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 |
---|---|---|---|---|
10.0.311663572684817408.3 | $x^{10} - 2 x^{9} + 78 x^{8} - 122 x^{7} + 2702 x^{6} - 3194 x^{5} + 51055 x^{4} - 41284 x^{3} + 522906 x^{2} - 220904 x + 2319481$ | $-\,2^{10}\cdot 11^{8}\cdot 17^{5}$ | $C_{10}$ (as 10T1) | $[5, 220]$ |
10.0.659594366463529519.3 | $x^{10} - 3 x^{9} + 94 x^{8} - 220 x^{7} + 3810 x^{6} - 6560 x^{5} + 82274 x^{4} - 93093 x^{3} + 945262 x^{2} - 527525 x + 4638019$ | $-\,11^{8}\cdot 79^{5}$ | $C_{10}$ (as 10T1) | $[1775]$ |
10.0.732082863999706112.1 | $x^{10} + 88 x^{8} + 2555 x^{6} + 27397 x^{4} + 89417 x^{2} + 89417$ | $-\,2^{10}\cdot 89417^{3}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 680]$ |
10.0.844368344447000483.3 | $x^{10} - 3 x^{9} + 99 x^{8} - 232 x^{7} + 4210 x^{6} - 7264 x^{5} + 95124 x^{4} - 107913 x^{3} + 1140491 x^{2} - 638489 x + 5822543$ | $-\,11^{8}\cdot 83^{5}$ | $C_{10}$ (as 10T1) | $[1965]$ |
10.0.850323586567180847.1 | $x^{10} - x^{9} + 141 x^{8} - 124 x^{7} + 7053 x^{6} - 4037 x^{5} + 149350 x^{4} - 16603 x^{3} + 1315915 x^{2} + 128411 x + 4675417$ | $-\,11^{8}\cdot 1583^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 998]$ |
10.0.850323586567180847.2 | $x^{10} - 2 x^{9} + 131 x^{8} - 165 x^{7} + 6462 x^{6} - 5089 x^{5} + 145138 x^{4} - 88891 x^{3} + 1420887 x^{2} - 748646 x + 4461007$ | $-\,11^{8}\cdot 1583^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 892]$ |
10.0.896474439937004544.3 | $x^{10} - 2 x^{9} + 98 x^{8} - 154 x^{7} + 4174 x^{6} - 4946 x^{5} + 95495 x^{4} - 77044 x^{3} + 1168338 x^{2} - 488760 x + 6109489$ | $-\,2^{10}\cdot 3^{5}\cdot 7^{5}\cdot 11^{8}$ | $C_{10}$ (as 10T1) | $[2, 1010]$ |
10.0.986083097105956663.1 | $x^{10} - x^{9} + 144 x^{8} - 144 x^{7} + 7580 x^{6} - 7580 x^{5} + 176749 x^{4} - 176749 x^{3} + 1747604 x^{2} - 1747604 x + 5831827$ | $-\,11^{9}\cdot 53^{5}$ | $C_{10}$ (as 10T1) | $[1208]$ |
10.0.106...367.3 | $x^{10} - 3 x^{9} + 104 x^{8} - 244 x^{7} + 4630 x^{6} - 8004 x^{5} + 109246 x^{4} - 124229 x^{3} + 1364464 x^{2} - 766089 x + 7237273$ | $-\,3^{5}\cdot 11^{8}\cdot 29^{5}$ | $C_{10}$ (as 10T1) | $[1830]$ |
10.0.121...000.45 | $x^{10} + 10 x^{8} - 10 x^{7} + 240 x^{6} + 158 x^{5} + 3185 x^{4} + 3040 x^{3} + 22730 x^{2} + 8740 x + 68257$ | $-\,2^{15}\cdot 3^{5}\cdot 5^{16}$ | $C_{10}$ (as 10T1) | $[1010]$ |
10.0.121...247.1 | $x^{10} - x^{9} + 120 x^{8} - 149 x^{7} + 5693 x^{6} - 7271 x^{5} + 132844 x^{4} - 144228 x^{3} + 1496392 x^{2} - 991120 x + 6223328$ | $-\,11^{8}\cdot 1783^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 882]$ |
10.0.121...247.2 | $x^{10} - x^{9} + 156 x^{8} - 158 x^{7} + 8913 x^{6} - 9231 x^{5} + 219557 x^{4} - 226758 x^{3} + 2082397 x^{2} - 1823262 x + 6890113$ | $-\,11^{8}\cdot 1783^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 976]$ |
