| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
| 25.5.190...049.1 |
$x^{25} - 4 x^{24} + 4 x^{23} + 5 x^{22} - 20 x^{21} + 18 x^{20} + 19 x^{19} - 28 x^{18} - 2 x^{16} + 2 x^{15} - 28 x^{14} - 29 x^{13} + 120 x^{12} + 59 x^{11} - 112 x^{10} - 35 x^{9} + 16 x^{8} - 23 x^{7} + 29 x^{6} + 32 x^{5} - 21 x^{4} - 12 x^{3} + 7 x^{2} + 2 x - 1$ |
$25$ |
(5, 10) |
$7^{10}\cdot 11^{20}$ |
$2$ |
$14.830417050837912$ |
$18.016198912314337$ |
|
|
? |
$C_5\times D_5$ (as 25T3) |
trivial |
trivial |
$2$ |
$14$ |
$40076.42524869914$ |
$5$ |
| 25.5.722...624.1 |
$x^{25} - 3 x^{24} + 4 x^{23} - 7 x^{22} + 5 x^{21} - 6 x^{20} + 28 x^{19} - 37 x^{18} + 24 x^{17} + 60 x^{15} - 133 x^{14} + 74 x^{13} + 37 x^{12} - 24 x^{11} - 112 x^{10} + 155 x^{9} - 56 x^{8} - 45 x^{7} + 51 x^{6} - 17 x^{5} + 3 x^{4} - 3 x^{3} + 3 x - 1$ |
$25$ |
(5, 10) |
$2^{30}\cdot 11^{20}$ |
$2$ |
$15.644084133929866$ |
$19.260126783385598$ |
|
|
? |
$C_5\times D_5$ (as 25T3) |
trivial |
trivial |
$2$ |
$14$ |
$87435.46969808154$ |
$5$ |
| 25.5.205...625.1 |
$x^{25} - 3 x^{22} - 7 x^{21} + 4 x^{20} + 26 x^{19} + 23 x^{18} - 69 x^{17} + 27 x^{16} + 12 x^{15} - 25 x^{14} - 141 x^{13} + 338 x^{12} - 235 x^{11} + 36 x^{10} - 58 x^{9} + 133 x^{8} - 227 x^{7} + 307 x^{6} - 244 x^{5} + 107 x^{4} - 40 x^{3} - 14 x^{2} + 33 x - 9$ |
$25$ |
(5, 10) |
$5^{16}\cdot 103^{10}$ |
$2$ |
$17.884454275070624$ |
|
|
|
|
$C_5\wr D_5$ (as 25T107) |
trivial |
trivial |
$2$ |
$14$ |
$686914.2923053632$ |
$5$ |
| 25.1.145...641.1 |
$x^{25} - 3 x^{24} + 9 x^{23} - 22 x^{22} + 41 x^{21} - 60 x^{20} + 66 x^{19} - 47 x^{18} + 6 x^{17} + 48 x^{16} - 82 x^{15} + 76 x^{14} + 11 x^{13} - 138 x^{12} + 280 x^{11} - 336 x^{10} + 317 x^{9} - 205 x^{8} + 144 x^{7} - 109 x^{6} + 126 x^{5} - 104 x^{4} + 76 x^{3} - 23 x^{2} + 10 x + 1$ |
$25$ |
(1, 12) |
$479^{12}$ |
$1$ |
$19.344657569539898$ |
$21.88606862823929$ |
|
|
? |
$D_{25}$ (as 25T4) |
trivial |
trivial |
$2$ |
$12$ |
$593552.1381003528$ |
$1$ |
| 25.5.710...125.1 |
$x^{25} - 5 x^{24} + 10 x^{23} - 25 x^{22} + 90 x^{21} - 215 x^{20} + 345 x^{19} - 540 x^{18} + 1125 x^{17} - 2285 x^{16} + 3635 x^{15} - 4855 x^{14} + 6660 x^{13} - 10200 x^{12} + 15165 x^{11} - 19475 x^{10} + 21270 x^{9} - 20390 x^{8} + 17650 x^{7} - 13685 x^{6} + 9075 x^{5} - 4830 x^{4} + 1910 x^{3} - 500 x^{2} + 65 x - 1$ |
$25$ |
(5, 10) |
$5^{47}$ |
$1$ |
$20.609317417867263$ |
|
|
|
? |
$C_5\times F_5$ (as 25T7) |
trivial |
trivial |
$2$ |
$14$ |
$6350595.028353693$ |
$5$ |
| 25.1.213...801.1 |
