## Results (1-50 of 139 matches)

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Label Polynomial Discriminant Galois group Class group
25.5.190...049.1 $x^{25} - 4 x^{24} + 4 x^{23} + 5 x^{22} - 20 x^{21} + 18 x^{20} + 19 x^{19} - 28 x^{18} - 2 x^{16} + 2 x^{15} - 28 x^{14} - 29 x^{13} + 120 x^{12} + 59 x^{11} - 112 x^{10} - 35 x^{9} + 16 x^{8} - 23 x^{7} + 29 x^{6} + 32 x^{5} - 21 x^{4} - 12 x^{3} + 7 x^{2} + 2 x - 1$ $7^{10}\cdot 11^{20}$ $C_5\times D_5$ (as 25T3) trivial
25.5.722...624.1 $x^{25} - 3 x^{24} + 4 x^{23} - 7 x^{22} + 5 x^{21} - 6 x^{20} + 28 x^{19} - 37 x^{18} + 24 x^{17} + 60 x^{15} - 133 x^{14} + 74 x^{13} + 37 x^{12} - 24 x^{11} - 112 x^{10} + 155 x^{9} - 56 x^{8} - 45 x^{7} + 51 x^{6} - 17 x^{5} + 3 x^{4} - 3 x^{3} + 3 x - 1$ $2^{30}\cdot 11^{20}$ $C_5\times D_5$ (as 25T3) trivial
25.1.145...641.1 $x^{25} - 3 x^{24} + 9 x^{23} - 22 x^{22} + 41 x^{21} - 60 x^{20} + 66 x^{19} - 47 x^{18} + 6 x^{17} + 48 x^{16} - 82 x^{15} + 76 x^{14} + 11 x^{13} - 138 x^{12} + 280 x^{11} - 336 x^{10} + 317 x^{9} - 205 x^{8} + 144 x^{7} - 109 x^{6} + 126 x^{5} - 104 x^{4} + 76 x^{3} - 23 x^{2} + 10 x + 1$ $479^{12}$ $D_{25}$ (as 25T4) trivial
25.1.213...801.1 $x^{25} - 2 x^{24} - x^{23} + 8 x^{22} + 6 x^{21} - 17 x^{20} - 5 x^{19} + 32 x^{18} - 13 x^{17} - 36 x^{16} + 22 x^{15} + 58 x^{14} - 6 x^{13} - 71 x^{12} + 35 x^{10} - 24 x^{9} - 66 x^{8} + 28 x^{7} + 63 x^{6} + 92 x^{5} - 82 x^{4} - 3 x^{3} + 25 x^{2} + 16 x - 1$ $599^{12}$ $D_{25}$ (as 25T4) trivial
25.5.953...000.1 $x^{25} - 5 x^{24} + 10 x^{23} - 10 x^{22} + 17 x^{20} - 25 x^{19} + 10 x^{18} + 55 x^{17} - 150 x^{16} + 156 x^{15} - 100 x^{14} + 115 x^{13} - 60 x^{12} - 175 x^{11} + 208 x^{10} + 70 x^{9} - 80 x^{8} - 70 x^{7} - 25 x^{6} + 20 x^{5} + 15 x^{4} + 15 x^{3} + 10 x^{2} - 1$ $2^{20}\cdot 5^{40}$ $C_5\times D_5$ (as 25T3) trivial
25.5.396...449.1 $x^{25} - 3 x^{24} + x^{23} - 3 x^{22} + 19 x^{21} - 17 x^{20} - 8 x^{19} - 27 x^{18} + 13 x^{17} + 72 x^{16} + 7 x^{15} + 58 x^{14} - 37 x^{13} - 186 x^{12} + 151 x^{11} - 314 x^{10} + 404 x^{9} - 330 x^{8} + 297 x^{7} - 201 x^{6} + 123 x^{5} - 65 x^{4} + 32 x^{3} - 18 x^{2} + 7 x - 1$ $3^{10}\cdot 31^{20}$ $C_5\times D_5$ (as 25T3) trivial
