3$ (as 14T44) | trivial |
14.8.627...744.2 | $x^{14} - 7 x^{13} + 26 x^{12} - 65 x^{11} + 99 x^{10} - 66 x^{9} - 53 x^{8} + 179 x^{7} - 173 x^{6} + 30 x^{5} + 79 x^{4} - 73 x^{3} + 6 x^{2} + 17 x + 1$ | $-\,2^{12}\cdot 19\cdot 73^{8}$ | $C_2\wr C_7:C_3$ (as 14T44) | trivial |
14.8.705...375.1 | $x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 3 x^{7} + 294 x^{6} + 21 x^{5} - 196 x^{4} - 42 x^{3} + 49 x^{2} + 21 x + 1$ | $-\,5^{7}\cdot 7^{14}\cdot 11^{3}$ | $D_7^2:C_6$ (as 14T32) | trivial |
14.8.145...144.1 | $x^{14} - 2 x^{13} - 15 x^{12} + 38 x^{11} + 55 x^{10} - 240 x^{9} + 75 x^{8} + 488 x^{7} - 613 x^{6} + 38 x^{5} + 407 x^{4} - 262 x^{3} - 11 x^{2} + 68 x - 19$ | $-\,2^{14}\cdot 11\cdot 73^{8}$ | $C_2\wr C_7:C_3$ (as 14T44) | trivial |
14.8.217...000.1 | $x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 2 x^{7} + 294 x^{6} + 14 x^{5} - 196 x^{4} - 28 x^{3} + 49 x^{2} + 14 x - 4$ | $-\,2^{12}\cdot 5^{7}\cdot 7^{14}$ | $D_7^2:C_6$ (as 14T32) | trivial |
14.8.303...392.1 | $x^{14} - 6 x^{13} - 3 x^{12} + 102 x^{11} - 281 x^{10} + 192 x^{9} + 343 x^{8} - 428 x^{7} - 625 x^{6} + 1330 x^{5} - 613 x^{4} + 6 x^{3} - 71 x^{2} + 36 x + 1$ | $-\,2^{14}\cdot 23\cdot 73^{8}$ | $C_2\wr C_7:C_3$ (as 14T44) | trivial |
14.8.618...156.1 | $x^{14} - 6 x^{12} - 25 x^{10} + 196 x^{8} - 313 x^{6} + 17 x^{4} + 173 x^{2} + 4$ | $-\,2^{2}\cdot 7^{8}\cdot 173^{6}$ | $C_2\wr F_7$ (as 14T48) | trivial |
14.8.773...667.1 | $x^{14} - 3 x^{13} - 18 x^{12} + 28 x^{11} + 114 x^{10} - 104 x^{9} - 289 x^{8} + 119 x^{7} + 365 x^{6} + 104 x^{5} - 343 x^{4} - 175 x^{3} + 158 x^{2} + 61 x - 17$ | $-\,3^{7}\cdot 29^{12}$ | $C_2\times F_8$ (as 14T9) | trivial |
14.8.845...656.1 | $x^{14} - 6 x^{13} + 12 x^{12} - 26 x^{11} + 110 x^{10} - 234 x^{9} + 248 x^{8} - 342 x^{7} + 538 x^{6} - 356 x^{5} + 186 x^{4} - 256 x^{3} + 64 x^{2} + 48 x - 10$ | $-\,2^{20}\cdot 73^{8}$ | $F_8:C_6$ (as 14T18) | trivial |
14.8.845...656.2 | $x^{14} - x^{12} - 27 x^{10} + 51 x^{8} + 67 x^{6} - 115 x^{4} - 41 x^{2} + 1$ | $-\,2^{20}\cdot 73^{8}$ | $F_8:C_6$ (as 14T18) | trivial |
14.8.845...656.3 | $x^{14} - 4 x^{12} - 40 x^{10} + 84 x^{8} + 136 x^{6} - 240 x^{4} + 4 x^{2} + 4$ | $-\,2^{20}\cdot 73^{8}$ | $F_8:C_6$ (as 14T18) | trivial |
14.8.108...023.1 | $x^{14} - 19 x^{12} + 87 x^{10} - 68 x^{8} - 213 x^{6} + 142 x^{4} + 153 x^{2} + 28$ | $-\,7^{9}\cdot 173^{6}$ | $C_2\wr F_7$ (as 14T48) | trivial |
