| 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 |
| 20.0.167...664.1 |
$x^{20} - 6 x^{19} + 18 x^{18} - 26 x^{17} - 2 x^{16} + 86 x^{15} - 154 x^{14} + 48 x^{13} + 323 x^{12} - 824 x^{11} + 1264 x^{10} - 1688 x^{9} + 2332 x^{8} - 3222 x^{7} + 4026 x^{6} - 4236 x^{5} + 3552 x^{4} - 2262 x^{3} + 1028 x^{2} - 292 x + 41$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{4}\cdot 41\cdot 631^{4}$ |
$4$ |
$18.24776444743771$ |
|
|
|
? |
$C_2^{10}.C_2^4:S_5$ (as 20T992) |
trivial |
trivial |
$2$ |
$9$ |
$23882.13667405108$ |
| 20.0.493...664.1 |
$x^{20} - 8 x^{19} + 34 x^{18} - 116 x^{17} + 338 x^{16} - 836 x^{15} + 1840 x^{14} - 3640 x^{13} + 6408 x^{12} - 10176 x^{11} + 14560 x^{10} - 18560 x^{9} + 21128 x^{8} - 21328 x^{7} + 18704 x^{6} - 14048 x^{5} + 8976 x^{4} - 4576 x^{3} + 1760 x^{2} - 704 x + 352$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$24.977294240287762$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
trivial |
$2$ |
$9$ |
$43044.7776734$ |
| 20.4.124...584.1 |
$x^{20} - 4 x^{19} + 40 x^{17} - 96 x^{16} - 44 x^{15} + 576 x^{14} - 616 x^{13} - 524 x^{12} + 3512 x^{11} - 1440 x^{10} - 2656 x^{9} + 7296 x^{8} - 3280 x^{7} - 25232 x^{6} - 36640 x^{5} - 50368 x^{4} - 117728 x^{3} - 212256 x^{2} - 168192 x - 41824$ |
$20$ |
[4,8] |
$2^{30}\cdot 47^{12}$ |
$2$ |
$28.497299598794257$ |
|
|
|
? |
$C_2^8:D_5$ (as 20T240) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$3180413.876043657$ |
| 20.8.131...872.3 |
$x^{20} - 4 x^{19} - 10 x^{18} + 58 x^{17} + 9 x^{16} - 318 x^{15} + 208 x^{14} + 980 x^{13} - 1233 x^{12} - 2012 x^{11} + 3486 x^{10} + 2862 x^{9} - 4702 x^{8} - 4420 x^{7} + 3654 x^{6} + 7798 x^{5} - 2695 x^{4} - 10164 x^{3} - 22 x^{2} + 6094 x + 2189$ |
$20$ |
[8,6] |
$2^{30}\cdot 3^{5}\cdot 11^{17}$ |
$3$ |
$28.576503519$ |
|
|
|
? |
$C_2^8:C_{10}$ (as 20T256) |
trivial |
$[2]$ |
$2$ |
$13$ |
$10823608.7$ |
| 20.4.581...544.1 |
$x^{20} - 6 x^{18} - 16 x^{17} - 17 x^{16} - 90 x^{15} + 180 x^{14} + 1204 x^{13} + 2025 x^{12} + 2004 x^{11} - 408 x^{10} - 15680 x^{9} - 43773 x^{8} - 40714 x^{7} + 6698 x^{6} + 65882 x^{5} + 109930 x^{4} + 60922 x^{3} - 66432 x^{2} - 113800 x - 47757$ |
$20$ |
[4,8] |
$2^{30}\cdot 3^{4}\cdot 401^{8}$ |
$3$ |
$38.74601064861941$ |
|
|
|
|
$C_2^8:D_5$ (as 20T240) |
trivial |
$[2]$ |
$2$ |
$11$ |
$301608950.90465146$ |
| 20.12.523...896.2 |
$x^{20} - 8 x^{19} + 4 x^{18} + 88 x^{17} - 72 x^{16} - 450 x^{15} - 46 x^{14} + 1372 x^{13} + 2325 x^{12} - 1446 x^{11} - 8238 x^{10} - 3980 x^{9} + 8264 x^{8} + 8840 x^{7} + 2446 x^{6} + 1298 x^{5} + 2130 x^{4} - 860 x^{3} - 3230 x^{2} - 1588 x - 127$ |
$20$ |
[12,4] |
$2^{30}\cdot 3^{6}\cdot 401^{8}$ |
$3$ |
$43.2453203863$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$1817295528.65$ |
| 20.4.523...896.4 |
