| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 24.0.368...000.1 |
$x^{24} - 6 x^{23} + 21 x^{22} - 54 x^{21} + 107 x^{20} - 178 x^{19} + 265 x^{18} - 376 x^{17} + 537 x^{16} - 744 x^{15} + 966 x^{14} - 1140 x^{13} + 1221 x^{12} - 1228 x^{11} + 1176 x^{10} - 1074 x^{9} + 914 x^{8} - 696 x^{7} + 471 x^{6} - 280 x^{5} + 140 x^{4} - 58 x^{3} + 21 x^{2} - 6 x + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 7^{8}$ |
$3$ |
$12.792541825661152$ |
$24.471252165227245$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$20$ |
$11$ |
$15456.373586053287$ |
| 24.0.275...000.1 |
$x^{24} - 2 x^{23} + 5 x^{22} - 12 x^{21} + 16 x^{20} - 30 x^{19} + 35 x^{18} - 36 x^{17} + 47 x^{16} - 36 x^{15} + 9 x^{14} - 16 x^{13} + 39 x^{12} + 80 x^{11} + 53 x^{10} - 46 x^{8} - 20 x^{7} + 34 x^{6} + 50 x^{5} + 38 x^{4} + 18 x^{3} + 9 x^{2} + 4 x + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{16}\cdot 5^{18}$ |
$3$ |
$13.910358902042523$ |
$28.934712524984697$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$20$ |
$11$ |
$48570.384925004604$ |
| 24.0.344...625.1 |
$x^{24} - x^{23} - 4 x^{22} + x^{21} + x^{20} - 5 x^{19} + 37 x^{18} + 33 x^{17} - 39 x^{16} - 57 x^{15} - 111 x^{14} - 16 x^{13} + 118 x^{12} + 13 x^{11} + 47 x^{9} + 156 x^{8} + 319 x^{7} + 175 x^{6} - 76 x^{5} - 127 x^{4} - 44 x^{3} + 48 x^{2} + 56 x + 16$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 19^{8}$ |
$3$ |
$15.453943884624808$ |
$41.237329340989255$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$30$ |
$11$ |
$242614.53860678803$ |
| 24.0.304...625.1 |
$x^{24} - x^{23} + x^{19} - x^{18} + x^{17} - x^{16} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{8} + x^{7} - x^{6} + x^{5} - x + 1$ |
$24$ |
[0,12] |
$5^{18}\cdot 7^{20}$ |
$2$ |
$16.9229421535$ |
$16.9229421535458$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$70$ |
$11$ |
$1695832.8006211799$ |
| 24.0.572...625.1 |
$x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1$ |
$24$ |
[0,12] |
$3^{36}\cdot 5^{18}$ |
$2$ |
$17.3743827793$ |
$17.374382779324037$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$90$ |
$11$ |
$2124832.236129185$ |
| 24.0.572...625.2 |
$x^{24} - 2 x^{21} - 2 x^{15} + 9 x^{12} - 8 x^{9} + 5 x^{6} - 3 x^{3} + 1$ |
$24$ |
[0,12] |
$3^{36}\cdot 5^{18}$ |
$2$ |
$17.374382779324037$ |
$22.178712478478406$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$30$ |
$11$ |
$1414385.0473488418$ |
| 24.0.711...256.1 |
$x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 7^{20}$ |
$3$ |
$17.5323038886$ |
$17.532303888591755$ |
✓ |
✓ |
✓ |
$C_2^2\times C_6$ (as 24T3) |
trivial |
$84$ |
$11$ |
$2172613.5864137784$ |