25.1.874...849.1 $x^{25} - x - 1$ $10667\cdot 282401201\cdot 925997749\cdot 31362479733103$ $S_{25}$ (as 25T211) trivial
25.1.901...401.1 $x^{25} + x - 1$ $13\cdot 2957\cdot 8969\cdot 6212881\cdot 42086382270382828249$ $S_{25}$ (as 25T211) trivial
25.5.111...125.1 $x^{25} - 120 x^{20} + 885 x^{15} + 28385 x^{10} - 3245 x^{5} + 1$ $5^{53}$ $C_5\times F_5$ (as 25T7) trivial
25.1.425...361.1 $x^{25} - 2 x^{24} - x^{23} + 13 x^{22} + 50 x^{21} + 3 x^{20} - 29 x^{19} - 5 x^{18} + 128 x^{17} - 146 x^{16} - 239 x^{15} + 32 x^{14} + 747 x^{13} - 262 x^{12} - 1333 x^{11} - 456 x^{10} + 1762 x^{9} + 962 x^{8} - 1685 x^{7} - 1308 x^{6} + 1439 x^{5} + 1916 x^{4} - 95 x^{3} - 410 x^{2} + 94 x - 1$ $1367^{12}$ $D_{25}$ (as 25T4) $[2, 2]$
25.5.188...376.1 $x^{25} - 2 x^{24} - 2 x^{23} - 10 x^{22} + 33 x^{21} + 5 x^{20} - 6 x^{19} - 115 x^{18} - 16 x^{17} + 168 x^{16} + 250 x^{15} - 16 x^{14} + 291 x^{13} - 1042 x^{12} + 750 x^{11} - 1666 x^{10} + 1541 x^{9} - 903 x^{8} + 418 x^{7} + 161 x^{6} - 27 x^{5} + 92 x^{4} + 3 x^{3} + 8 x^{2} + 4 x - 1$ $2^{20}\cdot 41^{20}$ $C_5\times D_5$ (as 25T3) trivial
25.1.114...401.1 $x^{25} - 4 x^{24} + x^{23} + 2 x^{22} + 5 x^{21} + 38 x^{20} + 24 x^{19} - 79 x^{18} - 45 x^{17} - 175 x^{16} - 246 x^{15} + 78 x^{14} + 160 x^{13} + 28 x^{12} + 1032 x^{11} + 953 x^{10} + 967 x^{9} + 1690 x^{8} + 1081 x^{7} - 1035 x^{6} - 715 x^{5} - 2390 x^{4} - 2966 x^{3} - 1925 x^{2} - 720 x - 1003$ $7^{12}\cdot 257^{12}$ $D_{25}$ (as 25T4) trivial
25.5.693...125.1 $x^{25} - 45 x^{20} + 235 x^{15} - 390 x^{10} + 205 x^{5} + 1$ $5^{57}$ $C_5^2:C_{20}$ (as 25T37) trivial
25.1.123...944.1 $x^{25} - x - 2$ $2^{24}\cdot 739\cdot 12239\cdot 2507149\cdot 272308609\cdot 118872926969$ $S_{25}$ (as 25T211) trivial
25.5.300...849.1 $x^{25} - 3 x^{24} + x^{23} - 15 x^{22} + 13 x^{21} - 5 x^{20} + 130 x^{19} - 132 x^{18} - 21 x^{17} + 437 x^{16} - 1713 x^{15} + 747 x^{14} + 4817 x^{13} - 3107 x^{12} - 7887 x^{11} + 4826 x^{10} + 5380 x^{9} - 3452 x^{8} + 864 x^{7} - 1052 x^{6} + 266 x^{5} - 67 x^{4} + 75 x^{3} - 10 x^{2} + 9 x - 1$ $3^{10}\cdot 61^{20}$ $C_5\times D_5$ (as 25T3) trivial
25.1.346...625.1 $x^{25} - 135 x^{20} - 460 x^{15} - 1580 x^{10} + 455 x^{5} - 32$ $5^{58}$ $C_5^2:C_{20}$ (as 25T34) trivial
25.1.447...857.1 $x^{25} + 2 x - 1$ $2377\cdot 5147\cdot 460493604849521\cdot 7943531120919741043$ $S_{25}$ (as 25T211) trivial