$x^{25} - 2 x^{24} - x^{23} + 8 x^{22} + 6 x^{21} - 17 x^{20} - 5 x^{19} + 32 x^{18} - 13 x^{17} - 36 x^{16} + 22 x^{15} + 58 x^{14} - 6 x^{13} - 71 x^{12} + 35 x^{10} - 24 x^{9} - 66 x^{8} + 28 x^{7} + 63 x^{6} + 92 x^{5} - 82 x^{4} - 3 x^{3} + 25 x^{2} + 16 x - 1$ |
$25$ |
(1, 12) |
$599^{12}$ |
$1$ |
$21.535991679204013$ |
$24.474476501040833$ |
|
|
? |
$D_{25}$ (as 25T4) |
trivial |
trivial |
$2$ |
$12$ |
$3027380.0731932656$ |
$1$ |
| 25.1.268...125.1 |
$x^{25} - 10 x^{24} + 45 x^{23} - 125 x^{22} + 270 x^{21} - 580 x^{20} + 1295 x^{19} - 2620 x^{18} + 4655 x^{17} - 7895 x^{16} + 13230 x^{15} - 20730 x^{14} + 29620 x^{13} - 39610 x^{12} + 49695 x^{11} - 56785 x^{10} + 58565 x^{9} - 54795 x^{8} + 45265 x^{7} - 31470 x^{6} + 18040 x^{5} - 8600 x^{4} + 3320 x^{3} - 895 x^{2} + 120 x - 9$ |
$25$ |
(1, 12) |
$3^{10}\cdot 5^{41}$ |
$2$ |
$21.734983207945696$ |
|
|
|
? |
$D_5\times F_5$ (as 25T18) |
trivial |
trivial |
$2$ |
$12$ |
$11102680.271526914$ |
$1$ |
| 25.5.313...625.1 |
$x^{25} - 3 x^{24} - 6 x^{23} + 20 x^{22} + 2 x^{21} + 31 x^{20} - 107 x^{19} - 215 x^{18} + 721 x^{17} - 428 x^{16} + 79 x^{15} - 286 x^{14} - 1247 x^{13} + 4950 x^{12} - 7501 x^{11} + 6149 x^{10} - 1520 x^{9} - 2452 x^{8} + 2602 x^{7} - 312 x^{6} - 784 x^{5} + 191 x^{4} + 120 x^{3} - 18 x^{2} - 11 x - 1$ |
$25$ |
(5, 10) |
$5^{24}\cdot 47^{10}$ |
$2$ |
$21.870078774396532$ |
|
|
|
? |
$C_5\wr D_5$ (as 25T107) |
trivial |
trivial |
$2$ |
$14$ |
$8215618.912629513$ |
$5$ |
| 25.5.313...625.2 |
$x^{25} - 2 x^{24} - x^{23} + 3 x^{22} + 46 x^{20} - 127 x^{19} + 65 x^{18} - 126 x^{17} + 541 x^{16} - 815 x^{15} - 308 x^{14} + 4778 x^{13} - 10746 x^{12} + 16077 x^{11} - 20753 x^{10} + 21830 x^{9} - 20004 x^{8} + 15416 x^{7} - 9494 x^{6} + 5380 x^{5} - 2793 x^{4} + 1402 x^{3} - 402 x^{2} + 56 x + 1$ |
$25$ |
(5, 10) |
$5^{24}\cdot 47^{10}$ |
$2$ |
$21.870078774396532$ |
|
|
|
? |
$C_5\wr D_5$ (as 25T107) |
trivial |
trivial |
$2$ |
$14$ |
$8607274.94259334$ |
$5$ |
| 25.1.321...125.1 |
$x^{25} - x^{15} - x^{10} + x^{5} + 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 1609^{5}$ |
$2$ |
$21.891786960153013$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$3393367.451549424$ |
$1$ |
| 25.1.363...125.1 |
$x^{25} - x^{20} + x^{10} - x^{5} + 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 17^{5}\cdot 97^{5}$ |
$3$ |
$21.99956712318824$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$3767606.5360989766$ |
$1$ |
| 25.1.409...000.1 |
$x^{25} - 5 x^{24} + 15 x^{23} - 35 x^{22} + 70 x^{21} - 120 x^{20} + 175 x^{19} - 195 x^{18} + 110 x^{17} + 130 x^{16} - 525 x^{15} + 1025 x^{14} - 1500 x^{13} + 1810 x^{12} - 1875 x^{11} + 1695 x^{10} - 1350 x^{9} + 950 x^{8} - 595 x^{7} + 335 x^{6} - 170 x^{5} + 80 x^{4} - 35 x^{3} + 15 x^{2} - 5 x + 1$ |