14.8.123...312.1 | $x^{14} - 11 x^{12} - 5 x^{11} + 16 x^{10} + 106 x^{9} + 98 x^{8} - 326 x^{7} - 1116 x^{6} + 1552 x^{5} + 1784 x^{4} - 3304 x^{3} + 885 x^{2} + 579 x - 127$ | $-\,2^{3}\cdot 7^{8}\cdot 173^{6}$ | $C_2\wr F_7$ (as 14T48) | trivial |
14.8.158...875.1 | $x^{14} - 4 x^{13} + 13 x^{12} - 41 x^{11} + 67 x^{10} - 111 x^{9} - 129 x^{8} + 595 x^{7} - 667 x^{6} + 491 x^{5} + 697 x^{4} - 974 x^{3} + 220 x^{2} + 28 x - 7$ | $-\,5^{3}\cdot 7^{3}\cdot 577^{6}$ | $C_2\wr D_7$ (as 14T38) | trivial |
14.8.228...672.1 | $x^{14} - 21 x^{12} - 14 x^{11} + 119 x^{10} + 238 x^{9} - 147 x^{8} - 652 x^{7} - 441 x^{6} + 84 x^{5} - 483 x^{4} - 966 x^{3} - 511 x^{2} - 98 x - 5$ | $-\,2^{12}\cdot 7^{21}$ | $F_8:C_6$ (as 14T18) | trivial |
14.8.293...491.1 | $x^{14} - 9 x^{12} - 12 x^{11} + 10 x^{10} + 203 x^{9} - 52 x^{8} - 740 x^{7} + 268 x^{6} + 840 x^{5} - 361 x^{4} - 279 x^{3} + 136 x^{2} + 21 x - 10$ | $-\,7^{8}\cdot 19\cdot 173^{6}$ | $C_2\wr F_7$ (as 14T48) | trivial |
14.8.579...744.1 | $x^{14} + x^{12} - 12 x^{10} - 7 x^{8} + 28 x^{6} + 14 x^{4} - 9 x^{2} + 1$ | $-\,2^{14}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |
14.8.579...744.2 | $x^{14} - 6 x^{12} + 3 x^{10} + 33 x^{8} - 49 x^{6} + 2 x^{4} + 16 x^{2} + 1$ | $-\,2^{14}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |
14.8.579...744.3 | $x^{14} - 13 x^{12} + 31 x^{10} + 9 x^{8} - 54 x^{6} + 3 x^{4} + 23 x^{2} + 1$ | $-\,2^{14}\cdot 29^{12}$ | $C_2\times F_8$ (as 14T9) | trivial |
14.8.579...744.4 | $x^{14} + 7 x^{12} - 8 x^{10} - 52 x^{8} + 6 x^{6} + 50 x^{4} - 22 x^{2} + 1$ | $-\,2^{14}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |
14.8.579...744.5 | $x^{14} + 7 x^{12} - 8 x^{10} - 52 x^{8} + 6 x^{6} + 50 x^{4} - 22 x^{2} + 1$ | $-\,2^{14}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |
14.8.522...792.1 | $x^{14} - 4 x^{13} + 7 x^{12} - 14 x^{11} - 38 x^{10} + 132 x^{9} - 109 x^{8} + 230 x^{7} + 394 x^{6} - 580 x^{5} - 769 x^{4} + 474 x^{3} + 325 x^{2} - 52 x - 8$ | $-\,2^{14}\cdot 3^{7}\cdot 11^{3}\cdot 13^{6}\cdot 61^{3}$ | $D_7 \wr C_2$ (as 14T20) | trivial |
14.8.985...648.1 | $x^{14} - 3 x^{12} - 21 x^{10} + 73 x^{8} + 6 x^{6} - 125 x^{4} - 7 x^{2} + 17$ | $-\,2^{14}\cdot 17\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |
14.8.985...648.2 | $x^{14} - 11 x^{12} + 27 x^{10} + 66 x^{8} - 286 x^{6} + 65 x^{4} + 354 x^{2} + 17$ | $-\,2^{14}\cdot 17\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | trivial |