| 24.0.170...729.1 |
$x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{17} + x^{15} - x^{14} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 13^{22}$ |
$2$ |
$18.1834114927$ |
$18.18341149267149$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[2]$ |
$78$ |
$11$ |
$2851634.018949717$ |
| 24.0.172...625.1 |
$x^{24} - 8 x^{23} + 35 x^{22} - 105 x^{21} + 233 x^{20} - 377 x^{19} + 373 x^{18} + 86 x^{17} - 1310 x^{16} + 3226 x^{15} - 4893 x^{14} + 4424 x^{13} - 205 x^{12} - 6944 x^{11} + 13153 x^{10} - 14094 x^{9} + 9116 x^{8} - 2660 x^{7} - 525 x^{6} + 689 x^{5} - 175 x^{4} - 37 x^{3} + 37 x^{2} - 10 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 31^{8}$ |
$3$ |
$18.193183303403575$ |
$57.15171403472212$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$30$ |
$11$ |
$2176553.0653759805$ |
| 24.0.227...625.1 |
$x^{24} - 5 x^{23} + 7 x^{22} + 9 x^{21} - 43 x^{20} + 66 x^{19} - 38 x^{18} - 93 x^{17} + 491 x^{16} - 1291 x^{15} + 2386 x^{14} - 3246 x^{13} + 3278 x^{12} - 2354 x^{11} + 1061 x^{10} - 234 x^{9} + 126 x^{8} - 282 x^{7} + 277 x^{6} - 136 x^{5} + 42 x^{4} - 19 x^{3} + 12 x^{2} - 5 x + 1$ |
$24$ |
[0,12] |
$3^{16}\cdot 5^{18}\cdot 7^{12}$ |
$3$ |
$18.401675151229$ |
$38.27702679912765$ |
|
|
|
$S_3\times C_{12}$ (as 24T65) |
trivial |
$10$ |
$11$ |
$1519657.3038774955$ |
| 24.0.385...816.1 |
$x^{24} - 3 x^{16} - 8 x^{12} + 18 x^{8} + 8 x^{4} + 1$ |
$24$ |
[0,12] |
$2^{72}\cdot 13^{8}$ |
$2$ |
$18.81067750176606$ |
$44.23019850943098$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$16$ |
$11$ |
$2446825.407448486$ |
| 24.0.103...625.1 |
$x^{24} - x^{23} - x^{22} + 4 x^{21} - 4 x^{20} - 4 x^{19} + 17 x^{18} + 12 x^{17} - 46 x^{16} + 43 x^{15} + 44 x^{14} - 188 x^{13} + 189 x^{12} + 188 x^{11} + 44 x^{10} - 43 x^{9} - 46 x^{8} - 12 x^{7} + 17 x^{6} + 4 x^{5} - 4 x^{4} - 4 x^{3} - x^{2} + x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{12}\cdot 7^{20}$ |
$3$ |
$19.6017116485$ |
$19.601711648537535$ |
✓ |
✓ |
? |
$C_2^2\times C_6$ (as 24T3) |
trivial |
$42$ |
$11$ |
$4608312.303502872$ |
| 24.0.180...000.1 |
$x^{24} - 6 x^{23} + 23 x^{22} - 58 x^{21} + 100 x^{20} - 160 x^{19} + 242 x^{18} - 156 x^{17} - 228 x^{16} + 452 x^{15} + 164 x^{14} - 1190 x^{13} + 1288 x^{12} - 326 x^{11} - 800 x^{10} + 832 x^{9} + 514 x^{8} - 1302 x^{7} + 500 x^{6} + 664 x^{5} - 155 x^{4} - 1418 x^{3} + 1951 x^{2} - 1112 x + 241$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{24}\cdot 5^{18}$ |
$3$ |
$20.06220914929266$ |
$34.748765558648074$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
$[2]$ |
$4$ |
$11$ |
$535957.6069656424$ |
| 24.4.200...000.1 |