$25$ |
(1, 12) |
$2^{42}\cdot 5^{30}$ |
$2$ |
$22.105197420270123$ |
|
|
|
? |
$D_5:F_5$ (as 25T19) |
trivial |
trivial |
$2$ |
$12$ |
$17167717.377215426$ |
$1$ |
| 25.1.528...125.1 |
$x^{25} - x^{20} + x^{15} - 2 x^{10} + x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 1777^{5}$ |
$2$ |
$22.33096494956414$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$4835271.439059946$ |
$1$ |
| 25.1.953...000.1 |
$x^{25} - 5 x^{23} + 35 x^{21} - 5 x^{20} - 150 x^{19} + 70 x^{18} + 425 x^{17} - 300 x^{16} - 855 x^{15} + 550 x^{14} + 1295 x^{13} - 375 x^{12} - 1460 x^{11} - 260 x^{10} + 1025 x^{9} + 670 x^{8} - 275 x^{7} - 470 x^{6} - 120 x^{5} + 75 x^{4} + 45 x^{3} - 5 x - 1$ |
$25$ |
(1, 12) |
$2^{20}\cdot 5^{40}$ |
$2$ |
$22.865252596366318$ |
|
|
|
? |
$C_5:F_5$ (as 25T10) |
trivial |
trivial |
$2$ |
$12$ |
$22962459.590461094$ |
$1$ |
| 25.5.953...000.1 |
$x^{25} - 5 x^{24} + 10 x^{23} - 10 x^{22} + 17 x^{20} - 25 x^{19} + 10 x^{18} + 55 x^{17} - 150 x^{16} + 156 x^{15} - 100 x^{14} + 115 x^{13} - 60 x^{12} - 175 x^{11} + 208 x^{10} + 70 x^{9} - 80 x^{8} - 70 x^{7} - 25 x^{6} + 20 x^{5} + 15 x^{4} + 15 x^{3} + 10 x^{2} - 1$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{40}$ |
$2$ |
$22.865252596366318$ |
$26.26527804403767$ |
|
|
? |
$C_5\times D_5$ (as 25T3) |
trivial |
trivial |
$2$ |
$14$ |
$22714715.777837068$ |
$5$ |
| 25.1.125...000.1 |
$x^{25} - 10 x^{24} + 45 x^{23} - 110 x^{22} + 120 x^{21} + 90 x^{20} - 440 x^{19} + 290 x^{18} + 795 x^{17} - 1470 x^{16} - 655 x^{15} + 4530 x^{14} - 3240 x^{13} - 9070 x^{12} + 26410 x^{11} - 33030 x^{10} + 20830 x^{9} - 200 x^{8} - 11640 x^{7} + 9520 x^{6} - 2130 x^{5} - 1820 x^{4} + 1760 x^{3} - 680 x^{2} + 120 x - 8$ |
$25$ |
(1, 12) |
$2^{32}\cdot 5^{35}$ |
$2$ |
$23.114068740473016$ |
|
|
|
|
$D_5\times F_5$ (as 25T18) |
trivial |
trivial |
$2$ |
$12$ |
$52421478.477477804$ |
$1$ |
| 25.1.156...125.1 |
$x^{25} - 2 x^{20} + 2 x^{15} - x^{10} + 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 47^{10}$ |
$2$ |
$23.32432839859247$ |
|
|
|
✓ |
$C_5^4:(C_4\times D_5)$ (as 25T104) |
trivial |
trivial |
$2$ |
$12$ |
$8335762.877696922$ |
$1$ |
| 25.1.190...125.1 |
$x^{25} - x^{20} + x^{15} - x^{10} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 2297^{5}$ |
$2$ |
$23.507270422240964$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$10527315.933199564$ |
$1$ |
| 25.1.309...625.1 |
$x^{25} - 5 x^{24} - 5 x^{23} + 50 x^{22} + 10 x^{21} - 225 x^{20} - 70 x^{19} + 585 x^{18} + 440 x^{17} - 920 x^{16} - 1245 x^{15} + 895 x^{14} + 1825 x^{13} - 680 x^{12} - 1720 x^{11} + 555 x^{10} + 1575 x^{9} + 50 x^{8} - 1100 x^{7} - 885 x^{6} - 85 x^{5} + 465 x^{4} + 465 x^{3} + 220 x^{2} + 55 x + 6$ |
