| 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 |
| 24.0.304...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 |
$90$ |
$11$ |
$2124832.236129185$ |
| 24.0.170...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) |
$[2]$ |
$78$ |
$11$ |
$2851634.018949717$ |
| 24.0.538...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) |
$[3]$ |
$52$ |
$11$ |
$7239917.885587101$ |
| 24.0.673...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 |
$30$ |
$11$ |
$8057321.833968681$ |
| 24.0.784...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) |
$[2, 2]$ |
$26$ |
$11$ |
$7346081.887826216$ |
| 24.0.212...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) |
$[3]$ |
$20$ |
$11$ |
$18292450.943147723$ |
| 24.0.444...169.1 |
$x^{24} - x^{23} - x^{22} + 3 x^{21} - x^{20} - 5 x^{19} + 7 x^{18} + 3 x^{17} - 17 x^{16} + 11 x^{15} + 23 x^{14} - 45 x^{13} - x^{12} - 90 x^{11} + 92 x^{10} + 88 x^{9} - 272 x^{8} + 96 x^{7} + 448 x^{6} - 640 x^{5} - 256 x^{4} + 1536 x^{3} - 1024 x^{2} - 2048 x + 4096$ |
$24$ |
[0,12] |
$7^{12}\cdot 13^{22}$ |
$2$ |
$27.7756198526$ |
$27.775619852565686$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[7]$ |
$26$ |
$11$ |
$42757649.54957395$ |
| 24.0.724...625.1 |
$x^{24} - x^{23} + 6 x^{22} - 7 x^{21} + 27 x^{20} - 19 x^{19} + 94 x^{18} - 58 x^{17} + 317 x^{16} - 205 x^{15} + 643 x^{14} - 353 x^{13} + 1114 x^{12} - 86 x^{11} + 1318 x^{10} - 237 x^{9} + 1501 x^{8} - 593 x^{7} + 614 x^{6} - 193 x^{5} + 250 x^{4} + 59 x^{3} + 15 x^{2} + 3 x + 1$ |
$24$ |
[0,12] |
$5^{18}\cdot 13^{20}$ |
$2$ |
$28.3474259946$ |
$28.34742599459173$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 2, 2, 2]$ |
$10$ |
$11$ |
$7346081.887826216$ |
| 24.0.118...000.1 |
$x^{24} - 6 x^{22} + 27 x^{20} - 109 x^{18} + 417 x^{16} - 927 x^{14} + 1918 x^{12} - 3582 x^{10} + 5157 x^{8} - 622 x^{6} + 75 x^{4} - 9 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{32}\cdot 5^{18}$ |
$3$ |
$28.934712525$ |
$28.934712524984697$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3]$ |
$20$ |
$11$ |
$68395599.77210574$ |
| 24.0.156...296.1 |
$x^{24} + 117 x^{16} + 650 x^{8} + 1$ |
$24$ |
[0,12] |
$2^{72}\cdot 7^{16}$ |
$2$ |
$29.2744456802$ |
$29.27444568018377$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3, 3]$ |
$16$ |
$11$ |
$39019312.21180779$ |
| 24.0.161...625.1 |
$x^{24} - x^{23} + 7 x^{22} - 7 x^{21} + 35 x^{20} - 34 x^{19} + 153 x^{18} - 146 x^{17} + 629 x^{16} - 588 x^{15} + 1618 x^{14} - 1394 x^{13} + 3557 x^{12} - 2395 x^{11} + 6504 x^{10} - 4802 x^{9} + 10534 x^{8} - 8224 x^{7} + 6187 x^{6} - 3548 x^{5} + 2534 x^{4} - 378 x^{3} + 56 x^{2} - 8 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$29.3113956235$ |
$29.3113956234904$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[26]$ |
$10$ |
$11$ |
$9216624.607005743$ |
| 24.24.161...625.1 |
$x^{24} - x^{23} - 23 x^{22} + 23 x^{21} + 230 x^{20} - 229 x^{19} - 1312 x^{18} + 1294 x^{17} + 4709 x^{16} - 4573 x^{15} - 11067 x^{14} + 10506 x^{13} + 17187 x^{12} - 15810 x^{11} - 17391 x^{10} + 15333 x^{9} + 11034 x^{8} - 9189 x^{7} - 4088 x^{6} + 3142 x^{5} + 784 x^{4} - 528 x^{3} - 64 x^{2} + 32 x + 1$ |
