| 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 |
| 20.0.302...896.1 |
$x^{20} + x^{18} - 4 x^{17} + 2 x^{16} - 4 x^{15} + 7 x^{14} - 6 x^{13} + 8 x^{12} - 6 x^{11} + 7 x^{10} - 6 x^{9} + 4 x^{8} - 2 x^{7} - 2 x^{5} - x^{4} + x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 220873^{2}$ |
$3$ |
$11.8578208872$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$1171.34610492$ |
| 20.0.452...625.1 |
$x^{20} - x^{19} + 2 x^{18} - 5 x^{17} + 7 x^{16} - 10 x^{15} + 15 x^{14} - 17 x^{13} + 22 x^{12} - 25 x^{11} + 25 x^{10} - 19 x^{9} + 22 x^{8} - 11 x^{7} + 11 x^{6} - 8 x^{5} + 5 x^{4} - x^{3} + 4 x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 280001^{2}$ |
$3$ |
$13.5756798542$ |
$2049.3938128139257$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$2451.4555058$ |
| 20.0.492...024.1 |
$x^{20} + 2 x^{18} + x^{16} - 4 x^{14} - 8 x^{12} - 5 x^{10} + 6 x^{8} + 14 x^{6} + 12 x^{4} + 5 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2}$ |
$4$ |
$13.6335832912$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$5086.93249334$ |
| 20.0.494...625.1 |
$x^{20} - x^{19} + 2 x^{18} - 5 x^{17} + 5 x^{16} - 8 x^{15} + 11 x^{14} - 10 x^{13} + 9 x^{12} - 15 x^{11} + 6 x^{10} - 6 x^{9} + 8 x^{8} + 4 x^{7} + 3 x^{6} + 9 x^{5} + 5 x^{4} + 4 x^{3} + x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 199^{2}\cdot 1471^{2}$ |
$4$ |
$13.636163644$ |
$2095.4557976726687$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$2740.01327388$ |
| 20.0.685...625.1 |
$x^{20} - 3 x^{19} + 4 x^{18} - 7 x^{17} + 15 x^{16} - 24 x^{15} + 34 x^{14} - 47 x^{13} + 67 x^{12} - 78 x^{11} + 72 x^{10} - 81 x^{9} + 81 x^{8} - 54 x^{7} + 45 x^{6} - 37 x^{5} + 20 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2}$ |
$4$ |
$15.5519457669$ |
$4043.3482412475923$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$9161.21223923$ |
| 20.0.690...625.1 |
$x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 28 x^{16} - 46 x^{15} + 63 x^{14} - 81 x^{13} + 92 x^{12} - 98 x^{11} + 89 x^{10} - 66 x^{9} + 54 x^{8} - 28 x^{7} + x^{6} - 3 x^{5} - 5 x^{4} + 10 x^{3} - x^{2} + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 61^{2}\cdot 17939^{2}$ |
$4$ |
$15.5581672565$ |
$4051.442335761426$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$8167.64790374$ |
| 20.0.121...625.1 |
$x^{20} + 2 x^{18} - 8 x^{17} + 8 x^{16} - 14 x^{15} + 26 x^{14} - 43 x^{13} + 62 x^{12} - 52 x^{11} + 99 x^{10} - 104 x^{9} + 89 x^{8} - 91 x^{7} + 67 x^{6} - 84 x^{5} + 22 x^{4} - 14 x^{3} + 29 x^{2} + 5 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 4588681^{2}$ |
$3$ |
$17.9561992646$ |
$8296.397712260425$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$34456.4237695$ |
| 20.0.155...625.1 |
$x^{20} - x^{19} + 2 x^{18} - 7 x^{17} + 9 x^{16} - 17 x^{15} + 11 x^{14} - 27 x^{13} + 32 x^{12} - 3 x^{11} + 23 x^{10} + 11 x^{9} + 32 x^{8} + 34 x^{7} + 6 x^{6} + 5 x^{5} + 17 x^{4} + 6 x^{3} + 5 x^{2} - x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2}$ |
$4$ |
$18.1818451118$ |
$8830.946438519486$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$35946.2759306$ |
| 20.0.348...056.1 |