10.0.124...800.1 | $x^{10} + 132 x^{8} + 5690 x^{6} + 94823 x^{4} + 536720 x^{2} + 912425$ | $-\,2^{10}\cdot 5^{2}\cdot 36497^{3}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 808]$ |
10.0.129...216.1 | $x^{10} + 154 x^{8} + 8624 x^{6} + 211288 x^{4} + 2112880 x^{2} + 5916064$ | $-\,2^{15}\cdot 7^{5}\cdot 11^{9}$ | $C_{10}$ (as 10T1) | $[2, 844]$ |
10.0.133...331.1 | $x^{10} - 3 x^{9} + 109 x^{8} - 256 x^{7} + 5070 x^{6} - 8780 x^{5} + 124700 x^{4} - 142113 x^{3} + 1619869 x^{2} - 911909 x + 8914201$ | $-\,7^{5}\cdot 11^{8}\cdot 13^{5}$ | $C_{10}$ (as 10T1) | $[2222]$ |
10.0.140...991.1 | $x^{10} - 3 x^{9} + 146 x^{8} - 435 x^{7} + 7643 x^{6} - 19717 x^{5} + 185649 x^{4} - 352237 x^{3} + 2084134 x^{2} - 2052823 x + 8104403$ | $-\,11^{8}\cdot 1871^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 976]$ |
10.0.140...991.2 | $x^{10} - 4 x^{9} + 131 x^{8} - 410 x^{7} + 6587 x^{6} - 15028 x^{5} + 156430 x^{4} - 225916 x^{3} + 1736475 x^{2} - 1115480 x + 7258877$ | $-\,11^{8}\cdot 1871^{3}$ | $C_2 \times (C_2^4 : C_5)$ (as 10T14) | $[2, 942]$ |
10.0.141...387.1 | $x^{10} - x^{9} + 155 x^{8} - 155 x^{7} + 8779 x^{6} - 8779 x^{5} + 220067 x^{4} - 220067 x^{3} + 2332947 x^{2} - 2332947 x + 8249011$ | $-\,3^{5}\cdot 11^{9}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[2, 802]$ |
10.0.165...375.3 | $x^{10} - 3 x^{9} + 114 x^{8} - 268 x^{7} + 5530 x^{6} - 9592 x^{5} + 141546 x^{4} - 161637 x^{3} + 1909514 x^{2} - 1077605 x + 10888151$ | $-\,5^{5}\cdot 11^{8}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[1640]$ |
10.0.183...000.1 | $x^{10} + 165 x^{8} + 9900 x^{6} + 259875 x^{4} + 2784375 x^{2} + 8353125$ | $-\,2^{10}\cdot 3^{5}\cdot 5^{5}\cdot 11^{9}$ | $C_{10}$ (as 10T1) | $[2, 2, 362]$ |
10.0.199...991.3 | $x^{10} - x^{9} + 166 x^{8} - 166 x^{7} + 10066 x^{6} - 10066 x^{5} + 269941 x^{4} - 269941 x^{3} + 3054316 x^{2} - 3054316 x + 11407441$ | $-\,11^{9}\cdot 61^{5}$ | $C_{10}$ (as 10T1) | $[1650]$ |
10.0.248...583.3 | $x^{10} - 3 x^{9} + 124 x^{8} - 292 x^{7} + 6510 x^{6} - 11324 x^{5} + 179654 x^{4} - 205893 x^{3} + 2603356 x^{2} - 1475609 x + 15881293$ | $-\,11^{8}\cdot 103^{5}$ | $C_{10}$ (as 10T1) | $[3, 3, 3, 75]$ |
10.0.260...144.1 | $x^{10} - 2 x^{9} + 123 x^{8} - 194 x^{7} + 6464 x^{6} - 7676 x^{5} + 180115 x^{4} - 145054 x^{3} + 2652783 x^{2} - 1100690 x + 16510339$ | $-\,2^{15}\cdot 11^{8}\cdot 13^{5}$ | $C_{10}$ (as 10T1) | $[1986]$ |
10.0.273...875.1 | $x^{10} - x^{9} + 177 x^{8} - 177 x^{7} + 11441 x^{6} - 11441 x^{5} + 326833 x^{4} - 326833 x^{3} + 3931313 x^{2} - 3931313 x + 15465649$ | $-\,5^{5}\cdot 11^{9}\cdot 13^{5}$ | $C_{10}$ (as 10T1) | $[2, 1382]$ |