$24$ |
[24,0] |
$3^{12}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$29.3113956235$ |
$29.3113956234904$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$5459008653.485176$ |
| 24.0.161...625.2 |
$x^{24} - x^{23} + 5 x^{22} - 5 x^{21} + 20 x^{20} - 19 x^{19} + 74 x^{18} - 99 x^{17} + 299 x^{16} - 380 x^{15} + 1106 x^{14} - 1331 x^{13} + 3936 x^{12} - 4456 x^{11} + 5996 x^{10} - 6745 x^{9} + 8969 x^{8} - 7509 x^{7} + 10409 x^{6} + 2176 x^{5} + 455 x^{4} + 95 x^{3} + 20 x^{2} + 4 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$29.3113956235$ |
$29.3113956234904$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[26]$ |
$14$ |
$11$ |
$16114643.667937363$ |
| 24.0.161...625.3 |
$x^{24} - x^{23} + 13 x^{22} - 10 x^{21} + 101 x^{20} - 67 x^{19} + 500 x^{18} - 254 x^{17} + 1781 x^{16} - 706 x^{15} + 4524 x^{14} - 1119 x^{13} + 8400 x^{12} - 1296 x^{11} + 11097 x^{10} - 456 x^{9} + 10104 x^{8} - 327 x^{7} + 5722 x^{6} + 151 x^{5} + 1858 x^{4} - 228 x^{3} + 104 x^{2} + 8 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$29.3113956235$ |
$29.3113956234904$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[26]$ |
$6$ |
$11$ |
$3391665.6012423597$ |
| 24.0.220...584.1 |
$x^{24} - 2 x^{22} + 4 x^{20} - 8 x^{18} + 16 x^{16} - 32 x^{14} + 64 x^{12} - 128 x^{10} + 256 x^{8} - 512 x^{6} + 1024 x^{4} - 2048 x^{2} + 4096$ |
$24$ |
[0,12] |
$2^{36}\cdot 13^{22}$ |
$2$ |
$29.6933866267$ |
$29.69338662673638$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[9]$ |
$26$ |
$11$ |
$60385547.84262381$ |
| 24.0.220...584.2 |
$x^{24} + 2 x^{22} + 4 x^{20} + 8 x^{18} + 16 x^{16} + 32 x^{14} + 64 x^{12} + 128 x^{10} + 256 x^{8} + 512 x^{6} + 1024 x^{4} + 2048 x^{2} + 4096$ |
$24$ |
[0,12] |
$2^{36}\cdot 13^{22}$ |
$2$ |
$29.6933866267$ |
$29.69338662673638$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[13]$ |
$26$ |
$11$ |
$34260599.803001165$ |
| 24.0.134...625.1 |
$x^{24} - x^{23} - 4 x^{22} + 15 x^{21} - 16 x^{20} + 62 x^{19} + 163 x^{18} - 809 x^{17} + 670 x^{16} + 3344 x^{15} + 2796 x^{14} - 2771 x^{13} - 4594 x^{12} - 11446 x^{11} - 11444 x^{10} + 8739 x^{9} + 34835 x^{8} + 8891 x^{7} - 162 x^{6} - 698 x^{5} - 196 x^{4} - 50 x^{3} + x^{2} + 4 x + 1$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 13^{16}$ |
$3$ |
$32.0196833045$ |
$32.01968330451422$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[4, 4]$ |
$30$ |
$11$ |
$183169998.253836$ |
| 24.24.510...000.1 |
$x^{24} - 23 x^{22} + 230 x^{20} - 1311 x^{18} + 4692 x^{16} - 10949 x^{14} + 16757 x^{12} - 16511 x^{10} + 10032 x^{8} - 3498 x^{6} + 628 x^{4} - 48 x^{2} + 1$ |
$24$ |
[24,0] |
$2^{24}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$33.8458843071$ |
$33.8458843070916$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$33400075541.82508$ |
| 24.0.510...000.1 |