$x^{24} - 6 x^{23} + 24 x^{22} - 76 x^{21} + 216 x^{20} - 464 x^{19} + 764 x^{18} - 946 x^{17} + 779 x^{16} - 144 x^{15} - 844 x^{14} + 1724 x^{13} - 2096 x^{12} + 1724 x^{11} - 844 x^{10} - 144 x^{9} + 779 x^{8} - 946 x^{7} + 764 x^{6} - 464 x^{5} + 216 x^{4} - 76 x^{3} + 24 x^{2} - 6 x + 1$ |
$24$ |
[4,10] |
$2^{32}\cdot 5^{31}$ |
$2$ |
$20.14696273561006$ |
$30.533517205848526$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$3633824.159135835$ |
| 24.4.200...000.2 |
$x^{24} - 6 x^{23} + 16 x^{22} - 26 x^{21} + 36 x^{20} - 66 x^{19} + 126 x^{18} - 176 x^{17} + 166 x^{16} - 116 x^{15} + 100 x^{14} - 120 x^{13} + 60 x^{12} - 80 x^{11} + 360 x^{10} - 752 x^{9} + 892 x^{8} - 952 x^{7} + 1232 x^{6} - 1592 x^{5} + 1208 x^{4} - 248 x^{3} - 152 x^{2} + 32 x + 8$ |
$24$ |
[4,10] |
$2^{32}\cdot 5^{31}$ |
$2$ |
$20.14696273561006$ |
$30.533517205848526$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$3633824.159135835$ |
| 24.0.224...656.1 |
$x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1$ |
$24$ |
[0,12] |
$2^{48}\cdot 7^{20}$ |
$2$ |
$20.2445607392$ |
$20.244560739185545$ |
✓ |
✓ |
✓ |
$C_2^2\times C_6$ (as 24T3) |
$[2]$ |
$56$ |
$11$ |
$7024849.183363979$ |
| 24.0.329...561.1 |
$x^{24} - 3 x^{23} + 9 x^{22} - 26 x^{21} + 57 x^{20} - 122 x^{19} + 241 x^{18} - 433 x^{17} + 746 x^{16} - 1222 x^{15} + 1898 x^{14} - 2838 x^{13} + 4105 x^{12} - 5676 x^{11} + 7592 x^{10} - 9776 x^{9} + 11936 x^{8} - 13856 x^{7} + 15424 x^{6} - 15616 x^{5} + 14592 x^{4} - 13312 x^{3} + 9216 x^{2} - 6144 x + 4096$ |
$24$ |
[0,12] |
$3^{12}\cdot 7^{20}\cdot 167^{4}$ |
$3$ |
$20.5713000709$ |
$113.28364897482143$ |
✓ |
|
? |
$C_2^3\times A_4$ (as 24T135) |
$[2]$ |
$42$ |
$11$ |
$7377024.54411426$ |
| 24.0.422...376.1 |
$x^{24} - x^{12} + 1$ |
$24$ |
[0,12] |
$2^{48}\cdot 3^{36}$ |
$2$ |
$20.7846096908$ |
$20.784609690826528$ |
✓ |
✓ |
✓ |
$C_2^2\times C_6$ (as 24T3) |
$[3]$ |
$72$ |
$11$ |
$7554465.931561073$ |
| 24.0.430...625.1 |
$x^{24} - x^{23} + 3 x^{22} + x^{21} + 7 x^{20} + 20 x^{19} + 16 x^{18} - 5 x^{17} + 80 x^{16} + 120 x^{15} - 277 x^{14} + 191 x^{13} + 511 x^{12} - 356 x^{11} - 47 x^{10} + 255 x^{9} - 75 x^{8} - 130 x^{7} + 96 x^{6} + 20 x^{5} - 43 x^{4} + 14 x^{3} + 3 x^{2} - 4 x + 1$ |
$24$ |
[0,12] |
$5^{18}\cdot 7^{12}\cdot 13^{8}$ |
$3$ |
$20.801323781159077$ |
$48.91087415715005$ |
|
|
? |
$S_3\times C_{12}$ (as 24T65) |
trivial |
$10$ |
$11$ |
$3136393.8562446074$ |
| 24.4.491...064.1 |
$x^{24} - 5 x^{23} + x^{22} + 40 x^{21} - 89 x^{20} + 10 x^{19} + 240 x^{18} - 427 x^{17} + 266 x^{16} + 215 x^{15} - 599 x^{14} + 533 x^{13} - 153 x^{12} - 191 x^{11} + 195 x^{10} + 9 x^{9} + 160 x^{8} - 37 x^{7} - 186 x^{6} - 202 x^{5} - 123 x^{4} - 10 x^{3} + x^{2} + 5 x - 1$ |