$25$ |
(1, 12) |
$5^{30}\cdot 7^{16}$ |
$2$ |
$23.967721564918175$ |
|
|
|
? |
$C_5^2:C_{12}$ (as 25T26) |
trivial |
trivial |
$2$ |
$12$ |
$43342746.21030794$ |
$1$ |
| 25.1.365...125.1 |
$x^{25} + x^{15} - 2 x^{10} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 2617^{5}$ |
$2$ |
$24.128523610174124$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$16496237.829925193$ |
$1$ |
| 25.5.385...625.1 |
$x^{25} - 10 x^{24} + 45 x^{23} - 110 x^{22} + 110 x^{21} + 200 x^{20} - 995 x^{19} + 1895 x^{18} - 1845 x^{17} - 15 x^{16} + 3105 x^{15} - 5255 x^{14} + 4170 x^{13} + 550 x^{12} - 6185 x^{11} + 8355 x^{10} - 4650 x^{9} - 2210 x^{8} + 6745 x^{7} - 5650 x^{6} + 1265 x^{5} + 1460 x^{4} - 1100 x^{3} + 60 x^{2} + 65 x + 14$ |
$25$ |
(5, 10) |
$5^{30}\cdot 23^{10}$ |
$2$ |
$24.17993558712727$ |
|
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 25T43) |
trivial |
trivial |
$2$ |
$14$ |
$99274214.04892638$ |
$5$ |
| 25.5.396...449.1 |
$x^{25} - 3 x^{24} + x^{23} - 3 x^{22} + 19 x^{21} - 17 x^{20} - 8 x^{19} - 27 x^{18} + 13 x^{17} + 72 x^{16} + 7 x^{15} + 58 x^{14} - 37 x^{13} - 186 x^{12} + 151 x^{11} - 314 x^{10} + 404 x^{9} - 330 x^{8} + 297 x^{7} - 201 x^{6} + 123 x^{5} - 65 x^{4} + 32 x^{3} - 18 x^{2} + 7 x - 1$ |
$25$ |
(5, 10) |
$3^{10}\cdot 31^{20}$ |
$2$ |
$24.206826473247943$ |
$27.01779999660944$ |
|
|
? |
$C_5\times D_5$ (as 25T3) |
trivial |
trivial |
$2$ |
$14$ |
$68852831.13170123$ |
$5$ |
| 25.1.400...125.1 |
$x^{25} - x^{20} + x^{15} - x^{10} + 2 x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{30}\cdot 13^{5}\cdot 41^{5}$ |
$3$ |
$24.216392496948405$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$15129001.925004756$ |
$1$ |
| 25.5.476...000.1 |
$x^{25} - 10 x^{24} + 35 x^{23} - 30 x^{22} - 110 x^{21} + 255 x^{20} + 120 x^{19} - 1090 x^{18} + 1715 x^{17} - 1640 x^{16} + 2295 x^{15} - 5380 x^{14} + 11070 x^{13} - 16125 x^{12} + 15190 x^{11} - 8190 x^{10} + 590 x^{9} + 3200 x^{8} - 2990 x^{7} + 2010 x^{6} - 945 x^{5} + 350 x^{4} - 145 x^{3} + 30 x^{2} - 10 x + 1$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{41}$ |
$2$ |
$24.385676246341415$ |
|
|
|
? |
$C_5^2:F_5$ (as 25T35) |
trivial |
trivial |
$2$ |
$14$ |
$34092554.06508241$ |
$5$ |
| 25.1.579...625.1 |
$x^{25} - x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 19^{5}\cdot 151^{5}$ |
$3$ |
$24.576278169088035$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$20844603.19570806$ |
$1$ |
| 25.1.744...125.1 |