$x^{24} + 25 x^{22} + 274 x^{20} + 1729 x^{18} + 6936 x^{16} + 18427 x^{14} + 32745 x^{12} + 38377 x^{10} + 28468 x^{8} + 12278 x^{6} + 2556 x^{4} + 144 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$33.8458843071$ |
$33.8458843070916$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[78]$ |
$4$ |
$11$ |
$3391665.6012423597$ |
| 24.0.510...000.2 |
$x^{24} + 7 x^{22} + 35 x^{20} + 154 x^{18} + 637 x^{16} + 1666 x^{14} + 3822 x^{12} + 7889 x^{10} + 13377 x^{8} + 9947 x^{6} + 7203 x^{4} + 4802 x^{2} + 2401$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$33.8458843071$ |
$33.8458843070916$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[26]$ |
$10$ |
$11$ |
$24838443.50460296$ |
| 24.0.510...000.3 |
$x^{24} + 5 x^{22} + 20 x^{20} + 75 x^{18} + 275 x^{16} + 1000 x^{14} + 3625 x^{12} + 5000 x^{10} + 6875 x^{8} + 9375 x^{6} + 12500 x^{4} + 15625 x^{2} + 15625$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 7^{20}$ |
$3$ |
$33.8458843071$ |
$33.8458843070916$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[26]$ |
$14$ |
$11$ |
$36584901.886295445$ |
| 24.0.588...464.1 |
$x^{24} - 4 x^{22} + 14 x^{20} - 48 x^{18} + 164 x^{16} - 560 x^{14} + 1912 x^{12} - 1120 x^{10} + 656 x^{8} - 384 x^{6} + 224 x^{4} - 128 x^{2} + 64$ |
$24$ |
[0,12] |
$2^{66}\cdot 7^{20}$ |
$2$ |
$34.0471571079$ |
$34.04715710793443$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3, 6]$ |
$14$ |
$11$ |
$215040822.68029645$ |
| 24.0.588...464.2 |
$x^{24} + 4 x^{22} + 14 x^{20} + 48 x^{18} + 164 x^{16} + 560 x^{14} + 1912 x^{12} + 1120 x^{10} + 656 x^{8} + 384 x^{6} + 224 x^{4} + 128 x^{2} + 64$ |
$24$ |
[0,12] |
$2^{66}\cdot 7^{20}$ |
$2$ |
$34.0471571079$ |
$34.04715710793443$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[52]$ |
$14$ |
$11$ |
$39019312.21180779$ |
| 24.0.871...000.1 |
$x^{24} - 10 x^{22} + 76 x^{20} - 528 x^{18} + 3536 x^{16} - 11456 x^{14} + 33920 x^{12} - 92544 x^{10} + 203008 x^{8} - 80384 x^{6} + 31744 x^{4} - 12288 x^{2} + 4096$ |
$24$ |
[0,12] |
$2^{36}\cdot 5^{18}\cdot 7^{16}$ |
$3$ |
$34.6075767003$ |
$34.607576700316336$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3, 3]$ |
$10$ |
$11$ |
$198346402.31462404$ |
| 24.0.871...000.2 |
$x^{24} + 10 x^{22} + 76 x^{20} + 528 x^{18} + 3536 x^{16} + 11456 x^{14} + 33920 x^{12} + 92544 x^{10} + 203008 x^{8} + 80384 x^{6} + 31744 x^{4} + 12288 x^{2} + 4096$ |
$24$ |
[0,12] |
$2^{36}\cdot 5^{18}\cdot 7^{16}$ |
$3$ |
$34.6075767003$ |
$34.607576700316336$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[73]$ |
$10$ |
$11$ |
$27409659.83250929$ |
| 24.0.875...336.1 |
$x^{24} + 186 x^{16} + 4725 x^{8} + 1$ |
$24$ |
[0,12] |
$2^{72}\cdot 3^{32}$ |
$2$ |
$34.6139896874$ |
$34.6139896873778$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[39]$ |
$16$ |
$11$ |
$165705493.8155171$ |
| 24.0.897...129.1 |
$x^{24} - x^{23} - x^{22} + 7 x^{21} - 12 x^{20} - 3 x^{19} + 58 x^{18} + 153 x^{17} - 245 x^{16} + 180 x^{15} + 748 x^{14} - 2547 x^{13} + 2506 x^{12} + 5040 x^{11} + 4818 x^{10} + 2767 x^{9} + 239 x^{8} - 1621 x^{7} - 2243 x^{6} - 1860 x^{5} - 855 x^{4} + 189 x^{3} + 810 x^{2} + 972 x + 729$ |
