Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 10.0.628...375.3 | $x^{10} - 3 x^{9} - 200 x^{8} + 50 x^{7} + 17637 x^{6} + 39445 x^{5} - 111526 x^{4} - 277572 x^{3} + 13054024 x^{2} + 41505856 x + 259861504$ | $-\,5^{5}\cdot 11^{9}\cdot 31^{8}$ | $C_{10}$ (as 10T1) | $[5, 323020]$ |
| 10.0.643...216.1 | $x^{10} - 4 x^{9} + 958 x^{8} - 4665 x^{7} + 278855 x^{6} - 1454066 x^{5} + 24175986 x^{4} - 84161493 x^{3} + 652991260 x^{2} - 937938928 x + 3403448896$ | $-\,2^{4}\cdot 7^{5}\cdot 11^{5}\cdot 683^{5}$ | $S_5\times C_2$ (as 10T22) | $[2, 2, 4, 87232]$ |
| 10.0.707...912.1 | $x^{10} - x^{9} + 1923 x^{8} - 816 x^{7} + 1157331 x^{6} + 321673 x^{5} + 281803831 x^{4} + 325170094 x^{3} + 25626726749 x^{2} + 49966208609 x + 482292936557$ | $-\,2^{8}\cdot 911\cdot 7877^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[1584452]$ |
| 10.0.750...664.1 | $x^{10} - 5 x^{9} + 2423 x^{8} - 8692 x^{7} + 1868443 x^{6} - 4498183 x^{5} + 530586161 x^{4} - 748640234 x^{3} + 49735891247 x^{2} + 5681312919 x + 471283132849$ | $-\,2^{8}\cdot 967\cdot 7877^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[1554084]$ |
| 10.0.108...576.1 | $x^{10} - x^{9} + 1893 x^{8} - 3504 x^{7} + 1276235 x^{6} - 2961223 x^{5} + 373233749 x^{4} - 853615520 x^{3} + 46350711425 x^{2} - 66930590451 x + 1954071052519$ | $-\,2^{8}\cdot 3^{5}\cdot 79\cdot 4663^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 542260]$ |
| 10.0.148...168.1 | $x^{10} - 2 x^{9} + 972 x^{8} - 1622 x^{7} + 346194 x^{6} - 403214 x^{5} + 54823876 x^{4} - 20970154 x^{3} + 3410502909 x^{2} + 2301148560 x + 27250245952$ | $-\,2^{12}\cdot 13^{4}\cdot 71\cdot 1123^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 577644]$ |
| 10.0.150...479.1 | $x^{10} - 3 x^{9} + 1192 x^{8} - 2271 x^{7} + 532279 x^{6} - 680787 x^{5} + 112056765 x^{4} - 97878333 x^{3} + 11084242194 x^{2} - 5593138587 x + 409655699073$ | $-\,3^{8}\cdot 47^{5}\cdot 127\cdot 151^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 403352]$ |
| 10.0.155...248.1 | $x^{10} - x^{9} + 1683 x^{8} - 6314 x^{7} + 778233 x^{6} - 3012297 x^{5} + 148852305 x^{4} - 449392578 x^{3} + 12436182423 x^{2} - 20758248877 x + 370378729961$ | $-\,2^{8}\cdot 23^{5}\cdot 167\cdot 563^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 611046]$ |
| 10.0.158...024.1 | $x^{10} - x^{9} + 2555 x^{8} - 7670 x^{7} + 1851333 x^{6} - 6420165 x^{5} + 496082907 x^{4} - 1610199486 x^{3} + 41845897883 x^{2} - 77128988463 x + 1032450676307$ | $-\,2^{8}\cdot 23\cdot 89\cdot 7877^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 555538]$ |
| 10.0.161...432.1 | $x^{10} - 5 x^{9} + 1840 x^{8} - 6098 x^{7} + 1152610 x^{6} - 2275598 x^{5} + 304703927 x^{4} - 386793039 x^{3} + 32286465364 x^{2} - 33147017568 x + 894763149292$ | $-\,2^{4}\cdot 23\cdot 33769^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[4792546]$ |