25.1.335...881.1 $x^{25} - 5 x^{24} + 18 x^{23} - 53 x^{22} + 184 x^{21} - 519 x^{20} + 1425 x^{19} - 2994 x^{18} + 4254 x^{17} - 2567 x^{16} - 3146 x^{15} + 8388 x^{14} - 11301 x^{13} - 6966 x^{12} + 13530 x^{11} + 11956 x^{10} + 18271 x^{9} + 21048 x^{8} - 41862 x^{7} - 65478 x^{6} - 1959 x^{5} + 35311 x^{4} + 17869 x^{3} - 2655 x^{2} - 3850 x - 2125$ $2887^{12}$ $D_{25}$ (as 25T4) trivial
25.1.121...625.1 $x^{25} - 11 x^{24} + 42 x^{23} - 37 x^{22} - 156 x^{21} + 345 x^{20} + 267 x^{19} - 2248 x^{18} + 5531 x^{17} - 338 x^{16} - 41434 x^{15} + 71882 x^{14} + 112392 x^{13} - 407865 x^{12} + 80824 x^{11} + 717928 x^{10} - 228258 x^{9} - 1185331 x^{8} + 280801 x^{7} + 1733675 x^{6} - 74160 x^{5} - 2202750 x^{4} - 202350 x^{3} + 1981500 x^{2} + 536000 x - 1401875$ $5^{12}\cdot 643^{12}$ $D_{25}$ (as 25T4) trivial
25.1.140...536.1 $x^{25} - 4 x - 4$ $2^{24}\cdot 7\cdot 19\cdot 2579\cdot 1081796927611\cdot 224982529004839973$ $S_{25}$ (as 25T211) trivial
25.1.144...768.1 $x^{25} - 2 x - 2$ $2^{24}\cdot 86\!\cdots\!73$ $S_{25}$ (as 25T211) trivial
25.1.149...464.1 $x^{25} - x - 4$ $2^{24}\cdot 389\cdot 766126533933601\cdot 298023226053735461$ $S_{25}$ (as 25T211) trivial
25.1.149...000.1 $x^{25} - 2$ $2^{24}\cdot 5^{50}$ $C_{25}:C_{20}$ (as 25T40) trivial
25.1.153...232.1 $x^{25} + 2 x - 2$ $2^{24}\cdot 11\cdot 83\cdot 139\cdot 177347\cdot 386150417\cdot 10526535234089689$ $S_{25}$ (as 25T211) trivial
25.1.157...464.1 $x^{25} + 4 x - 4$ $2^{24}\cdot 8054869\cdot 11688928159776857914348061941$ $S_{25}$ (as 25T211) trivial
25.5.433...125.1 $x^{25} - 30 x^{20} - 65 x^{15} + 640 x^{10} - 720 x^{5} - 1$ $5^{61}$ $C_5^3:C_{20}$ (as 25T67) trivial
25.1.106...201.1 $x^{25} - 10 x^{24} + 41 x^{23} - 105 x^{22} + 177 x^{21} - 437 x^{20} + 1470 x^{19} - 3743 x^{18} + 4598 x^{17} - 1850 x^{16} + 3734 x^{15} - 33702 x^{14} + 37801 x^{13} + 70620 x^{12} - 146863 x^{11} - 115089 x^{10} + 114649 x^{9} + 185307 x^{8} - 74232 x^{7} - 239939 x^{6} - 516736 x^{5} - 486684 x^{4} - 187312 x^{3} - 162320 x^{2} + 32064 x - 22784$ $3851^{12}$ $D_{25}$ (as 25T4) trivial