$24$ |
[4,10] |
$2^{16}\cdot 487^{10}$ |
$2$ |
$20.91656659419456$ |
$35.030887836273955$ |
|
|
? |
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$1432261.5638336123$ |
| 24.4.491...064.2 |
$x^{24} - 4 x^{23} + 7 x^{22} - 10 x^{21} + 23 x^{20} - 32 x^{19} - 21 x^{18} + 156 x^{17} - 359 x^{16} + 654 x^{15} - 876 x^{14} + 646 x^{13} + 61 x^{12} - 1012 x^{11} + 2338 x^{10} - 3178 x^{9} + 2897 x^{8} - 2474 x^{7} + 1335 x^{6} - 52 x^{5} - 44 x^{4} + 454 x^{3} - 524 x^{2} + 62 x - 197$ |
$24$ |
[4,10] |
$2^{16}\cdot 487^{10}$ |
$2$ |
$20.91656659419456$ |
$35.030887836273955$ |
|
|
? |
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$1432261.5638336123$ |
| 24.0.538...704.1 |
$x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 13^{22}$ |
$2$ |
$20.9963950402$ |
$20.99639504015924$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[3]$ |
$52$ |
$11$ |
$7239917.885587101$ |
| 24.0.639...616.1 |
$x^{24} + 12 x^{22} + 96 x^{20} + 412 x^{18} + 1260 x^{16} + 2511 x^{14} + 3666 x^{12} + 3492 x^{10} + 2322 x^{8} + 736 x^{6} + 165 x^{4} + 15 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{36}\cdot 71^{4}$ |
$3$ |
$21.1473004645$ |
$87.56711711595854$ |
✓ |
|
? |
$C_2^3\times A_4$ (as 24T135) |
$[2]$ |
$36$ |
$11$ |
$7833899.703521124$ |
| 24.0.673...625.1 |
$x^{24} - x^{23} - 2 x^{22} + 5 x^{21} - 4 x^{20} + 8 x^{19} + 15 x^{18} - 59 x^{17} + 26 x^{16} + 114 x^{15} + 34 x^{14} - 119 x^{13} - 10 x^{12} - 196 x^{11} - 198 x^{10} + 289 x^{9} + 559 x^{8} - 307 x^{7} + 22 x^{6} + 46 x^{5} - 22 x^{4} + 12 x^{3} - x^{2} - 2 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 7^{16}$ |
$3$ |
$21.1927260375$ |
$21.192726037501743$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$30$ |
$11$ |
$8057321.833968681$ |
| 24.4.119...000.1 |
$x^{24} - 5 x^{23} + 8 x^{22} - 41 x^{20} + 127 x^{19} - 165 x^{18} + 91 x^{17} + 150 x^{16} - 477 x^{15} + 604 x^{14} - 565 x^{13} + 507 x^{12} - 350 x^{11} + 306 x^{10} - 297 x^{9} + 300 x^{8} - 351 x^{7} + 350 x^{6} - 263 x^{5} + 171 x^{4} - 65 x^{3} + 18 x^{2} - 1$ |
$24$ |
[4,10] |
$2^{16}\cdot 5^{39}$ |
$2$ |
$21.702657708188987$ |
$36.616613186499904$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$2868875.586527176$ |
| 24.4.119...000.2 |
$x^{24} - 6 x^{23} + 16 x^{22} - 11 x^{21} - 9 x^{20} + 9 x^{19} + 51 x^{18} - 36 x^{17} - 54 x^{16} + 19 x^{15} + 54 x^{14} - 54 x^{13} - x^{12} + 56 x^{11} + 4 x^{10} - 77 x^{9} + 42 x^{8} - 42 x^{7} + 57 x^{6} + 3 x^{5} - 21 x^{4} + x^{3} - 6 x^{2} + 6 x - 1$ |
$24$ |
[4,10] |
$2^{16}\cdot 5^{39}$ |
$2$ |