$24$ |
[0,12] |
$7^{20}\cdot 13^{18}$ |
$2$ |
$34.6502107884$ |
$34.650210788360646$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[4, 4]$ |
$14$ |
$11$ |
$209675214.65936095$ |
| 24.24.960...000.1 |
$x^{24} - 24 x^{22} + 252 x^{20} - 1519 x^{18} + 5796 x^{16} - 14553 x^{14} + 24206 x^{12} - 26169 x^{10} + 17523 x^{8} - 6623 x^{6} + 1182 x^{4} - 72 x^{2} + 1$ |
$24$ |
[24,0] |
$2^{24}\cdot 3^{36}\cdot 5^{18}$ |
$3$ |
$34.7487655586$ |
$34.748765558648074$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$46780365797.01783$ |
| 24.0.960...000.1 |
$x^{24} + 24 x^{22} + 252 x^{20} + 1521 x^{18} + 5832 x^{16} + 14823 x^{14} + 25298 x^{12} + 28743 x^{10} + 21087 x^{8} + 9393 x^{6} + 2250 x^{4} + 216 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{36}\cdot 5^{18}$ |
$3$ |
$34.7487655586$ |
$34.748765558648074$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[5, 30]$ |
$4$ |
$11$ |
$4249664.47225837$ |
| 24.0.960...000.2 |
$x^{24} + 6 x^{22} + 27 x^{20} + 111 x^{18} + 441 x^{16} + 837 x^{14} + 1386 x^{12} + 2106 x^{10} + 2673 x^{8} + 1242 x^{6} + 567 x^{4} + 243 x^{2} + 81$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{36}\cdot 5^{18}$ |
$3$ |
$34.7487655586$ |
$34.748765558648074$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[5, 10]$ |
$10$ |
$11$ |
$27273221.26089917$ |
| 24.0.960...000.3 |
$x^{24} + 50 x^{18} + 2375 x^{12} + 6250 x^{6} + 15625$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{36}\cdot 5^{18}$ |
$3$ |
$34.7487655586$ |
$34.748765558648074$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[5, 10]$ |
$18$ |
$11$ |
$136791199.54421148$ |
| 24.0.100...049.1 |
$x^{24} - x^{23} - 2 x^{22} + 5 x^{21} + x^{20} - 16 x^{19} + 13 x^{18} + 35 x^{17} - 74 x^{16} - 31 x^{15} + 253 x^{14} - 160 x^{13} - 599 x^{12} - 480 x^{11} + 2277 x^{10} - 837 x^{9} - 5994 x^{8} + 8505 x^{7} + 9477 x^{6} - 34992 x^{5} + 6561 x^{4} + 98415 x^{3} - 118098 x^{2} - 177147 x + 531441$ |
$24$ |
[0,12] |
$11^{12}\cdot 13^{22}$ |
$2$ |
$34.8185821491$ |
$34.818582149143644$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[35]$ |
$26$ |
$11$ |
$166366823.90883145$ |
| 24.0.110...144.1 |
$x^{24} - 40 x^{18} + 1592 x^{12} - 320 x^{6} + 64$ |
$24$ |
[0,12] |
$2^{66}\cdot 3^{36}$ |
$2$ |
$34.9554075629$ |
$34.955407562927284$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[13]$ |
$18$ |
$11$ |
$156828331.03427416$ |
| 24.0.110...144.2 |
$x^{24} + 40 x^{18} + 1592 x^{12} + 320 x^{6} + 64$ |
$24$ |
[0,12] |
$2^{66}\cdot 3^{36}$ |
$2$ |
$34.9554075629$ |
$34.955407562927284$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[13]$ |
$18$ |
$11$ |
$165705493.8155171$ |
| 24.24.122...625.1 |
$x^{24} - x^{23} - 24 x^{22} + 23 x^{21} + 252 x^{20} - 229 x^{19} - 1521 x^{18} + 1292 x^{17} + 5832 x^{16} - 4540 x^{15} - 14822 x^{14} + 10282 x^{13} + 25284 x^{12} - 15001 x^{11} - 28667 x^{10} + 13653 x^{9} + 20886 x^{8} - 7168 x^{7} - 9126 x^{6} + 1802 x^{5} + 2085 x^{4} - 101 x^{3} - 180 x^{2} - 12 x + 1$ |