$x^{25} - x^{10} + 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 7^{5}\cdot 431^{5}$ |
$3$ |
$24.82476044821414$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$20549742.8113788$ |
$1$ |
| 25.1.838...125.1 |
$x^{25} - x^{15} + 2 x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 3089^{5}$ |
$2$ |
$24.942132729686577$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$24081866.5020844$ |
$1$ |
| 25.1.874...849.1 |
$x^{25} - x - 1$ |
$25$ |
(1, 12) |
$10667\cdot 282401201\cdot 925997749\cdot 31362479733103$ |
$4$ |
$24.9848741581$ |
$2.9577712249794144e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
trivial |
$2$ |
$12$ |
$13759573.23594141$ |
$1$ |
| 25.1.901...401.1 |
$x^{25} + x - 1$ |
$25$ |
(1, 12) |
$13\cdot 2957\cdot 8969\cdot 6212881\cdot 42086382270382828249$ |
$5$ |
$25.0149093419$ |
$3.002525232980779e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
trivial |
$2$ |
$12$ |
$36955124.38960424$ |
$1$ |
| 25.1.105...125.1 |
$x^{25} - x^{10} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 53^{5}\cdot 61^{5}$ |
$3$ |
$25.17045957899617$ |
|
|
|
✓ |
$C_5^4:(C_4\times S_5)$ (as 25T131) |
trivial |
trivial |
$2$ |
$12$ |
$24509448.604573514$ |
$1$ |
| 25.1.136...000.1 |
$x^{25} - 5 x^{24} + 10 x^{23} - 5 x^{22} - 25 x^{21} + 80 x^{20} - 120 x^{19} + 95 x^{18} - 155 x^{16} + 420 x^{15} - 860 x^{14} + 1375 x^{13} - 1545 x^{12} + 1060 x^{11} - 205 x^{10} - 150 x^{9} - 275 x^{8} + 870 x^{7} - 870 x^{6} + 405 x^{5} - 5 x^{4} - 90 x^{3} + 45 x^{2} - 10 x + 1$ |
$25$ |
(1, 12) |
$2^{20}\cdot 3^{20}\cdot 5^{28}$ |
$3$ |
$25.431232313608692$ |
|
|
|
? |
$C_5:F_5$ (as 25T9) |
trivial |
trivial |
$2$ |
$12$ |
$106797269.80793719$ |
$1$ |
| 25.1.536...000.1 |
$x^{25} - 10 x^{24} + 40 x^{23} - 80 x^{22} + 85 x^{21} - 70 x^{20} + 110 x^{19} - 160 x^{18} + 225 x^{17} - 510 x^{16} + 820 x^{15} - 800 x^{14} + 800 x^{13} - 800 x^{12} + 320 x^{11} + 120 x^{9} - 40 x^{7} - 240 x^{6} + 300 x^{5} - 200 x^{4} + 200 x^{3} - 160 x^{2} + 60 x - 8$ |
$25$ |
(1, 12) |
$2^{56}\cdot 5^{27}$ |
$2$ |
$26.8654917871941$ |
|
|
|
|
$C_5^2:\OD_{16}$ (as 25T31) |
trivial |
trivial |
$2$ |
$12$ |
$301678383.52133197$ |
$1$ |
| 25.5.763...625.1 |
$x^{25} - 5 x^{24} + 5 x^{23} + 30 x^{22} - 110 x^{21} + 105 x^{20} + 140 x^{19} - 335 x^{18} - 185 x^{17} + 1150 x^{16} - 450 x^{15} - 2935 x^{14} + 5015 x^{13} - 1450 x^{12} - 3410 x^{11} + 60 x^{10} + 7365 x^{9} - 8060 x^{8} + 3910 x^{7} - 5455 x^{6} + 9110 x^{5} - 6505 x^{4} + 910 x^{3} + 595 x^{2} + 15 x - 14$ |
$25$ |
(5, 10) |
$5^{30}\cdot 31^{10}$ |
$2$ |
$27.246372056781542$ |
|
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 25T43) |
trivial |
trivial |