10.0.300...467.3 | $x^{10} - 3 x^{9} + 129 x^{8} - 304 x^{7} + 7030 x^{6} - 12244 x^{5} + 201036 x^{4} - 230769 x^{3} + 3013769 x^{2} - 1711589 x + 18985373$ | $-\,11^{8}\cdot 107^{5}$ | $C_{10}$ (as 10T1) | $[3615]$ |
10.0.361...431.1 | $x^{10} - 3 x^{9} + 134 x^{8} - 316 x^{7} + 7570 x^{6} - 13200 x^{5} + 224050 x^{4} - 257573 x^{3} + 3470854 x^{2} - 1974789 x + 22556491$ | $-\,3^{5}\cdot 11^{8}\cdot 37^{5}$ | $C_{10}$ (as 10T1) | $[3448]$ |
10.0.368...159.1 | $x^{10} - x^{9} + 188 x^{8} - 188 x^{7} + 12904 x^{6} - 12904 x^{5} + 391205 x^{4} - 391205 x^{3} + 4984860 x^{2} - 4984860 x + 20603287$ | $-\,3^{5}\cdot 11^{9}\cdot 23^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 2, 132]$ |
10.0.431...875.1 | $x^{10} - 3 x^{9} + 139 x^{8} - 328 x^{7} + 8130 x^{6} - 14192 x^{5} + 248756 x^{4} - 286377 x^{3} + 3978019 x^{2} - 2267225 x + 26645431$ | $-\,5^{5}\cdot 11^{8}\cdot 23^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 202]$ |
10.0.436...375.3 | $x^{10} - 5 x^{9} + 30 x^{8} - 80 x^{7} + 520 x^{6} - 1494 x^{5} + 8050 x^{4} - 18165 x^{3} + 65760 x^{2} - 73895 x + 192493$ | $-\,5^{16}\cdot 31^{5}$ | $C_{10}$ (as 10T1) | $[1965]$ |
10.0.450...456.3 | $x^{10} - 2 x^{9} + 138 x^{8} - 218 x^{7} + 8078 x^{6} - 9602 x^{5} + 249271 x^{4} - 200596 x^{3} + 4044546 x^{2} - 1672088 x + 27589441$ | $-\,2^{10}\cdot 11^{8}\cdot 29^{5}$ | $C_{10}$ (as 10T1) | $[11, 330]$ |
10.0.476...896.1 | $x^{10} + 60 x^{8} + 1152 x^{6} + 8721 x^{4} + 22842 x^{2} + 10449$ | $-\,2^{10}\cdot 3^{5}\cdot 19^{4}\cdot 43^{5}$ | $D_{10}$ (as 10T3) | $[2, 534]$ |
10.0.479...007.1 | $x^{10} + 42 x^{8} + 709 x^{6} + 5628 x^{4} + 17956 x^{2} + 5447$ | $-\,13^{5}\cdot 419^{5}$ | $D_5$ (as 10T2) | $[11, 132]$ |
10.0.488...763.3 | $x^{10} - x^{9} + 199 x^{8} - 199 x^{7} + 14455 x^{6} - 14455 x^{5} + 463519 x^{4} - 463519 x^{3} + 6237199 x^{2} - 6237199 x + 27022447$ | $-\,11^{9}\cdot 73^{5}$ | $C_{10}$ (as 10T1) | $[6050]$ |
10.0.491...875.3 | $x^{10} + 110 x^{8} - 30 x^{7} + 2825 x^{6} - 2491 x^{5} + 15100 x^{4} + 8495 x^{3} + 29515 x^{2} + 65125 x + 180299$ | $-\,5^{17}\cdot 23^{5}$ | $C_{10}$ (as 10T1) | $[1822]$ |
10.0.511...719.3 | $x^{10} - 3 x^{9} + 144 x^{8} - 340 x^{7} + 8710 x^{6} - 15220 x^{5} + 275214 x^{4} - 317253 x^{3} + 4538792 x^{2} - 2590985 x + 31306529$ | $-\,7^{5}\cdot 11^{8}\cdot 17^{5}$ | $C_{10}$ (as 10T1) | $[3550]$ |
10.0.533...000.1 | $x^{10} - 2 x^{9} + 143 x^{8} - 226 x^{7} + 8656 x^{6} - 10292 x^{5} + 275747 x^{4} - 221854 x^{3} + 4611783 x^{2} - 1904586 x + 32377951$ | $-\,2^{15}\cdot 3^{5}\cdot 5^{5}\cdot 11^{8}$ | $C_{10}$ (as 10T1) | $[2, 3310]$ |
10.0.550...527.1 | $x^{10} - x^{9} + 64 x^{8} - 69 x^{7} + 1239 x^{6} + 363 x^{5} + 11501 x^{4} + 11077 x^{3} + 71822 x^{2} + 31101 x + 16893$ | $-\,7^{5}\cdot 41^{9}$ | $C_{10}$ (as 10T1) | $[11, 154]$ |