| 10.0.191...375.1 | $x^{10} - 2 x^{9} + 2123 x^{8} - 4935 x^{7} + 1590810 x^{6} - 3831663 x^{5} + 530400204 x^{4} - 1016090979 x^{3} + 78545129335 x^{2} - 82253825368 x + 4074757701173$ | $-\,5^{4}\cdot 823\cdot 8209^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[1982006]$ |
| 10.0.199...296.1 | $x^{10} - x^{9} + 1979 x^{8} + 856 x^{7} + 1325433 x^{6} + 2526999 x^{5} + 343943117 x^{4} + 987550224 x^{3} + 31632555517 x^{2} + 55797224205 x + 877969004033$ | $-\,2^{8}\cdot 7\cdot 43^{5}\cdot 137\cdot 223^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 93034]$ |
| 10.0.238...544.1 | $x^{10} - 2 x^{9} + 2622 x^{8} - 2162 x^{7} + 2475674 x^{6} - 1237012 x^{5} + 1070277192 x^{4} - 371808344 x^{3} + 214692324912 x^{2} - 38342140748 x + 16080825035788$ | $-\,2^{8}\cdot 43^{5}\cdot 223^{5}\cdot 1151$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 225114]$ |
| 10.0.253...032.1 | $x^{10} - 5 x^{9} + 2305 x^{8} - 8972 x^{7} + 1813565 x^{6} - 5390981 x^{5} + 609511595 x^{4} - 1359279508 x^{3} + 79611803567 x^{2} - 125243148359 x + 1625837749351$ | $-\,2^{8}\cdot 3271\cdot 7877^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2618098]$ |
| 10.0.284...000.1 | $x^{10} - 4 x^{9} + 1312 x^{8} - 2812 x^{7} + 334866 x^{6} - 622792 x^{5} + 35968970 x^{4} - 58590024 x^{3} + 1796508891 x^{2} - 1963442484 x + 36465933124$ | $-\,2^{17}\cdot 5^{4}\cdot 127\cdot 1223^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 4, 446120]$ |
| 10.0.312...607.1 | $x^{10} - x^{9} + 1171 x^{8} - 3079 x^{7} + 379552 x^{6} - 1641187 x^{5} + 44301709 x^{4} - 235375210 x^{3} + 1550199577 x^{2} - 5232980281 x + 15965643561$ | $-\,23^{4}\cdot 127\cdot 3881^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 299880]$ |
| 10.0.326...232.1 | $x^{10} - 4 x^{9} + 938 x^{8} - 1403 x^{7} + 259003 x^{6} + 13428 x^{5} + 28185507 x^{4} + 34286094 x^{3} + 1154343708 x^{2} + 2299452837 x + 9587289093$ | $-\,2^{3}\cdot 3^{9}\cdot 7^{5}\cdot 11^{4}\cdot 89^{5}\cdot 151$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 83444]$ |
| 10.0.357...368.1 | $x^{10} + 1414 x^{8} - 602 x^{7} + 714469 x^{6} - 283896 x^{5} + 160084733 x^{4} - 34597226 x^{3} + 15816893686 x^{2} - 2620814348 x + 537780706553$ | $-\,2^{10}\cdot 32257^{5}$ | $S_5\times C_2$ (as 10T22) | $[4, 643448]$ |
| 10.0.475...312.1 | $x^{10} - 5 x^{9} + 2105 x^{8} - 7592 x^{7} + 1194462 x^{6} - 2014928 x^{5} + 170806878 x^{4} - 63735179 x^{3} + 9620616688 x^{2} + 1657616602 x + 186530290757$ | $-\,2^{4}\cdot 3^{8}\cdot 41^{6}\cdot 157^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 357246]$ |
| 10.0.484...375.1 | $x^{10} - 2 x^{9} + 1747 x^{8} + 944 x^{7} + 971954 x^{6} + 2722455 x^{5} + 192827610 x^{4} + 884798920 x^{3} + 9397543880 x^{2} + 23585975120 x + 102522563680$ | $-\,3^{5}\cdot 5^{7}\cdot 23^{5}\cdot 71\cdot 89^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 136620]$ |