$2$ |
$14$ |
$474122835.1616641$ |
$5$ |
| 25.1.800...000.1 |
$x^{25} - 5 x^{24} + 10 x^{23} - 40 x^{21} + 80 x^{20} - 30 x^{19} - 120 x^{18} + 225 x^{17} - 125 x^{16} - 180 x^{15} + 360 x^{14} - 120 x^{13} - 200 x^{12} + 140 x^{11} - 40 x^{10} + 115 x^{9} - 15 x^{8} - 150 x^{7} + 120 x^{6} + 80 x^{5} - 120 x^{4} + 50 x^{3} - 5 x + 1$ |
$25$ |
(1, 12) |
$2^{38}\cdot 5^{35}$ |
$2$ |
$27.297545558276344$ |
|
|
|
? |
$F_5\times A_5$ (as 25T54) |
$[3]$ |
$[3]$ |
$2$ |
$12$ |
$91521891.01252215$ |
$1$ |
| 25.1.222...625.1 |
$x^{25} - 5 x^{20} - 115 x^{15} - 385 x^{10} + 5 x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{52}$ |
$1$ |
$28.43528654390072$ |
|
|
|
|
$C_5:F_5$ (as 25T10) |
trivial |
trivial |
$2$ |
$12$ |
$480039477.691946$ |
$1$ |
| 25.1.282...125.1 |
$x^{25} - x^{20} + x^{15} - 2 x^{10} + 3 x^{5} - 1$ |
$25$ |
(1, 12) |
$5^{25}\cdot 79^{10}$ |
$2$ |
$28.70918347876793$ |
|
|
|
✓ |
$C_5^4:(C_4\times D_5)$ (as 25T104) |
trivial |
trivial |
$2$ |
$12$ |
$176034270.0356158$ |
$1$ |
| 25.1.400...000.1 |
$x^{25} - 15 x^{23} - 20 x^{22} + 95 x^{21} + 220 x^{20} - 195 x^{19} - 880 x^{18} - 355 x^{17} + 1120 x^{16} + 1475 x^{15} + 1020 x^{14} + 445 x^{13} - 2180 x^{12} - 4985 x^{11} - 2960 x^{10} + 2970 x^{9} + 8560 x^{8} + 12780 x^{7} + 14680 x^{6} + 12660 x^{5} + 7880 x^{4} + 3340 x^{3} + 800 x^{2} + 40 x - 16$ |
$25$ |
(1, 12) |
$2^{38}\cdot 5^{36}$ |
$2$ |
$29.1126942726042$ |
|
|
|
|
$D_5\times A_5$ (as 25T46) |
$[3]$ |
$[3]$ |
$2$ |
$12$ |
$2590060161.071452$ |
$1$ |
| 25.3.517...875.1 |
$x^{25} - 5 x^{24} + 20 x^{22} + 50 x^{21} - 180 x^{20} - 155 x^{19} + 640 x^{18} + 330 x^{17} - 1510 x^{16} - 220 x^{15} + 1785 x^{14} + 580 x^{13} - 1625 x^{12} - 1290 x^{11} + 1565 x^{10} + 1190 x^{9} - 930 x^{8} - 845 x^{7} + 280 x^{6} + 525 x^{5} - 70 x^{4} - 145 x^{3} + 15 x^{2} + 10 x + 1$ |
$25$ |
(3, 11) |
$-\,3^{33}\cdot 5^{30}$ |
$2$ |
$29.414675485109115$ |
|
|
|
? |
$F_5\times S_5$ (as 25T64) |
trivial |
trivial |
$2$ |
$13$ |
$617362747.9220549$ |
$3$ |
| 25.5.557...000.1 |
$x^{25} - 11 x^{23} + 34 x^{21} - 13 x^{20} + 100 x^{18} - 402 x^{17} - 204 x^{16} + 1658 x^{15} - 660 x^{14} - 1756 x^{13} + 2742 x^{12} - 1852 x^{11} - 4396 x^{10} + 10865 x^{9} - 2484 x^{8} - 4239 x^{7} - 332 x^{6} + 2074 x^{5} - 1065 x^{4} + 3228 x^{3} + 1416 x^{2} - 32$ |
$25$ |
(5, 10) |
$2^{30}\cdot 3^{20}\cdot 5^{26}$ |
$3$ |
$29.502702712967505$ |
|
|
|
|
$C_5\wr A_5$ (as 25T128) |
trivial |
trivial |
$2$ |
$14$ |
$9740608311.419806$ |
$5$ |
| 25.5.801...625.1 |