$21.702657708188987$ |
$36.616613186499904$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$2868875.586527176$ |
| 24.0.138...681.1 |
$x^{24} - 2 x^{23} + 2 x^{22} + 10 x^{21} - 20 x^{20} + 13 x^{19} + 57 x^{18} - 98 x^{17} + 19 x^{16} + 228 x^{15} - 267 x^{14} - 159 x^{13} + 711 x^{12} - 318 x^{11} - 1068 x^{10} + 1824 x^{9} + 304 x^{8} - 3136 x^{7} + 3648 x^{6} + 1664 x^{5} - 5120 x^{4} + 5120 x^{3} + 2048 x^{2} - 4096 x + 4096$ |
$24$ |
[0,12] |
$3^{12}\cdot 7^{20}\cdot 239^{4}$ |
$3$ |
$21.837787931$ |
$135.52142029437744$ |
✓ |
|
? |
$C_2^3\times A_4$ (as 24T135) |
$[3]$ |
$42$ |
$11$ |
$9137650.497592166$ |
| 24.0.326...000.1 |
$x^{24} - 3 x^{22} + 8 x^{20} - 21 x^{18} + 55 x^{16} - 144 x^{14} + 377 x^{12} - 144 x^{10} + 55 x^{8} - 21 x^{6} + 8 x^{4} - 3 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{12}\cdot 7^{20}$ |
$3$ |
$22.6341069937$ |
$22.634106993721137$ |
✓ |
✓ |
? |
$C_2^2\times C_6$ (as 24T3) |
$[3]$ |
$28$ |
$11$ |
$12419221.75230148$ |
| 24.2.339...000.1 |
$x^{24} + 6 x^{22} - 2 x^{21} + 9 x^{20} + 6 x^{19} + 7 x^{18} - 18 x^{16} - 20 x^{15} - 12 x^{14} - 120 x^{13} - 62 x^{12} + 48 x^{11} + 108 x^{10} + 172 x^{9} - 3 x^{8} + 276 x^{7} + 202 x^{6} - 630 x^{5} - 267 x^{4} + 106 x^{3} + 129 x^{2} + 36 x + 4$ |
$24$ |
[2,11] |
$-\,2^{45}\cdot 3^{31}\cdot 5^{6}$ |
$3$ |
$22.67020063043222$ |
$43.96267530256803$ |
|
|
|
$\SOPlus(4,3):C_2$ (as 24T2787) |
trivial |
$2$ |
$12$ |
$65851712.69295301$ |
| 24.2.339...000.2 |
$x^{24} - 3 x^{22} - 6 x^{20} + 75 x^{18} - 228 x^{16} + 222 x^{14} + 84 x^{12} - 102 x^{10} - 291 x^{8} + 465 x^{6} - 270 x^{4} + 63 x^{2} - 6$ |
$24$ |
[2,11] |
$-\,2^{45}\cdot 3^{31}\cdot 5^{6}$ |
$3$ |
$22.67020063043222$ |
$43.96267530256803$ |
|
|
|
$\SOPlus(4,3):C_2$ (as 24T2787) |
trivial |
$2$ |
$12$ |
$35280193.016457416$ |
| 24.4.500...000.1 |
$x^{24} - 8 x^{23} + 34 x^{22} - 102 x^{21} + 216 x^{20} - 308 x^{19} + 184 x^{18} + 418 x^{17} - 1369 x^{16} + 1582 x^{15} + 510 x^{14} - 4760 x^{13} + 7390 x^{12} - 3760 x^{11} - 6580 x^{10} + 17884 x^{9} - 22357 x^{8} + 18746 x^{7} - 11018 x^{6} + 3314 x^{5} + 564 x^{4} - 1212 x^{3} + 846 x^{2} - 238 x + 49$ |
$24$ |
[4,10] |
$2^{32}\cdot 5^{33}$ |
$2$ |
$23.038652994620875$ |
$30.533517205848526$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$2$ |
$13$ |
$7820988.84952936$ |
| 24.4.500...000.2 |
$x^{24} - 2 x^{23} + 6 x^{21} - 26 x^{20} - 18 x^{19} + 106 x^{18} - 80 x^{17} - 58 x^{16} + 208 x^{15} + 104 x^{14} - 728 x^{13} + 180 x^{12} + 624 x^{11} + 256 x^{10} + 168 x^{9} - 996 x^{8} - 160 x^{7} - 392 x^{6} + 1512 x^{5} - 1024 x^{4} + 888 x^{3} - 760 x^{2} + 256 x + 104$ |
$24$ |