$x^{20} + 18 x^{18} + 135 x^{16} + 540 x^{14} + 1231 x^{12} + 1604 x^{10} + 1167 x^{8} + 462 x^{6} + 106 x^{4} + 16 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 59^{2}\cdot 402107^{2}$ |
$4$ |
$18.9282292608$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$182622.47508$ |
| 20.0.436...625.1 |
$x^{20} - 2 x^{19} + 5 x^{18} + 2 x^{17} + 2 x^{16} + 8 x^{15} + 21 x^{14} + 14 x^{13} + 45 x^{12} - 12 x^{11} + 144 x^{10} - 43 x^{9} + 147 x^{8} - 63 x^{7} + 113 x^{6} - 42 x^{5} + 44 x^{4} - 15 x^{3} + 12 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 27517559^{2}$ |
$3$ |
$21.4786321479$ |
$20316.57906735285$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$218812.807689$ |
| 20.0.463...625.1 |
$x^{20} - x^{19} + 3 x^{18} + 8 x^{17} + 2 x^{16} + 24 x^{15} + 35 x^{14} + 54 x^{13} + 122 x^{12} + 41 x^{11} + 348 x^{10} + 25 x^{9} + 467 x^{8} + 9 x^{7} + 475 x^{6} + 31 x^{5} + 205 x^{4} + 26 x^{3} + 67 x^{2} + 8 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2}$ |
$4$ |
$21.5439339612$ |
$20627.306780091287$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
$[3]$ |
$6$ |
$9$ |
$71627.8364606$ |
| 20.4.822...000.1 |
$x^{20} - 6 x^{18} + 4 x^{16} + 40 x^{14} - 48 x^{12} - 480 x^{10} + 2112 x^{8} - 4480 x^{6} + 5376 x^{4} - 3584 x^{2} + 1024$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{10}\cdot 280001^{2}$ |
$3$ |
$22.1689923695$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$11$ |
$283297.510859$ |
| 20.4.898...000.1 |
$x^{20} - 6 x^{18} + 20 x^{16} - 56 x^{14} + 272 x^{12} - 992 x^{10} + 1856 x^{8} - 1024 x^{6} - 512 x^{4} - 512 x^{2} + 1024$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{10}\cdot 199^{2}\cdot 1471^{2}$ |
$4$ |
$22.2677619846$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$11$ |
$296326.894559$ |
| 20.8.124...000.1 |
$x^{20} + 2 x^{18} - 12 x^{16} - 32 x^{14} - 320 x^{10} + 1408 x^{8} - 640 x^{6} - 256 x^{4} - 1536 x^{2} + 1024$ |
$20$ |
[8,6] |
$2^{30}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2}$ |
$4$ |
$25.3962210909$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$13$ |
$2871383.16477$ |
| 20.8.125...000.1 |
$x^{20} - 14 x^{18} + 76 x^{16} - 240 x^{14} + 656 x^{12} - 1536 x^{10} + 2560 x^{8} - 3968 x^{6} + 3328 x^{4} + 1024 x^{2} + 1024$ |
$20$ |
[8,6] |
$2^{30}\cdot 5^{10}\cdot 61^{2}\cdot 17939^{2}$ |
$4$ |
$25.4063807408$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$13$ |
$2626631.04545$ |
| 20.0.376...000.1 |
$x^{20} + 13 x^{18} + 68 x^{16} + 176 x^{14} + 198 x^{12} - 39 x^{10} - 267 x^{8} - 62 x^{6} + 217 x^{4} + 140 x^{2} + 16$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{10}\cdot 60662149^{2}$ |
$3$ |
$26.8414996821$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
$[2]$ |
$4$ |
$9$ |
$1236148.79502$ |
| 20.0.490...625.1 |
$x^{20} - 4 x^{19} + 19 x^{18} - 32 x^{17} + 95 x^{16} - 91 x^{15} + 320 x^{14} - 163 x^{13} + 676 x^{12} - 43 x^{11} + 1048 x^{10} + 129 x^{9} + 927 x^{8} + 299 x^{7} + 576 x^{6} + 152 x^{5} + 130 x^{4} + 34 x^{3} + 21 x^{2} + 4 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2}$ |
$4$ |
$27.1965405285$ |
$66128.06314266281$ |
✓ |
|
? |
$S_5^2:C_2^2$ (as 20T656) |
$[15]$ |
$6$ |
$9$ |
$161078.71489$ |
| 20.0.553...625.1 |