$x^{25} - 11 x^{24} + 53 x^{23} - 136 x^{22} + 136 x^{21} + 339 x^{20} - 1842 x^{19} + 4592 x^{18} - 7635 x^{17} + 8317 x^{16} - 4706 x^{15} + 2450 x^{14} - 20077 x^{13} + 79101 x^{12} - 179495 x^{11} + 282950 x^{10} - 307355 x^{9} + 163008 x^{8} + 121051 x^{7} - 343050 x^{6} + 334482 x^{5} - 167092 x^{4} + 29414 x^{3} + 10094 x^{2} - 4953 x + 359$ |
$25$ |
(5, 10) |
$5^{24}\cdot 103^{10}$ |
$2$ |
$29.932713857094004$ |
|
|
|
? |
$C_5\wr D_5$ (as 25T107) |
trivial |
trivial |
$2$ |
$14$ |
$317712477.94415575$ |
$5$ |
| 25.5.839...625.1 |
$x^{25} + 5 x^{23} - 35 x^{22} + 20 x^{20} + 225 x^{19} + 400 x^{18} - 1400 x^{17} - 800 x^{16} + 2570 x^{15} + 1625 x^{14} - 3250 x^{13} - 3700 x^{12} + 3550 x^{11} + 4810 x^{10} - 3025 x^{9} - 2425 x^{8} - 300 x^{7} + 3250 x^{6} - 1700 x^{5} - 250 x^{4} + 575 x^{3} - 225 x^{2} + 25 x + 5$ |
$25$ |
(5, 10) |
$3^{10}\cdot 5^{46}$ |
$2$ |
$29.988401023364105$ |
|
|
|
? |
$C_5\times D_5$ (as 25T3) |
trivial |
trivial |
$2$ |
$14$ |
$942981969.5767462$ |
$5$ |
| 25.5.111...125.1 |
$x^{25} - 120 x^{20} + 885 x^{15} + 28385 x^{10} - 3245 x^{5} + 1$ |
$25$ |
(5, 10) |
$5^{53}$ |
$1$ |
$30.32608927931576$ |
$31.82625288866059$ |
|
|
? |
$C_5\times F_5$ (as 25T7) |
trivial |
trivial |
$2$ |
$14$ |
$875697737.5008765$ |
$5$ |
| 25.1.111...832.1 |
$x^{25} - 6 x^{24} + 20 x^{23} - 16 x^{22} - 38 x^{21} + 108 x^{20} + 92 x^{19} - 368 x^{18} + 65 x^{17} + 818 x^{16} - 352 x^{15} - 2192 x^{14} - 856 x^{13} + 1504 x^{12} + 1064 x^{11} - 1088 x^{10} - 1240 x^{9} - 80 x^{8} + 424 x^{7} + 48 x^{6} - 120 x^{5} - 64 x^{4} + 16 x^{3} - 2 x - 4$ |
$25$ |
(1, 12) |
$2^{95}\cdot 7^{10}$ |
$2$ |
$30.335642634235708$ |
|
|
|
|
$C_5^2:\OD_{16}$ (as 25T31) |
trivial |
trivial |
$2$ |
$12$ |
$3072596440.828861$ |
$1$ |
| 25.5.298...000.1 |
$x^{25} + 15 x^{23} - 35 x^{22} + 75 x^{21} - 215 x^{20} - 50 x^{19} + 370 x^{18} - 1705 x^{17} + 4000 x^{16} - 1465 x^{15} - 275 x^{14} + 8260 x^{13} - 16565 x^{12} + 3625 x^{11} + 395 x^{10} - 11750 x^{9} + 22855 x^{8} - 8895 x^{7} - 15375 x^{6} + 30 x^{5} + 825 x^{4} + 8565 x^{3} + 1715 x^{2} + 75 x - 73$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{45}$ |
$2$ |
$31.54786722400966$ |
|
|
|
? |
$C_5^2:F_5$ (as 25T35) |
trivial |
trivial |
$2$ |
$14$ |
$1150743885.6632953$ |
$5$ |
| 25.5.298...000.2 |
$x^{25} + 15 x^{23} - 20 x^{22} + 60 x^{21} - 210 x^{20} - 250 x^{19} + 60 x^{18} - 1255 x^{17} + 1640 x^{16} + 3785 x^{15} - 6350 x^{14} - 11610 x^{13} - 15170 x^{12} - 11990 x^{11} + 13550 x^{10} + 13300 x^{9} - 9340 x^{8} - 5280 x^{7} + 5240 x^{6} + 2280 x^{5} - 1600 x^{4} - 2560 x^{3} - 1920 x^{2} - 640 x - 64$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{45}$ |
$2$ |
$31.54786722400966$ |
|
|
|
|
$C_5^2:F_5$ (as 25T35) |