| 10.0.507...375.1 | $x^{10} - 4 x^{9} + 627 x^{8} - 2412 x^{7} + 158169 x^{6} - 492927 x^{5} + 19965215 x^{4} - 41299184 x^{3} + 1235206776 x^{2} - 1220448555 x + 29655558069$ | $-\,3^{8}\cdot 5^{4}\cdot 311\cdot 2089^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 317248]$ |
| 10.0.555...375.1 | $x^{10} - 3 x^{9} + 1635 x^{8} - 1976 x^{7} + 955517 x^{6} - 292235 x^{5} + 252290186 x^{4} + 35353907 x^{3} + 30099880585 x^{2} + 7960847135 x + 1309604152695$ | $-\,5^{4}\cdot 2383\cdot 8209^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[5392456]$ |
| 10.0.588...375.3 | $x^{10} - 3 x^{9} - 288 x^{8} + 842 x^{7} + 30309 x^{6} - 92907 x^{5} - 231118 x^{4} + 2902660 x^{3} + 22742472 x^{2} - 121997088 x + 574971904$ | $-\,5^{5}\cdot 11^{9}\cdot 41^{8}$ | $C_{10}$ (as 10T1) | $[1237220]$ |
| 10.0.593...944.1 | $x^{10} - 2 x^{9} + 2129 x^{8} - 5376 x^{7} + 1232617 x^{6} - 2123466 x^{5} + 295820867 x^{4} - 231640878 x^{3} + 30746005365 x^{2} - 3259792792 x + 1124127344513$ | $-\,2^{11}\cdot 47\cdot 14389^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 1166384]$ |
| 10.0.604...552.1 | $x^{10} - x^{9} + 2267 x^{8} - 2104 x^{7} + 1219415 x^{6} - 983671 x^{5} + 277545205 x^{4} - 182841618 x^{3} + 29019544121 x^{2} - 12222711205 x + 1154562525973$ | $-\,2^{8}\cdot 383\cdot 14389^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 802302]$ |
| 10.0.732...699.1 | $x^{10} - 4 x^{9} + 1360 x^{8} - 1252 x^{7} + 609123 x^{6} + 876933 x^{5} + 103448760 x^{4} + 241242808 x^{3} + 6091093773 x^{2} + 8533424737 x + 71637635729$ | $-\,7^{5}\cdot 21277^{5}$ | $S_5\times C_2$ (as 10T22) | $[3172128]$ |
| 10.0.760...087.1 | $x^{10} + 668 x^{8} - 546 x^{7} + 164005 x^{6} - 223799 x^{5} + 18561287 x^{4} - 31137382 x^{3} + 927828436 x^{2} - 1386673298 x + 14492860427$ | $-\,3^{2}\cdot 7^{4}\cdot 11^{5}\cdot 17^{5}\cdot 109^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 72998]$ |
| 10.0.856...736.1 | $x^{10} - 2 x^{9} + 2828 x^{8} - 7998 x^{7} + 2578878 x^{6} - 6635962 x^{5} + 961498292 x^{4} - 1708634208 x^{3} + 150059785732 x^{2} - 106106580684 x + 7961919160916$ | $-\,2^{8}\cdot 23^{5}\cdot 563^{5}\cdot 919$ | $C_2 \wr S_5$ (as 10T39) | $[2, 1429620]$ |
| 10.0.865...664.1 | $x^{10} - 3 x^{9} + 2347 x^{8} - 6384 x^{7} + 1766089 x^{6} - 4424351 x^{5} + 527063913 x^{4} - 1143145264 x^{3} + 56022399849 x^{2} - 85910173107 x + 1752294565441$ | $-\,2^{8}\cdot 3^{5}\cdot 631\cdot 4663^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 1018200]$ |
| 10.0.901...504.1 | $x^{10} - 4 x^{9} + 1333 x^{8} - 1448 x^{7} + 536438 x^{6} + 247396 x^{5} + 70257090 x^{4} + 87693456 x^{3} + 3449697060 x^{2} + 6299207484 x + 32775855180$ | $-\,2^{10}\cdot 3^{8}\cdot 73\cdot 2837^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 678578]$ |
