Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (46 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
14.0.121...711.1 | $x^{14} + 12 x^{12} - 60 x^{11} - 567 x^{10} + 237 x^{9} + 1873 x^{8} + 9867 x^{7} + 13383 x^{6} - 49512 x^{5} + 153774 x^{4} - 127299 x^{3} + 116395 x^{2} - 72588 x + 28167$ | $-\,3^{7}\cdot 1277^{7}$ | $D_{7}$ (as 14T2) | $[13, 78]$ |
14.0.284...272.1 | $x^{14} + 43 x^{12} + 722 x^{10} + 5993 x^{8} + 25558 x^{6} + 51799 x^{4} + 38148 x^{2} + 4913$ | $-\,2^{14}\cdot 17^{3}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | $[2, 2, 300]$ |
14.0.284...272.3 | $x^{14} + 48 x^{12} + 627 x^{10} + 3694 x^{8} + 11315 x^{6} + 18564 x^{4} + 15317 x^{2} + 4913$ | $-\,2^{14}\cdot 17^{3}\cdot 29^{12}$ | $C_2 \wr C_7$ (as 14T29) | $[2, 2, 352]$ |
14.0.604...375.1 | $x^{14} - 5 x^{13} + 13 x^{12} - 19 x^{11} + 150 x^{10} - 514 x^{9} + 2438 x^{8} - 6347 x^{7} + 22552 x^{6} - 42720 x^{5} + 123031 x^{4} - 143071 x^{3} + 363084 x^{2} - 231593 x + 499381$ | $-\,3^{7}\cdot 5^{7}\cdot 29^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 2, 226]$ |
14.0.752...296.1 | $x^{14} - 6 x^{13} + 62 x^{12} - 216 x^{11} + 1342 x^{10} - 3380 x^{9} + 16766 x^{8} - 24824 x^{7} + 116798 x^{6} - 76004 x^{5} + 491768 x^{4} + 348032 x^{3} + 1136904 x^{2} + 1104360 x + 328124$ | $-\,2^{28}\cdot 809^{6}$ | $C_2\times \GL(3,2)$ (as 14T17) | $[2, 4, 184]$ |
14.0.752...296.2 | $x^{14} - 6 x^{13} + 62 x^{12} - 216 x^{11} + 1342 x^{10} - 3380 x^{9} + 16766 x^{8} - 24824 x^{7} + 116798 x^{6} - 76004 x^{5} + 491768 x^{4} + 348032 x^{3} + 1136904 x^{2} + 1104360 x + 328124$ | $-\,2^{28}\cdot 809^{6}$ | $C_2\times \GL(3,2)$ (as 14T17) | $[2, 4, 184]$ |
14.0.134...375.1 | $x^{14} - x^{13} + 45 x^{12} + 67 x^{11} + 585 x^{10} + 2263 x^{9} + 4916 x^{8} + 17291 x^{7} + 36289 x^{6} + 71331 x^{5} + 129077 x^{4} + 181931 x^{3} + 270017 x^{2} + 169588 x + 119189$ | $-\,5^{7}\cdot 43^{13}$ | $C_{14}$ (as 14T1) | $[2842]$ |
14.0.199...319.1 | $x^{14} - x^{13} + 74 x^{12} - 75 x^{11} + 1806 x^{10} - 1882 x^{9} + 17670 x^{8} - 25893 x^{7} + 68157 x^{6} - 189003 x^{5} + 252348 x^{4} - 306967 x^{3} + 1166437 x^{2} - 1133182 x + 741761$ | $-\,11^{7}\cdot 29^{13}$ | $C_{14}$ (as 14T1) | $[2, 8, 8, 40]$ |
14.0.268...544.1 | $x^{14} + 61 x^{12} + 1402 x^{10} + 15247 x^{8} + 80418 x^{6} + 185798 x^{4} + 127429 x^{2} + 18769$ | $-\,2^{14}\cdot 71^{12}$ | $C_{14}$ (as 14T1) | $[3277]$ |
14.0.301...184.1 | $x^{14} - 3 x^{13} + 53 x^{12} - 138 x^{11} + 974 x^{10} - 3260 x^{9} + 12820 x^{8} - 35464 x^{7} + 93202 x^{6} - 154986 x^{5} + 383670 x^{4} - 324844 x^{3} + 666130 x^{2} - 377314 x + 391402$ | $-\,2^{30}\cdot 809^{6}$ | $C_2^4:\GL(3,2)$ (as 14T43) | $[2, 2, 504]$ |