trivial |
trivial |
$2$ |
$14$ |
$20632182826.40873$ |
$5$ |
| 25.5.298...000.3 |
$x^{25} - 25 x^{23} - 10 x^{22} + 250 x^{21} + 5 x^{20} - 1250 x^{19} - 50 x^{18} + 5085 x^{17} - 1750 x^{16} - 16115 x^{15} + 21200 x^{14} + 10000 x^{13} - 43135 x^{12} + 31750 x^{11} + 4520 x^{10} - 18600 x^{9} + 7500 x^{8} + 1860 x^{7} - 1750 x^{6} + 5 x^{5} + 200 x^{4} - 25 x^{3} - 10 x^{2} + 1$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{45}$ |
$2$ |
$31.54786722400966$ |
|
|
|
? |
$C_5\times F_5$ (as 25T7) |
trivial |
trivial |
$2$ |
$14$ |
$1601939125.473172$ |
$5$ |
| 25.5.298...000.4 |
$x^{25} + 15 x^{23} - 45 x^{22} + 95 x^{21} - 235 x^{20} + 500 x^{19} - 760 x^{18} + 605 x^{17} - 2330 x^{16} - 1835 x^{15} - 1375 x^{14} - 5310 x^{13} + 13755 x^{12} - 12555 x^{11} + 11755 x^{10} - 13250 x^{9} + 1465 x^{8} + 3355 x^{7} - 3655 x^{6} + 3280 x^{5} - 2125 x^{4} + 215 x^{3} - 295 x^{2} - 55 x + 9$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{45}$ |
$2$ |
$31.54786722400966$ |
|
|
|
|
$C_5^2:F_5$ (as 25T35) |
trivial |
trivial |
$2$ |
$14$ |
$6619342681.783736$ |
$5$ |
| 25.5.298...000.5 |
$x^{25} + 15 x^{23} + 140 x^{21} - 35 x^{20} + 350 x^{19} - 570 x^{18} - 875 x^{17} - 1320 x^{16} - 4975 x^{15} + 5200 x^{14} - 12040 x^{13} + 25025 x^{12} - 25340 x^{11} + 36260 x^{10} - 30000 x^{9} + 13870 x^{8} - 26600 x^{7} - 880 x^{6} - 18195 x^{5} + 22150 x^{4} + 4365 x^{3} - 5900 x^{2} + 3140 x + 1273$ |
$25$ |
(5, 10) |
$2^{20}\cdot 5^{45}$ |
$2$ |
$31.54786722400966$ |
|
|
|
? |
$C_5^2:F_5$ (as 25T35) |
trivial |
trivial |
$2$ |
$14$ |
$1025726545.4439231$ |
$5$ |
| 25.5.360...592.1 |
$x^{25} - x^{24} - 6 x^{23} + 2 x^{22} + 44 x^{21} - 118 x^{20} - 30 x^{19} + 990 x^{18} - 2359 x^{17} + 2241 x^{16} - 300 x^{15} - 1884 x^{14} + 2776 x^{13} - 484 x^{12} - 4060 x^{11} + 7292 x^{10} - 8933 x^{9} + 9745 x^{8} - 8526 x^{7} + 5338 x^{6} - 2612 x^{5} + 1354 x^{4} - 390 x^{3} - 26 x^{2} - 21 x - 1$ |
$25$ |
(5, 10) |
$2^{63}\cdot 7^{22}$ |
$2$ |
$31.789365835786285$ |
|
|
|
? |
$F_5\wr C_2$ (as 25T50) |
trivial |
trivial |
$2$ |
$14$ |
$6787733630.32287$ |
$5$ |
| 25.5.390...000.1 |
$x^{25} - 10 x^{24} + 50 x^{23} - 170 x^{22} + 425 x^{21} - 770 x^{20} + 870 x^{19} - 2680 x^{17} + 7250 x^{16} - 11990 x^{15} + 13670 x^{14} - 8775 x^{13} - 5870 x^{12} + 31550 x^{11} - 62100 x^{10} + 80865 x^{9} - 76200 x^{8} + 58120 x^{7} - 46000 x^{6} + 44080 x^{5} - 41600 x^{4} + 32000 x^{3} - 17920 x^{2} + 6400 x - 1024$ |
$25$ |
(5, 10) |
$2^{32}\cdot 5^{40}$ |
$2$ |
$31.891166238284082$ |
|
|
|
|
$D_5\wr C_2$ (as 25T21) |
trivial |
trivial |
$2$ |
$14$ |
$16593723282.085997$ |
$5$ |