[4,10] |
$2^{32}\cdot 5^{33}$ |
$2$ |
$23.038652994620875$ |
$30.533517205848526$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$2$ |
$13$ |
$7820988.84952936$ |
| 24.4.547...125.1 |
$x^{24} - 6 x^{23} + 16 x^{22} - 21 x^{21} - 4 x^{20} + 79 x^{19} - 234 x^{18} + 464 x^{17} - 714 x^{16} + 874 x^{15} - 1062 x^{14} + 1412 x^{13} - 1762 x^{12} + 1947 x^{11} - 1682 x^{10} + 996 x^{9} - 211 x^{8} - 124 x^{7} + 204 x^{6} - 404 x^{5} + 56 x^{4} + 179 x^{3} + 6 x^{2} - 6 x + 1$ |
$24$ |
[4,10] |
$5^{23}\cdot 11^{16}$ |
$2$ |
$23.126400597626308$ |
$31.483085955652367$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$21993486.43039912$ |
| 24.4.547...125.2 |
$x^{24} - 4 x^{23} - 2 x^{22} + 30 x^{21} - 35 x^{20} - 71 x^{19} + 209 x^{18} - 18 x^{17} - 445 x^{16} + 360 x^{15} + 406 x^{14} - 579 x^{13} - 477 x^{12} + 565 x^{11} + 1260 x^{10} - 1051 x^{9} - 1496 x^{8} + 1117 x^{7} + 935 x^{6} + 400 x^{5} - 1234 x^{4} - 1114 x^{3} + 1108 x^{2} + 355 x + 25$ |
$24$ |
[4,10] |
$5^{23}\cdot 11^{16}$ |
$2$ |
$23.126400597626308$ |
$31.483085955652367$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$21993486.43039912$ |
| 24.0.614...000.1 |
$x^{24} - 18 x^{18} + 323 x^{12} - 18 x^{6} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{36}\cdot 5^{12}$ |
$3$ |
$23.2379000772$ |
$23.2379000772445$ |
✓ |
✓ |
? |
$C_2^2\times C_6$ (as 24T3) |
$[3]$ |
$36$ |
$11$ |
$13636610.630449586$ |
| 24.4.641...125.1 |
$x^{24} - 3 x^{23} - 4 x^{22} + 33 x^{21} - 26 x^{20} - 152 x^{19} + 261 x^{18} + 338 x^{17} - 941 x^{16} - 193 x^{15} + 1674 x^{14} - 522 x^{13} - 1501 x^{12} + 1017 x^{11} + 641 x^{10} - 738 x^{9} - 171 x^{8} + 372 x^{7} + 21 x^{6} - 137 x^{5} + 6 x^{4} + 27 x^{3} + x^{2} - 2 x - 1$ |
$24$ |
[4,10] |
$5^{31}\cdot 13^{10}$ |
$2$ |
$23.27980397483945$ |
$43.68930970521314$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$6022924.686750277$ |
| 24.4.641...125.2 |
$x^{24} - 6 x^{23} + 16 x^{22} - 26 x^{21} + 31 x^{20} - 48 x^{19} + 128 x^{18} - 293 x^{17} + 478 x^{16} - 623 x^{15} + 874 x^{14} - 1534 x^{13} + 2419 x^{12} - 2374 x^{11} + 149 x^{10} + 3878 x^{9} - 7423 x^{8} + 8318 x^{7} - 6533 x^{6} + 3783 x^{5} - 1636 x^{4} + 521 x^{3} - 116 x^{2} + 16 x - 1$ |
$24$ |
[4,10] |
$5^{31}\cdot 13^{10}$ |
$2$ |
$23.27980397483945$ |
$43.68930970521314$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$6022924.686750277$ |
| 24.4.641...125.3 |
$x^{24} - 2 x^{23} - 6 x^{22} + 22 x^{21} + 26 x^{20} - 50 x^{19} - 155 x^{18} + 240 x^{17} + 540 x^{16} - 980 x^{15} - 1026 x^{14} + 3472 x^{13} - 1974 x^{12} - 2377 x^{11} + 4934 x^{10} - 4973 x^{9} + 4066 x^{8} - 2637 x^{7} + 1284 x^{6} - 348 x^{5} + 56 x^{4} - 32 x^{3} - x^{2} + 2 x + 1$ |