14.0.316...299.1 | $x^{14} - 5 x^{13} + 20 x^{12} - 49 x^{11} + 288 x^{10} - 863 x^{9} + 4381 x^{8} - 11303 x^{7} + 44797 x^{6} - 86598 x^{5} + 279108 x^{4} - 343260 x^{3} + 959807 x^{2} - 625188 x + 1493501$ | $-\,19^{7}\cdot 29^{12}$ | $C_{14}$ (as 14T1) | $[4, 4, 284]$ |
14.0.383...176.1 | $x^{14} - 24 x^{12} + 474 x^{10} + 1144 x^{8} - 21471 x^{6} + 13728 x^{4} + 92356 x^{2} + 100416$ | $-\,2^{14}\cdot 3^{7}\cdot 523^{7}$ | $D_{7}$ (as 14T2) | $[86, 86]$ |
14.0.452...000.1 | $x^{14} - 2 x^{13} + 12 x^{12} - 22 x^{11} + 261 x^{10} - 332 x^{9} + 3687 x^{8} - 2596 x^{7} + 35841 x^{6} - 17536 x^{5} + 240758 x^{4} - 110934 x^{3} + 986314 x^{2} - 244032 x + 1783541$ | $-\,2^{14}\cdot 5^{7}\cdot 29^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 2, 406]$ |
14.0.564...168.1 | $x^{14} - 4 x^{12} + 122 x^{10} + 4936 x^{8} + 46193 x^{6} + 26604 x^{4} + 692068 x^{2} + 106112$ | $-\,2^{21}\cdot 829^{7}$ | $D_{7}$ (as 14T2) | $[13, 78]$ |
14.0.120...327.1 | $x^{14} - 5 x^{13} + 27 x^{12} - 79 x^{11} + 468 x^{10} - 1362 x^{9} + 7314 x^{8} - 18671 x^{7} + 80950 x^{6} - 158128 x^{5} + 561187 x^{4} - 714115 x^{3} + 2179894 x^{2} - 1446221 x + 3780979$ | $-\,23^{7}\cdot 29^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 1806]$ |
14.0.162...384.1 | $x^{14} - 2 x^{13} + 19 x^{12} - 34 x^{11} + 402 x^{10} - 528 x^{9} + 6227 x^{8} - 4968 x^{7} + 67046 x^{6} - 36022 x^{5} + 492458 x^{4} - 218804 x^{3} + 2200477 x^{2} - 533070 x + 4387351$ | $-\,2^{21}\cdot 3^{7}\cdot 29^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 2, 602]$ |
14.0.169...719.1 | $x^{14} - 4 x^{13} + 44 x^{12} - 131 x^{11} + 223 x^{10} - 2372 x^{9} - 1828 x^{8} + 4867 x^{7} + 79816 x^{6} + 233126 x^{5} + 1093209 x^{4} + 1284789 x^{3} - 851090 x^{2} - 4392150 x + 4773375$ | $-\,7759^{7}$ | $D_{7}$ (as 14T2) | $[29, 203]$ |
14.0.175...875.1 | $x^{14} - x^{13} + 103 x^{12} - 104 x^{11} + 3546 x^{10} - 3651 x^{9} + 50063 x^{8} - 69132 x^{7} + 283946 x^{6} - 695198 x^{5} + 1099322 x^{4} - 1801888 x^{3} + 5495644 x^{2} - 5241351 x + 3832639$ | $-\,3^{7}\cdot 5^{7}\cdot 29^{13}$ | $C_{14}$ (as 14T1) | $[2, 2, 4, 4, 116]$ |
14.0.188...759.1 | $x^{14} + 32 x^{12} + 236 x^{10} + 1227 x^{8} + 24852 x^{6} + 110594 x^{4} + 6367700 x^{2} + 6626239$ | $-\,7879^{7}$ | $D_{7}$ (as 14T2) | $[13, 91]$ |
14.0.281...664.1 | $x^{14} + 84 x^{12} + 2156 x^{10} + 19208 x^{8} + 60368 x^{6} + 47040 x^{4} + 12544 x^{2} + 896$ | $-\,2^{21}\cdot 7^{25}$ | $C_{14}$ (as 14T1) | $[2468]$ |