10.0.589...087.1 | $x^{10} - 3 x^{9} - 8 x^{8} + 20 x^{7} + 88 x^{6} - 104 x^{5} - 89 x^{4} + 91 x^{3} + 1032 x^{2} + 220 x + 2816$ | $-\,7^{5}\cdot 11^{2}\cdot 13^{2}\cdot 269^{2}\cdot 487^{2}$ | $S_5\times C_2$ (as 10T22) | $[1019]$ |
10.0.597...816.3 | $x^{10} + 209 x^{8} + 15884 x^{6} + 528143 x^{4} + 7167655 x^{2} + 27237089$ | $-\,2^{10}\cdot 11^{9}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[2, 2050]$ |
10.0.603...683.1 | $x^{10} - 3 x^{9} + 149 x^{8} - 352 x^{7} + 9310 x^{6} - 16284 x^{5} + 303484 x^{4} - 350273 x^{3} + 5156821 x^{2} - 2948229 x + 36597793$ | $-\,3^{5}\cdot 11^{8}\cdot 41^{5}$ | $C_{10}$ (as 10T1) | $[3410]$ |
10.0.633...799.1 | $x^{10} - 2 x^{9} - 7 x^{8} + 93 x^{7} + 798 x^{6} - 1355 x^{5} + 11444 x^{4} + 11524 x^{3} + 90928 x^{2} + 39504 x + 212800$ | $-\,13^{5}\cdot 443^{5}$ | $D_{10}$ (as 10T3) | $[1188]$ |
10.0.679...184.1 | $x^{10} - 2 x^{9} + 7 x^{8} + 18 x^{7} + 200 x^{6} - 768 x^{5} + 5083 x^{4} - 11958 x^{3} + 39139 x^{2} - 46270 x + 99175$ | $-\,2^{15}\cdot 3^{5}\cdot 31^{8}$ | $C_{10}$ (as 10T1) | $[1310]$ |
10.0.708...567.1 | $x^{10} - 3 x^{9} + 154 x^{8} - 364 x^{7} + 9930 x^{6} - 17384 x^{5} + 333626 x^{4} - 385509 x^{3} + 5835874 x^{2} - 3341189 x + 42581023$ | $-\,11^{8}\cdot 127^{5}$ | $C_{10}$ (as 10T1) | $[3025]$ |
10.0.787...375.1 | $x^{10} - 2 x^{9} + 95 x^{8} - 198 x^{7} + 3203 x^{6} - 6660 x^{5} + 45416 x^{4} - 87734 x^{3} + 267949 x^{2} - 200010 x + 579441$ | $-\,3^{5}\cdot 5^{5}\cdot 401^{5}$ | $D_{10}$ (as 10T3) | $[2, 2, 2, 198]$ |
10.0.826...531.2 | $x^{10} - 3 x^{9} + 159 x^{8} - 376 x^{7} + 10570 x^{6} - 18520 x^{5} + 365700 x^{4} - 423033 x^{3} + 6579839 x^{2} - 3772169 x + 49321931$ | $-\,11^{8}\cdot 131^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 550]$ |
10.0.997...056.1 | $x^{10} - 2 x^{9} + 163 x^{8} - 258 x^{7} + 11168 x^{6} - 13292 x^{5} + 400371 x^{4} - 321886 x^{3} + 7495711 x^{2} - 3084418 x + 58603931$ | $-\,2^{15}\cdot 11^{8}\cdot 17^{5}$ | $C_{10}$ (as 10T1) | $[7964]$ |
10.0.104...375.1 | $x^{10} - x^{9} + 232 x^{8} - 232 x^{7} + 19636 x^{6} - 19636 x^{5} + 732733 x^{4} - 732733 x^{3} + 11429188 x^{2} - 11429188 x + 56354299$ | $-\,5^{5}\cdot 11^{9}\cdot 17^{5}$ | $C_{10}$ (as 10T1) | $[2, 4354]$ |
10.0.111...819.1 | $x^{10} - 3 x^{9} + 169 x^{8} - 400 x^{7} + 11910 x^{6} - 20900 x^{5} + 435884 x^{4} - 505233 x^{3} + 8278657 x^{2} - 4757765 x + 65359909$ | $-\,11^{8}\cdot 139^{5}$ | $C_{10}$ (as 10T1) | $[5, 5, 165]$ |
10.0.119...176.1 | $x^{10} + 60 x^{8} + 1252 x^{6} + 10560 x^{4} + 30976 x^{2} + 26144$ | $-\,2^{15}\cdot 19^{5}\cdot 43^{5}$ | $D_{10}$ (as 10T3) | $[2, 992]$ |
10.0.123...375.1 | $x^{10} - 2 x^{9} + 75 x^{8} - 169 x^{7} + 785 x^{6} - 2430 x^{5} + 10231 x^{4} - 19733 x^{3} + 52899 x^{2} - 61257 x + 84969$ | $-\,3^{4}\cdot 5^{5}\cdot 547^{5}$ | $D_{10}$ (as 10T3) | $[31, 62]$ |