$24$ |
[4,10] |
$5^{31}\cdot 13^{10}$ |
$2$ |
$23.27980397483945$ |
$43.68930970521314$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$9344905.652391985$ |
| 24.4.641...125.4 |
$x^{24} - 6 x^{23} + 11 x^{22} - x^{21} - 42 x^{20} + 132 x^{19} - 157 x^{18} - 93 x^{17} + 463 x^{16} - 504 x^{15} + 89 x^{14} + 756 x^{13} - 1626 x^{12} + 841 x^{11} + 2572 x^{10} - 3447 x^{9} - 1348 x^{8} + 4593 x^{7} - 688 x^{6} - 3121 x^{5} + 1191 x^{4} + 1049 x^{3} - 514 x^{2} - 151 x + 83$ |
$24$ |
[4,10] |
$5^{31}\cdot 13^{10}$ |
$2$ |
$23.27980397483945$ |
$43.68930970521314$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$9344905.652391985$ |
| 24.0.784...625.1 |
$x^{24} - x^{23} + 2 x^{22} - 3 x^{21} + 5 x^{20} - 8 x^{19} + 13 x^{18} - 21 x^{17} + 34 x^{16} - 55 x^{15} + 89 x^{14} - 144 x^{13} + 233 x^{12} + 144 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$24$ |
[0,12] |
$5^{12}\cdot 13^{22}$ |
$2$ |
$23.4746832961$ |
$23.474683296117743$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 2]$ |
$26$ |
$11$ |
$7346081.887826216$ |
| 24.4.940...625.1 |
$x^{24} - 10 x^{23} + 48 x^{22} - 158 x^{21} + 381 x^{20} - 714 x^{19} + 1213 x^{18} - 1907 x^{17} + 2614 x^{16} - 3516 x^{15} + 4694 x^{14} - 5466 x^{13} + 6009 x^{12} - 6785 x^{11} + 7506 x^{10} - 8491 x^{9} + 9365 x^{8} - 8498 x^{7} + 5899 x^{6} - 3118 x^{5} + 1203 x^{4} - 296 x^{3} + 36 x^{2} - 7 x + 1$ |
$24$ |
[4,10] |
$5^{16}\cdot 151^{10}$ |
$2$ |
$23.65304533909512$ |
$35.93093151785668$ |
|
|
|
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$8548806.54922059$ |
| 24.4.940...625.2 |
$x^{24} - 2 x^{23} + 6 x^{22} - 5 x^{21} + 11 x^{20} - 17 x^{19} + 2 x^{18} - 34 x^{17} - 139 x^{16} - 108 x^{15} - 455 x^{14} - 497 x^{13} - 1230 x^{12} - 1691 x^{11} - 2719 x^{10} - 4214 x^{9} - 4936 x^{8} - 6130 x^{7} - 5653 x^{6} - 4317 x^{5} - 2323 x^{4} - 45 x^{3} - 323 x^{2} + 428 x + 173$ |
$24$ |
[4,10] |
$5^{16}\cdot 151^{10}$ |
$2$ |
$23.65304533909512$ |
$35.93093151785668$ |
|
|
|
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$8548806.54922059$ |
| 24.0.104...336.1 |
$x^{24} + 9 x^{22} + 42 x^{20} + 139 x^{18} + 376 x^{16} + 896 x^{14} + 1905 x^{12} + 3584 x^{10} + 6016 x^{8} + 8896 x^{6} + 10752 x^{4} + 9216 x^{2} + 4096$ |
$24$ |
[0,12] |
$2^{24}\cdot 7^{20}\cdot 167^{4}$ |
$3$ |
$23.7536912671$ |
$130.80869046079246$ |
✓ |
|
|
$C_2^3\times A_4$ (as 24T135) |
$[4]$ |
$28$ |
$11$ |
$18217606.15517919$ |
| 24.4.128...000.1 |