14.0.360...936.1 | $x^{14} + 86 x^{12} + 2408 x^{10} + 27176 x^{8} + 136224 x^{6} + 288960 x^{4} + 195392 x^{2} + 5504$ | $-\,2^{21}\cdot 43^{13}$ | $C_{14}$ (as 14T1) | $[1970]$ |
14.0.363...375.1 | $x^{14} + 12 x^{12} - 36 x^{10} + 2431 x^{8} + 35784 x^{6} + 52722 x^{4} + 7209736 x^{2} + 2501295$ | $-\,3^{7}\cdot 5^{7}\cdot 577^{7}$ | $D_{7}$ (as 14T2) | $[26, 78]$ |
14.0.373...571.1 | $x^{14} - 7 x^{13} + 49 x^{11} + 238 x^{10} - 623 x^{9} - 497 x^{8} + 1135 x^{7} + 15785 x^{6} + 2002 x^{5} + 16814 x^{4} + 4662 x^{3} + 298305 x^{2} + 401044 x + 766979$ | $-\,7^{24}\cdot 11^{7}$ | $C_{14}$ (as 14T1) | $[2059]$ |
14.0.522...875.1 | $x^{14} - 6 x^{13} + 47 x^{12} - 96 x^{11} + 817 x^{10} - 1614 x^{9} + 15353 x^{8} - 11976 x^{7} + 129647 x^{6} + 14466 x^{5} + 2094349 x^{4} - 5253552 x^{3} + 26472884 x^{2} - 34197120 x + 63264400$ | $-\,5^{7}\cdot 1823^{7}$ | $D_{7}$ (as 14T2) | $[29, 58]$ |
14.0.682...375.1 | $x^{14} - 5 x^{13} + x^{12} - 15 x^{11} + 290 x^{10} - 82 x^{9} + 1576 x^{8} - 399 x^{7} + 22358 x^{6} + 20590 x^{5} + 123285 x^{4} + 99663 x^{3} + 589214 x^{2} + 602483 x + 1228891$ | $-\,3^{7}\cdot 5^{7}\cdot 43^{12}$ | $C_{14}$ (as 14T1) | $[1766]$ |
14.0.947...747.1 | $x^{14} - x^{13} + 49 x^{12} + 122 x^{11} + 1955 x^{10} + 2412 x^{9} + 16259 x^{8} - 10342 x^{7} + 95434 x^{6} + 70 x^{5} + 15469 x^{4} - 1212 x^{3} + 2389 x^{2} - 49 x + 1$ | $-\,3^{7}\cdot 113^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 254]$ |
14.0.344...632.1 | $x^{14} - 2 x^{13} - 45 x^{12} + 30 x^{11} + 1030 x^{10} + 632 x^{9} - 11085 x^{8} - 20276 x^{7} + 43102 x^{6} + 151674 x^{5} + 206418 x^{4} + 411952 x^{3} + 987997 x^{2} + 1336242 x + 1953011$ | $-\,2^{21}\cdot 71^{12}$ | $C_{14}$ (as 14T1) | $[1247]$ |
14.0.385...827.1 | $x^{14} - x^{13} + 55 x^{12} - 8 x^{11} + 2389 x^{10} - 526 x^{9} + 27699 x^{8} + 21346 x^{7} + 220112 x^{6} + 184596 x^{5} + 991629 x^{4} + 1196220 x^{3} + 2970241 x^{2} + 1920273 x + 1256641$ | $-\,3^{7}\cdot 127^{12}$ | $C_{14}$ (as 14T1) | $[7, 301]$ |
14.0.710...304.1 | $x^{14} + 97 x^{12} + 2854 x^{10} + 31395 x^{8} + 102938 x^{6} + 30646 x^{4} + 2377 x^{2} + 1$ | $-\,2^{14}\cdot 113^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 406]$ |
14.0.910...875.1 | $x^{14} - x^{13} + 74 x^{12} - 82 x^{11} + 1819 x^{10} + 937 x^{9} + 14518 x^{8} + 14729 x^{7} + 152364 x^{6} + 274929 x^{5} + 790947 x^{4} + 804688 x^{3} + 2049631 x^{2} + 913390 x + 867961$ | $-\,5^{7}\cdot 71^{13}$ | $C_{14}$ (as 14T1) | $[2, 2, 2, 2, 2, 2, 116]$ |