25.1.397...641.1 $x^{25} - x^{24} + 2 x^{23} - 2 x^{22} + 114 x^{21} + 14 x^{20} + 388 x^{19} + 1085 x^{18} + 7513 x^{17} + 4819 x^{16} + 1219 x^{15} - 640 x^{14} + 110085 x^{13} + 396579 x^{12} + 932255 x^{11} + 3052375 x^{10} + 5536096 x^{9} + 12433767 x^{8} + 17351055 x^{7} + 27726417 x^{6} + 30856797 x^{5} + 36500635 x^{4} + 30496620 x^{3} + 26587890 x^{2} + 14289723 x + 8362683$ $11^{20}\cdot 79^{12}$ $D_{25}$ (as 25T4) $[5]$
25.3.113...143.1 $x^{25} - 3 x - 1$ $-\,131\cdot 13259\cdot 3933670000864773133\cdot 165394543991056112099$ $S_{25}$ (as 25T211) trivial
25.1.113...393.1 $x^{25} + 3 x - 1$ $7\cdot 14691751\cdot 10\!\cdots\!49$ $S_{25}$ (as 25T211) trivial
25.1.113...768.1 $x^{25} + 3 x - 2$ $2^{24}\cdot 7\cdot 1777\cdot 19854823\cdot 273087660366642710101853209$ $S_{25}$ (as 25T211) trivial
25.5.271...125.1 $x^{25} - 5 x^{20} - 30 x^{15} + 25 x^{10} + 15 x^{5} + 1$ $5^{65}$ $C_5^4:C_{20}$ (as 25T94) trivial
25.5.271...125.2 $x^{25} - 150 x^{20} - 35 x^{15} + 795 x^{10} - 365 x^{5} - 1$ $5^{65}$ $C_5^4:C_{20}$ (as 25T94) trivial
25.1.118...921.1 $x^{25} - x^{24} - 19 x^{23} - 76 x^{22} + 156 x^{21} + 1005 x^{20} + 1755 x^{19} - 1564 x^{18} - 17480 x^{17} + 14003 x^{16} - 40555 x^{15} + 158147 x^{14} - 336486 x^{13} - 456783 x^{12} + 2807964 x^{11} - 9825280 x^{10} + 32382901 x^{9} - 51222985 x^{8} + 76250162 x^{7} - 82760080 x^{6} + 46691010 x^{5} + 4604688 x^{4} - 3014982 x^{3} - 12748972 x^{2} + 5156073 x + 1384173$ $11^{20}\cdot 127^{12}$ $D_{25}$ (as 25T4) $[5]$
25.1.171...161.1 $x^{25} + 18 x^{23} - 17 x^{22} + 163 x^{21} + 778 x^{20} + 668 x^{19} + 6093 x^{18} + 8161 x^{17} - 16824 x^{16} + 24958 x^{15} + 156175 x^{14} + 317021 x^{13} + 1220510 x^{12} + 3228424 x^{11} + 5166827 x^{10} + 7607147 x^{9} + 10396892 x^{8} + 8655374 x^{7} + 3386053 x^{6} + 971637 x^{5} + 379214 x^{4} - 252700 x^{3} + 96379 x^{2} - 14488 x + 1088$ $11^{20}\cdot 131^{12}$ $D_{25}$ (as 25T4) $[5]$
25.1.239...857.1 $x^{25} - 3 x - 3$ $3^{24}\cdot 102715785599666749\cdot 825740991458053453$ $S_{25}$ (as 25T211) trivial
25.1.250...393.1 $x^{25} - 2 x - 3$ $3^{24}\cdot 4213063\cdot 105716820911311\cdot 199414803057521$ $S_{25}$ (as 25T211) trivial
25.1.250...849.1 $x^{25} - x - 3$ $3^{25}\cdot 2351\cdot 126764421589739\cdot 99341097532143287$ $S_{25}$ (as 25T211) trivial
25.1.250...625.1 $x^{25} - 3$ $3^{24}\cdot 5^{50}$ $C_{25}:C_{20}$ (as 25T40) trivial