$x^{24} - 10 x^{23} + 38 x^{22} - 56 x^{21} - 24 x^{20} + 160 x^{19} - 70 x^{18} - 240 x^{17} + 80 x^{16} + 890 x^{15} - 1180 x^{14} - 940 x^{13} + 3410 x^{12} - 2300 x^{11} - 1700 x^{10} + 4040 x^{9} - 2450 x^{8} - 580 x^{7} + 1810 x^{6} - 1260 x^{5} + 240 x^{4} + 200 x^{3} - 180 x^{2} + 60 x - 10$ |
$24$ |
[4,10] |
$2^{38}\cdot 5^{31}$ |
$2$ |
$23.958911430882168$ |
$36.31067590725307$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$20547515.71936001$ |
| 24.4.128...000.2 |
$x^{24} - 12 x^{23} + 74 x^{22} - 308 x^{21} + 966 x^{20} - 2412 x^{19} + 4884 x^{18} - 7968 x^{17} + 10016 x^{16} - 8392 x^{15} + 820 x^{14} + 12680 x^{13} - 29520 x^{12} + 44840 x^{11} - 53520 x^{10} + 50544 x^{9} - 38528 x^{8} + 24016 x^{7} - 13652 x^{6} + 7544 x^{5} - 3696 x^{4} + 1472 x^{3} - 384 x^{2} + 88 x + 4$ |
$24$ |
[4,10] |
$2^{38}\cdot 5^{31}$ |
$2$ |
$23.958911430882168$ |
$36.31067590725307$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$20547515.71936001$ |
| 24.0.131...209.1 |
$x^{24} - x + 1$ |
$24$ |
[0,12] |
$6361\cdot 61167766669\cdot 3374184647743911301$ |
$3$ |
$23.984225717$ |
$3.623334526165692e+16$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$11$ |
$9163307.175032053$ |
| 24.2.135...343.1 |
$x^{24} - x - 1$ |
$24$ |
[2,11] |
$-\,101\cdot 2347\cdot 5714547093403974893094772369$ |
$3$ |
$24.015539369$ |
$3.680511166740474e+16$ |
|
|
✓ |
$S_{24}$ (as 24T25000) |
trivial |
$2$ |
$12$ |
$6241504.123318238$ |
| 24.4.153...449.1 |
$x^{24} - 2 x^{23} - 8 x^{22} - 2 x^{21} + 70 x^{20} - 33 x^{19} - 156 x^{18} + 43 x^{17} + 433 x^{16} - 998 x^{15} + 433 x^{14} + 1850 x^{13} - 1996 x^{12} - 1334 x^{11} + 1462 x^{10} + 5 x^{9} - 1195 x^{8} - 1071 x^{7} - 747 x^{6} - 160 x^{5} + 26 x^{4} - 66 x^{3} - 57 x^{2} - 14 x - 1$ |
$24$ |
[4,10] |
$2083^{10}$ |
$1$ |
$24.142775491634545$ |
$45.639894828976104$ |
|
|
? |
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$10781013.84232622$ |
| 24.4.153...449.2 |
$x^{24} + 5 x^{22} - 9 x^{21} - 17 x^{20} - 76 x^{19} - 136 x^{18} - 174 x^{17} - 166 x^{16} + 28 x^{15} + 141 x^{14} + 361 x^{13} + 448 x^{12} + 1384 x^{11} + 3389 x^{10} + 8270 x^{9} + 11234 x^{8} + 16185 x^{7} + 17718 x^{6} + 15868 x^{5} + 15966 x^{4} + 10226 x^{3} + 4276 x^{2} + 3258 x + 1459$ |
$24$ |
[4,10] |
$2083^{10}$ |
$1$ |
$24.142775491634545$ |
$45.639894828976104$ |
|
|
? |
$\SL(2,5):C_2$ (as 24T576) |
trivial |
$2$ |
$13$ |
$10781013.84232622$ |
| 24.0.212...000.1 |
$x^{24} - 5 x^{22} + 19 x^{20} - 66 x^{18} + 221 x^{16} - 358 x^{14} + 530 x^{12} - 723 x^{10} + 793 x^{8} - 157 x^{6} + 31 x^{4} - 6 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 7^{16}$ |
$3$ |
$24.4712521652$ |
$24.471252165227245$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3]$ |
$20$ |
$11$ |
$18292450.943147723$ |