14.0.136...247.1 | $x^{14} - 5 x^{13} + 15 x^{12} - 75 x^{11} + 512 x^{10} - 682 x^{9} + 6620 x^{8} - 4227 x^{7} + 79540 x^{6} + 24230 x^{5} + 605069 x^{4} + 323699 x^{3} + 3152636 x^{2} + 2157359 x + 7742617$ | $-\,23^{7}\cdot 43^{12}$ | $C_{14}$ (as 14T1) | $[7899]$ |
14.0.288...864.1 | $x^{14} + 109 x^{12} + 4094 x^{10} + 64587 x^{8} + 492142 x^{6} + 1843230 x^{4} + 3006113 x^{2} + 1256641$ | $-\,2^{14}\cdot 127^{12}$ | $C_{14}$ (as 14T1) | $[43, 43]$ |
14.0.660...375.2 | $x^{14} - 4 x^{13} - 34 x^{12} + 43 x^{11} + 366 x^{10} + 1216 x^{9} + 3543 x^{8} - 8008 x^{7} - 34422 x^{6} + 10861 x^{5} - 72730 x^{4} + 16752 x^{3} + 704216 x^{2} - 1267280 x + 2152640$ | $-\,5^{7}\cdot 7^{7}\cdot 29^{13}$ | $D_{14}$ (as 14T3) | $[2, 728]$ |
14.0.107...411.1 | $x^{14} - x^{13} + 61 x^{12} - 82 x^{11} + 908 x^{10} - 5925 x^{9} + 1220 x^{8} - 34756 x^{7} + 145654 x^{6} + 6877 x^{5} + 1495378 x^{4} + 369519 x^{3} + 4546573 x^{2} + 398747 x + 3805387$ | $-\,3^{7}\cdot 113^{13}$ | $C_{14}$ (as 14T1) | $[2, 2, 2, 426]$ |
14.0.244...872.1 | $x^{14} + 142 x^{12} + 6248 x^{10} + 106216 x^{8} + 838368 x^{6} + 3176256 x^{4} + 5266496 x^{2} + 2626432$ | $-\,2^{21}\cdot 71^{13}$ | $C_{14}$ (as 14T1) | $[5212]$ |
14.0.356...383.1 | $x^{14} - 5 x^{13} - 73 x^{12} + 489 x^{11} + 1036 x^{10} - 13306 x^{9} + 27880 x^{8} - 19951 x^{7} + 48006 x^{6} - 117192 x^{5} + 670781 x^{4} - 1091251 x^{3} + 2003814 x^{2} - 1429473 x + 1305077$ | $-\,7^{7}\cdot 113^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 1582]$ |
14.0.747...867.1 | $x^{14} - x^{13} + 85 x^{12} - 350 x^{11} + 5925 x^{10} - 19520 x^{9} + 153467 x^{8} - 374872 x^{7} + 2559802 x^{6} - 4851594 x^{5} + 17583457 x^{4} + 2579356 x^{3} + 6691533 x^{2} - 1666579 x + 1352569$ | $-\,3^{7}\cdot 197^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 1682]$ |
14.0.144...503.1 | $x^{14} - 5 x^{13} - 85 x^{12} + 413 x^{11} + 2536 x^{10} - 12422 x^{9} - 23248 x^{8} + 150497 x^{7} + 150754 x^{6} - 1228000 x^{5} + 66341 x^{4} + 5215705 x^{3} - 2368956 x^{2} - 14809311 x + 22851677$ | $-\,7^{7}\cdot 127^{12}$ | $C_{14}$ (as 14T1) | $[8141]$ |
14.0.170...627.1 | $x^{14} - x^{13} + 91 x^{12} + 228 x^{11} + 6725 x^{10} + 8698 x^{9} + 111679 x^{8} - 102522 x^{7} + 1215344 x^{6} - 1305976 x^{5} + 7192317 x^{4} - 11528880 x^{3} + 28130213 x^{2} - 24476087 x + 21743569$ | $-\,3^{7}\cdot 211^{12}$ | $C_{14}$ (as 14T1) | $[29, 203]$ |
14.0.559...144.1 | $x^{14} + 169 x^{12} + 10186 x^{10} + 284395 x^{8} + 3790966 x^{6} + 20272254 x^{4} + 11329577 x^{2} + 1352569$ | $-\,2^{14}\cdot 197^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 1582]$ |