25.1.250...401.1 $x^{25} + x - 3$ $3^{24}\cdot 13\cdot 2298962364929\cdot 2971837118443792802173$ $S_{25}$ (as 25T211) trivial
25.1.262...393.1 $x^{25} + 3 x - 3$ $3^{24}\cdot 7\cdot 67\cdot 19\!\cdots\!37$ $S_{25}$ (as 25T211) trivial
25.25.338...625.1 $x^{25} - 50 x^{23} + 1025 x^{21} - 11250 x^{19} - 125 x^{18} + 72525 x^{17} + 3100 x^{16} - 283885 x^{15} - 28375 x^{14} + 674550 x^{13} + 121800 x^{12} - 942450 x^{11} - 261005 x^{10} + 718625 x^{9} + 269475 x^{8} - 258425 x^{7} - 117125 x^{6} + 33010 x^{5} + 16625 x^{4} - 1100 x^{3} - 650 x^{2} - 50 x - 1$ $5^{68}$ $C_{25}$ (as 25T1) trivial
25.25.126...401.1 $x^{25} - x^{24} - 48 x^{23} + 43 x^{22} + 946 x^{21} - 752 x^{20} - 9993 x^{19} + 6962 x^{18} + 62052 x^{17} - 37341 x^{16} - 234195 x^{15} + 119366 x^{14} + 538390 x^{13} - 226505 x^{12} - 737819 x^{11} + 249907 x^{10} + 571793 x^{9} - 151052 x^{8} - 224456 x^{7} + 42136 x^{6} + 35494 x^{5} - 2561 x^{4} - 1633 x^{3} + 57 x^{2} + 19 x - 1$ $101^{24}$ $C_{25}$ (as 25T1) trivial
25.3.150...224.1 $x^{25} - 4 x - 2$ $-\,2^{24}\cdot 7\cdot 11\cdot 173\cdot 431\cdot 2029499\cdot 218979707\cdot 3166728751\cdot 11077240423$ $S_{25}$ (as 25T211) trivial
25.3.150...599.1 $x^{25} - 4 x - 1$ $-\,7\cdot 53\cdot 3847\cdot 1012717\cdot 140141898521\cdot 847814229733\cdot 8744131694867$ $S_{25}$ (as 25T211) trivial
25.1.150...849.1 $x^{25} + 4 x - 1$ $38117394317861\cdot 39\!\cdots\!09$ $S_{25}$ (as 25T211) $[2]$
25.1.150...224.1 $x^{25} + 4 x - 2$ $2^{24}\cdot 29\cdot 11136449\cdot 3349154609\cdot 82750417248561907056701$ $S_{25}$ (as 25T211) trivial
25.1.152...849.1 $x^{25} + 4 x - 3$ $3^{24}\cdot 54\!\cdots\!29$ $S_{25}$ (as 25T211) trivial
25.5.169...125.1 $x^{25} - 25 x^{22} + 25 x^{21} + 110 x^{20} - 625 x^{19} + 1250 x^{18} - 3625 x^{17} + 21750 x^{16} - 57200 x^{15} + 112500 x^{14} - 240625 x^{13} + 448125 x^{12} - 1126250 x^{11} + 1744825 x^{10} - 1006875 x^{9} - 705000 x^{8} + 4269125 x^{7} - 3551000 x^{6} + 949625 x^{5} - 792500 x^{4} + 1303750 x^{3} - 899750 x^{2} + 291625 x - 36535$ $5^{69}$ $A_5^5.C_{10}$ (as 25T187) trivial
25.5.169...125.2 $x^{25} - 5 x^{20} + 25 x^{10} - 25 x^{5} + 5$ $5^{69}$ $C_5^5.C_{20}$ (as 25T115) trivial
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