$24$ |
[24,0] |
$5^{18}\cdot 13^{22}$ |
$2$ |
$35.1028390564$ |
$35.10283905640381$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$58142934011.05266$ |
| 24.0.168...609.1 |
$x^{24} - 17 x^{21} + 218 x^{18} - 1277 x^{15} + 5609 x^{12} + 3403 x^{9} - 692 x^{6} + 945 x^{3} + 729$ |
$24$ |
[0,12] |
$3^{36}\cdot 13^{18}$ |
$2$ |
$35.5745484537$ |
$35.57454845374513$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[3, 6]$ |
$18$ |
$11$ |
$533054958.55350393$ |
| 24.24.286...464.1 |
$x^{24} - 23 x^{22} + 230 x^{20} - 1312 x^{18} + 4709 x^{16} - 11067 x^{14} + 17187 x^{12} - 17391 x^{10} + 11033 x^{8} - 4081 x^{6} + 770 x^{4} - 56 x^{2} + 1$ |
$24$ |
[24,0] |
$2^{24}\cdot 3^{12}\cdot 13^{22}$ |
$3$ |
$36.3668229853$ |
$36.36682298534298$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$90864396382.97002$ |
| 24.0.286...464.1 |
$x^{24} + 3 x^{22} + 9 x^{20} + 27 x^{18} + 81 x^{16} + 243 x^{14} + 729 x^{12} + 2187 x^{10} + 6561 x^{8} + 19683 x^{6} + 59049 x^{4} + 177147 x^{2} + 531441$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 13^{22}$ |
$3$ |
$36.3668229853$ |
$36.36682298534298$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 26]$ |
$26$ |
$11$ |
$134652762.86314306$ |
| 24.0.286...464.2 |
$x^{24} + 25 x^{22} + 274 x^{20} + 1728 x^{18} + 6917 x^{16} + 18277 x^{14} + 32111 x^{12} + 36841 x^{10} + 26365 x^{8} + 10815 x^{6} + 2198 x^{4} + 168 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 13^{22}$ |
$3$ |
$36.3668229853$ |
$36.36682298534298$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[2, 78]$ |
$4$ |
$11$ |
$5703268.037899434$ |
| 24.0.286...464.3 |
$x^{24} + 13 x^{22} + 104 x^{20} + 533 x^{18} + 2015 x^{16} + 5499 x^{14} + 11349 x^{12} + 16731 x^{10} + 18083 x^{8} + 12506 x^{6} + 5915 x^{4} + 1183 x^{2} + 169$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 13^{22}$ |
$3$ |
$36.3668229853$ |
$36.36682298534298$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 52]$ |
$6$ |
$11$ |
$14479835.771174202$ |
| 24.0.425...000.1 |
$x^{24} - 9 x^{22} + 67 x^{20} - 478 x^{18} + 3373 x^{16} - 6558 x^{14} + 12278 x^{12} - 22063 x^{10} + 33233 x^{8} - 2493 x^{6} + 187 x^{4} - 14 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 13^{16}$ |
$3$ |
$36.9731455505$ |
$36.9731455504557$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[4, 12]$ |
$20$ |
$11$ |
$352314418.0293608$ |
| 24.0.978...625.1 |
$x^{24} - 12 x^{23} + 96 x^{22} - 548 x^{21} + 2526 x^{20} - 9648 x^{19} + 31555 x^{18} - 89118 x^{17} + 218325 x^{16} - 461214 x^{15} + 823281 x^{14} - 1193121 x^{13} + 1278473 x^{12} - 705375 x^{11} - 619155 x^{10} + 2131658 x^{9} - 2709069 x^{8} + 1618335 x^{7} + 600240 x^{6} - 2358960 x^{5} + 2561604 x^{4} - 1563601 x^{3} + 522033 x^{2} - 47436 x + 7541$ |
$24$ |
[0,12] |
$3^{32}\cdot 5^{18}\cdot 7^{12}$ |
$3$ |
$38.2770267991$ |
$38.27702679912765$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3, 3]$ |
$10$ |
$11$ |
$423268882.10391355$ |
| 24.0.143...625.1 |