14.0.759...827.1 | $x^{14} - x^{13} + 103 x^{12} - 288 x^{11} + 8749 x^{10} - 17168 x^{9} + 207881 x^{8} + 164988 x^{7} + 2712410 x^{6} + 2203236 x^{5} + 18493219 x^{4} + 27913574 x^{3} + 74729515 x^{2} + 46299739 x + 26863489$ | $-\,3^{7}\cdot 239^{12}$ | $C_{14}$ (as 14T1) | $[2, 2, 1906]$ |
14.0.100...688.1 | $x^{14} - 7 x^{13} + 35 x^{12} - 119 x^{11} + 329 x^{10} - 721 x^{9} + 1337 x^{8} + 2011 x^{7} - 11522 x^{6} - 130648 x^{5} + 357532 x^{4} + 69076 x^{3} - 467348 x^{2} + 127316 x + 4139276$ | $-\,2^{12}\cdot 3^{12}\cdot 7^{11}\cdot 13^{12}$ | $F_7$ (as 14T4) | $[7, 14, 14]$ |
14.0.127...464.1 | $x^{14} + 181 x^{12} + 10574 x^{10} + 250587 x^{8} + 2642670 x^{6} + 13082270 x^{4} + 28708425 x^{2} + 21743569$ | $-\,2^{14}\cdot 211^{12}$ | $C_{14}$ (as 14T1) | $[5923]$ |
14.0.332...739.1 | $x^{14} - x^{13} + 14 x^{12} + 754 x^{11} + 840 x^{10} - 19828 x^{9} - 8271 x^{8} + 300557 x^{7} - 186895 x^{6} - 3184843 x^{5} + 2562883 x^{4} + 17073682 x^{3} - 11883459 x^{2} - 10003960 x + 148699319$ | $-\,379^{13}$ | $C_{14}$ (as 14T1) | $[4497]$ |
14.0.584...576.1 | $x^{14} + 406 x^{12} - 16730854 x^{8} - 1089212740 x^{6} + 276531310818 x^{4} + 40488433813828 x^{2} + 1912907783410246$ | $-\,2^{27}\cdot 3^{12}\cdot 7^{15}\cdot 29^{7}$ | $F_7 \times C_2$ (as 14T7) | $[2, 2, 2, 2, 168]$ |
14.0.198...763.1 | $x^{14} - x^{13} + 32 x^{12} - 766 x^{11} - 3350 x^{10} - 49474 x^{9} + 1057143 x^{8} - 6931854 x^{7} + 98559596 x^{6} - 654977697 x^{5} + 2734738830 x^{4} - 9840332223 x^{3} + 18337865967 x^{2} - 41024712654 x + 132193055349$ | $-\,883^{13}$ | $C_{14}$ (as 14T1) | $[3489]$ |
14.0.116...784.1 | $x^{14} + 154 x^{12} + 8316 x^{10} + 251174 x^{8} + 1847384 x^{6} - 125641362 x^{4} - 1580335988 x^{2} + 27024383386$ | $-\,2^{27}\cdot 3^{12}\cdot 7^{15}\cdot 11^{13}$ | $F_7 \times C_2$ (as 14T7) | $[14, 84]$ |
14.0.248...007.1 | $x^{14} - 7 x^{13} + 135 x^{12} + 1975 x^{11} - 6476 x^{10} + 17252 x^{9} - 1085600 x^{8} + 9712208 x^{7} + 91040832 x^{6} + 1779503808 x^{5} + 18283373824 x^{4} + 20411874304 x^{3} + 896560656384 x^{2} - 1105033789440 x + 12202986700800$ | $-\,7^{7}\cdot 449^{13}$ | $D_{14}$ (as 14T3) | $[7, 728]$ |
14.0.872...544.1 | $x^{14} - 7 x^{13} + 91 x^{12} - 455 x^{11} + 3185 x^{10} - 11921 x^{9} + 57057 x^{8} - 161157 x^{7} + 569646 x^{6} - 1244768 x^{5} + 3318980 x^{4} - 3806180 x^{3} + 7849828 x^{2} - 8070916 x + 10765732$ | $-\,2^{12}\cdot 3^{13}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7}$ | $F_7 \times C_2$ (as 14T7) | $[2, 28, 84]$ |
14.0.319...328.1 | $x^{14} - 500742 x^{7} + 80813044224$ | $-\,2^{12}\cdot 3^{12}\cdot 7^{14}\cdot 11^{13}\cdot 13^{7}$ | $F_7 \times C_2$ (as 14T7) | $[2, 14, 210]$ |