| 10.0.100...000.1 | $x^{10} - 3 x^{9} + 831 x^{8} - 3475 x^{7} + 231241 x^{6} - 806295 x^{5} + 22896754 x^{4} - 33057950 x^{3} + 626597324 x^{2} - 1601563068 x + 2454515504$ | $-\,2^{12}\cdot 5^{7}\cdot 7\cdot 17\cdot 1213^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 190938]$ |
| 10.0.109...743.1 | $x^{10} - 5 x^{9} + 1995 x^{8} - 7133 x^{7} + 1377392 x^{6} - 3181881 x^{5} + 391178085 x^{4} - 396247368 x^{3} + 39811743411 x^{2} + 22468783287 x + 880177492257$ | $-\,3^{7}\cdot 127\cdot 13147^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 841912]$ |
| 10.0.110...832.1 | $x^{10} - 2 x^{9} + 1827 x^{8} - 762 x^{7} + 1185465 x^{6} + 302218 x^{5} + 350197986 x^{4} + 145150870 x^{3} + 46804624505 x^{2} + 12920134602 x + 2157772108942$ | $-\,2^{10}\cdot 7^{5}\cdot 5779^{5}$ | $S_5\times C_2$ (as 10T22) | $[2, 1713764]$ |
| 10.0.115...016.1 | $x^{10} - 4 x^{9} + 3392 x^{8} - 13470 x^{7} + 4291614 x^{6} - 13629578 x^{5} + 2573889748 x^{4} - 5461060248 x^{3} + 739039434840 x^{2} - 757743289344 x + 81770028569532$ | $-\,2^{8}\cdot 3^{5}\cdot 839\cdot 4663^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 897250]$ |
| 10.0.115...879.1 | $x^{10} - 3 x^{9} + 2183 x^{8} - 10083 x^{7} + 1298893 x^{6} - 4875372 x^{5} + 293387043 x^{4} - 660147399 x^{3} + 23766510915 x^{2} - 10928925468 x + 518699737689$ | $-\,3^{7}\cdot 31\cdot 17627^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 1369566]$ |
| 10.0.118...059.1 | $x^{10} - 2 x^{9} + 940 x^{8} - 1936 x^{7} + 243290 x^{6} - 673382 x^{5} + 11965452 x^{4} - 77699019 x^{3} + 527024301 x^{2} - 1780032332 x + 4164253584$ | $-\,13^{5}\cdot 23\cdot 53^{4}\cdot 281^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 283300]$ |
| 10.0.126...848.1 | $x^{10} - x^{9} + 1841 x^{8} + 350 x^{7} + 1202355 x^{6} + 1266759 x^{5} + 359404539 x^{4} + 537328376 x^{3} + 50016352213 x^{2} + 62710319617 x + 2623601526179$ | $-\,2^{8}\cdot 919\cdot 13997^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 1287838]$ |
| 10.0.139...000.1 | $x^{10} + 1554 x^{8} - 2230 x^{7} + 866721 x^{6} - 1787214 x^{5} + 200972215 x^{4} - 421212102 x^{3} + 16704918729 x^{2} - 20874379680 x + 368682083226$ | $-\,2^{15}\cdot 3^{10}\cdot 5^{4}\cdot 23\cdot 347^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 385044]$ |
| 10.0.141...439.1 | $x^{10} + 967 x^{8} - 1267 x^{7} + 281810 x^{6} - 211065 x^{5} + 32568404 x^{4} + 6546983 x^{3} + 1334640067 x^{2} + 414535864 x + 18644013911$ | $-\,13^{5}\cdot 23^{4}\cdot 103\cdot 421^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 139138]$ |
| 10.0.148...048.1 | $x^{10} - 2 x^{9} + 2402 x^{8} - 50 x^{7} + 1873770 x^{6} + 3000424 x^{5} + 509156690 x^{4} + 1188924564 x^{3} + 35059842221 x^{2} + 49796108120 x + 567761540428$ | $-\,2^{6}\cdot 3^{9}\cdot 47\cdot 4787^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 4, 122520]$ |