$x^{24} - x^{23} - x^{22} + 11 x^{21} - 16 x^{20} + 61 x^{19} + 56 x^{18} - 283 x^{17} + 595 x^{16} + 483 x^{15} + 1068 x^{14} + 1736 x^{13} + 1610 x^{12} + 2951 x^{11} + 2205 x^{10} + 2925 x^{9} + 1727 x^{8} - 7188 x^{7} + 3314 x^{6} - 3879 x^{5} - 3407 x^{4} + 1379 x^{3} + 1568 x^{2} - 1715 x + 2401$ |
$24$ |
[0,12] |
$5^{18}\cdot 19^{20}$ |
$2$ |
$38.891572567$ |
$38.89157256696073$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[52]$ |
$10$ |
$11$ |
$694660924.0250753$ |
| 24.24.376...696.1 |
$x^{24} - 24 x^{22} + 252 x^{20} - 1520 x^{18} + 5813 x^{16} - 14672 x^{14} + 24648 x^{12} - 27104 x^{10} + 18646 x^{8} - 7344 x^{6} + 1400 x^{4} - 96 x^{2} + 1$ |
$24$ |
[24,0] |
$2^{72}\cdot 7^{20}$ |
$2$ |
$40.4891214784$ |
$40.48912147837109$ |
|
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$360688478301.3431$ |
| 24.0.376...696.1 |
$x^{24} + 24 x^{22} + 252 x^{20} + 1520 x^{18} + 5813 x^{16} + 14672 x^{14} + 24648 x^{12} + 27104 x^{10} + 18646 x^{8} + 7344 x^{6} + 1400 x^{4} + 96 x^{2} + 1$ |
$24$ |
[0,12] |
$2^{72}\cdot 7^{20}$ |
$2$ |
$40.4891214784$ |
$40.48912147837109$ |
✓ |
✓ |
✓ |
$C_2\times C_{12}$ (as 24T2) |
$[6, 78]$ |
$2$ |
$11$ |
$7024849.183363979$ |
| 24.0.376...696.2 |
$x^{24} + 245 x^{16} + 7546 x^{8} + 2401$ |
$24$ |
[0,12] |
$2^{72}\cdot 7^{20}$ |
$2$ |
$40.4891214784$ |
$40.48912147837109$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 26]$ |
$8$ |
$11$ |
$215040822.68029645$ |
| 24.0.397...625.1 |
$x^{24} - x^{23} - 3 x^{22} + 4 x^{21} - 18 x^{20} - 73 x^{19} + 153 x^{18} + 160 x^{17} + 166 x^{16} + 640 x^{15} + 1363 x^{14} - 4490 x^{13} - 19199 x^{12} + 2486 x^{11} + 33907 x^{10} - 20248 x^{9} + 355120 x^{8} - 52357 x^{7} - 937497 x^{6} + 356623 x^{5} + 2830245 x^{4} + 91235 x^{3} - 10298763 x^{2} - 1431644 x + 25411681$ |
$24$ |
[0,12] |
$5^{18}\cdot 7^{16}\cdot 11^{12}$ |
$3$ |
$40.5809807911$ |
$40.580980791115465$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3, 6]$ |
$10$ |
$11$ |
$486434529.8152184$ |
| 24.24.416...625.1 |
$x^{24} - x^{23} - 37 x^{22} + 36 x^{21} + 551 x^{20} - 515 x^{19} - 4277 x^{18} + 3762 x^{17} + 18936 x^{16} - 15174 x^{15} - 50091 x^{14} + 34917 x^{13} + 81925 x^{12} - 46487 x^{11} - 84021 x^{10} + 34947 x^{9} + 53243 x^{8} - 13356 x^{7} - 19591 x^{6} + 1711 x^{5} + 3541 x^{4} + 172 x^{3} - 180 x^{2} - 12 x + 1$ |
$24$ |
[24,0] |
$3^{12}\cdot 5^{12}\cdot 13^{22}$ |
$3$ |
$40.6593441605$ |
$40.65934416046437$ |
|
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$340731139253.48956$ |
| 24.0.416...625.1 |
$x^{24} - x^{23} + 23 x^{22} - 19 x^{21} + 226 x^{20} - 150 x^{19} + 1248 x^{18} - 648 x^{17} + 4301 x^{16} - 1709 x^{15} + 9699 x^{14} - 2863 x^{13} + 14455 x^{12} - 2482 x^{11} + 13614 x^{10} + 3087 x^{9} + 5663 x^{8} + 15854 x^{7} - 1326 x^{6} + 19186 x^{5} - 869 x^{4} + 18947 x^{3} - 13105 x^{2} - 15272 x + 67861$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{12}\cdot 13^{22}$ |
$3$ |
$40.6593441605$ |
$40.65934416046437$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[2, 2, 8, 8]$ |
$2$ |
$11$ |
$5703268.037899434$ |