$x^{20} - x^{19} + 11 x^{18} - 6 x^{17} + 74 x^{16} - 35 x^{15} + 289 x^{14} - 114 x^{13} + 804 x^{12} - 320 x^{11} + 1455 x^{10} - 554 x^{9} + 1882 x^{8} - 802 x^{7} + 1473 x^{6} - 659 x^{5} + 810 x^{4} - 316 x^{3} + 149 x^{2} - 13 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 11^{2}\cdot 28162171^{2}$ |
$4$ |
$27.3622313871$ |
$68167.13441974805$ |
✓ |
|
? |
$S_5^2:C_2^2$ (as 20T656) |
$[2, 6]$ |
$6$ |
$9$ |
$170321.970246$ |
| 20.12.220...000.1 |
$x^{20} - 8 x^{18} - 16 x^{16} + 144 x^{14} + 320 x^{12} - 2112 x^{10} + 2112 x^{8} - 3712 x^{6} + 16384 x^{4} - 16896 x^{2} + 1024$ |
$20$ |
[12,4] |
$2^{30}\cdot 5^{10}\cdot 4588681^{2}$ |
$3$ |
$29.322350612$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$15$ |
$26042038.1541$ |
| 20.12.283...000.1 |
$x^{20} - 6 x^{18} + 4 x^{16} - 112 x^{14} + 992 x^{12} - 1824 x^{10} - 1536 x^{8} + 4224 x^{6} + 2560 x^{4} - 4608 x^{2} + 1024$ |
$20$ |
[12,4] |
$2^{30}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2}$ |
$4$ |
$29.6908287375$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$15$ |
$29201247.8591$ |
| 20.16.793...000.1 |
$x^{20} - 12 x^{18} - 4 x^{16} + 384 x^{14} - 624 x^{12} - 4416 x^{10} + 18240 x^{8} - 28160 x^{6} + 21248 x^{4} - 7680 x^{2} + 1024$ |
$20$ |
[16,2] |
$2^{30}\cdot 5^{10}\cdot 27517559^{2}$ |
$3$ |
$35.0744594235$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$17$ |
$354979481.121$ |
| 20.16.843...000.1 |
$x^{20} - 10 x^{18} - 16 x^{16} + 344 x^{14} + 784 x^{12} - 16896 x^{10} + 68224 x^{8} - 124288 x^{6} + 106752 x^{4} - 35840 x^{2} + 1024$ |
$20$ |
[16,2] |
$2^{30}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2}$ |
$4$ |
$35.1810968382$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$17$ |
$349149904.569$ |
| 20.20.891...000.1 |
$x^{20} - 8 x^{19} - 10 x^{18} + 216 x^{17} - 211 x^{16} - 2148 x^{15} + 4032 x^{14} + 9190 x^{13} - 25208 x^{12} - 12028 x^{11} + 68730 x^{10} - 21794 x^{9} - 72358 x^{8} + 58352 x^{7} + 9825 x^{6} - 21616 x^{5} + 3888 x^{4} + 1414 x^{3} - 259 x^{2} - 38 x - 1$ |
$20$ |
[20,0] |
$2^{30}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2}$ |
$4$ |
$44.4117647092$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$19$ |
$9826665156.55$ |
| 20.20.100...000.1 |
$x^{20} - 2 x^{19} - 39 x^{18} + 72 x^{17} + 594 x^{16} - 1010 x^{15} - 4486 x^{14} + 6924 x^{13} + 17696 x^{12} - 23766 x^{11} - 36003 x^{10} + 37522 x^{9} + 37694 x^{8} - 24108 x^{7} - 18366 x^{6} + 5110 x^{5} + 2784 x^{4} - 616 x^{3} - 119 x^{2} + 30 x - 1$ |
$20$ |
[20,0] |
$2^{30}\cdot 5^{10}\cdot 11^{2}\cdot 28162171^{2}$ |
$4$ |
$44.6823367483$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$19$ |
$10034305882.8$ |
| 20.12.265...625.1 |
$x^{20} - 253 x^{18} + 28290 x^{16} - 6 x^{15} - 1840209 x^{14} - 679 x^{13} + 77072033 x^{12} + 129241 x^{11} - 2170492588 x^{10} - 5916096 x^{9} + 41603791746 x^{8} + 94277553 x^{7} - 535688310011 x^{6} + 140062232 x^{5} + 4431198685244 x^{4} - 16737690057 x^{3} - 21240654931404 x^{2} + 108814306471 x + 44742407803561$ |
$20$ |
[12,4] |
$5^{10}\cdot 97^{10}\cdot 60662149^{2}$ |
$3$ |
$132.179056778$ |
$171525.92301165443$ |
|
|
|
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$2$ |
$15$ |
$140481468190000$ |