| 10.0.155...391.1 | $x^{10} - x^{9} + 1501 x^{8} + 48 x^{7} + 731647 x^{6} + 32499 x^{5} + 156160426 x^{4} - 11079745 x^{3} + 15008674468 x^{2} - 1621990254 x + 531314066473$ | $-\,3^{8}\cdot 29^{5}\cdot 229^{5}\cdot 1831$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 6, 44106]$ |
| 10.0.156...904.1 | $x^{10} - x^{9} + 1107 x^{8} + 1795 x^{7} + 404408 x^{6} + 814001 x^{5} + 59166967 x^{4} + 92490055 x^{3} + 3309808979 x^{2} + 2406413398 x + 48688199722$ | $-\,2^{3}\cdot 23^{4}\cdot 151\cdot 3413^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 625882]$ |
| 10.0.173...432.1 | $x^{10} - 4 x^{9} + 1796 x^{8} - 4870 x^{7} + 961806 x^{6} - 1163732 x^{5} + 203833709 x^{4} - 49069234 x^{3} + 16779818818 x^{2} + 5317643780 x + 468319912708$ | $-\,2^{10}\cdot 7^{5}\cdot 71^{5}\cdot 89^{5}$ | $S_5\times C_2$ (as 10T22) | $[2, 2, 2, 2, 113100]$ |
| 10.0.210...375.1 | $x^{10} - 5 x^{9} - 180 x^{8} + 310 x^{7} + 13085 x^{6} + 13891 x^{5} - 237410 x^{4} - 44500 x^{3} + 3391800 x^{2} + 3901600 x + 30270976$ | $-\,5^{16}\cdot 11^{8}\cdot 23^{5}$ | $C_{10}$ (as 10T1) | $[3744015]$ |
| 10.0.222...512.1 | $x^{10} - 4 x^{9} + 1941 x^{8} - 8272 x^{7} + 1277577 x^{6} - 4868700 x^{5} + 347356512 x^{4} - 994097780 x^{3} + 34536749080 x^{2} - 61850635184 x + 1136106636256$ | $-\,2^{4}\cdot 3^{5}\cdot 19^{4}\cdot 31\cdot 1699^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 930492]$ |
| 10.0.230...408.1 | $x^{10} + 2986 x^{8} + 2363197 x^{6} + 702929132 x^{4} + 83051518676 x^{2} + 3356154614552$ | $-\,2^{15}\cdot 3^{8}\cdot 103\cdot 1597^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2970896]$ |
| 10.0.274...896.1 | $x^{10} - 4 x^{9} + 938 x^{8} - 5268 x^{7} + 327145 x^{6} - 1851038 x^{5} + 50648222 x^{4} - 228290328 x^{3} + 3235091003 x^{2} - 8668109104 x + 62409315651$ | $-\,2^{3}\cdot 11^{4}\cdot 18797^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 1375000]$ |
| 10.0.276...048.1 | $x^{10} - 3 x^{9} + 2473 x^{8} - 4860 x^{7} + 2217978 x^{6} - 2126444 x^{5} + 870817298 x^{4} - 174743012 x^{3} + 142348051573 x^{2} - 6550416929 x + 8218104160841$ | $-\,2^{8}\cdot 167\cdot 23029^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2668172]$ |
| 10.0.277...127.1 | $x^{10} - 5 x^{9} + 2650 x^{8} - 9605 x^{7} + 1855351 x^{6} - 5032283 x^{5} + 381181667 x^{4} - 872036485 x^{3} + 32056224596 x^{2} - 50274292479 x + 928597927617$ | $-\,3^{8}\cdot 47^{5}\cdot 151^{5}\cdot 2351$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 796264]$ |
| 10.0.299...011.1 | $x^{10} - x^{9} + 1821 x^{8} - 1982 x^{7} + 1106083 x^{6} - 1279557 x^{5} + 240857082 x^{4} - 77765854 x^{3} + 10137715179 x^{2} + 8637174918 x + 94158929841$ | $-\,3^{8}\cdot 7\cdot 23053^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 991852]$ |