$x^{20} - 8 x^{19} + 12 x^{18} + 52 x^{17} - 100 x^{16} - 336 x^{15} + 560 x^{14} + 258 x^{13} + 7870 x^{12} - 32546 x^{11} + 29212 x^{10} + 53436 x^{9} - 169937 x^{8} + 266926 x^{7} - 322312 x^{6} + 212394 x^{5} + 72794 x^{4} - 253182 x^{3} + 196170 x^{2} - 94618 x + 39607$ |
$20$ |
[4,8] |
$2^{30}\cdot 3^{6}\cdot 401^{8}$ |
$3$ |
$43.2453203863$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$252399544.533$ |
| 20.8.613...168.1 |
$x^{20} - 26 x^{18} - 52 x^{17} + 114 x^{16} + 1114 x^{15} + 660 x^{14} - 6202 x^{13} - 6816 x^{12} + 2590 x^{11} + 29930 x^{10} + 27898 x^{9} - 54473 x^{8} - 366 x^{7} - 46534 x^{6} + 251128 x^{5} - 161650 x^{4} - 7582 x^{3} - 321116 x^{2} + 142390 x - 9721$ |
$20$ |
[8,6] |
$2^{30}\cdot 89417^{5}$ |
$2$ |
$48.9102651521$ |
|
|
|
? |
$C_2^9.C_2^4:S_5$ (as 20T965) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$2349491049.78$ |
| 20.16.613...168.2 |
$x^{20} - 14 x^{18} - 109 x^{16} + 3154 x^{14} - 21961 x^{12} + 54172 x^{10} + 47600 x^{8} - 485554 x^{6} + 845737 x^{4} - 536502 x^{2} + 89417$ |
$20$ |
[16,2] |
$2^{30}\cdot 89417^{5}$ |
$2$ |
$48.9102651521$ |
|
|
|
? |
$C_2^9.C_2^4:S_5$ (as 20T965) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$12923699826.5$ |
| 20.20.730...296.2 |
$x^{20} - 8 x^{19} - 26 x^{18} + 398 x^{17} - 557 x^{16} - 5658 x^{15} + 21734 x^{14} + 2950 x^{13} - 161406 x^{12} + 328090 x^{11} - 83864 x^{10} - 525816 x^{9} + 641159 x^{8} + 15436 x^{7} - 485786 x^{6} + 263660 x^{5} + 54989 x^{4} - 87604 x^{3} + 22770 x^{2} + 22 x - 473$ |
$20$ |
[20,0] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$119.78689508462926$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$43619173869.6$ |
| 20.0.307...776.2 |
$x^{20} - 6 x^{19} + 28 x^{18} - 90 x^{17} + 358 x^{16} - 964 x^{15} + 2050 x^{14} - 3094 x^{13} + 14361 x^{12} - 55026 x^{11} + 165154 x^{10} - 358718 x^{9} + 778116 x^{8} - 1566690 x^{7} + 2883856 x^{6} - 4076374 x^{5} + 4301402 x^{4} - 2903736 x^{3} + 1314506 x^{2} - 337920 x + 53467$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{4}\cdot 23^{2}\cdot 401^{8}$ |
$4$ |
$53.0151234568$ |
|
✓ |
|
|
$C_2^8.D_{10}$ (as 20T322) |
$[4, 60]$ |
$[4, 60]$ |
$2$ |
$9$ |
$3869785.5269$ |
| 20.4.115...824.1 |
$x^{20} - 16 x^{18} - 2 x^{17} - 59 x^{16} + 698 x^{15} - 2138 x^{14} + 8204 x^{13} - 26789 x^{12} + 63730 x^{11} - 141578 x^{10} + 274176 x^{9} - 445798 x^{8} + 682914 x^{7} - 927368 x^{6} + 1086626 x^{5} - 1196393 x^{4} + 1107462 x^{3} - 828622 x^{2} + 565472 x - 225947$ |
$20$ |
[4,8] |
$2^{30}\cdot 401^{10}$ |
$2$ |
$56.639209034025185$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
$[4]$ |
$[2, 4]$ |
$2$ |
$11$ |
$1231919730.5913754$ |
| 20.12.757...264.1 |
$x^{20} - 76 x^{18} - 100 x^{17} + 2145 x^{16} + 6524 x^{15} - 23244 x^{14} - 147428 x^{13} - 78002 x^{12} + 1230572 x^{11} + 3616332 x^{10} + 798692 x^{9} - 18789922 x^{8} - 51652252 x^{7} - 47295812 x^{6} + 76852932 x^{5} + 287733537 x^{4} + 336715092 x^{3} + 85346352 x^{2} - 190544576 x - 121229551$ |
$20$ |
[12,4] |
$2^{30}\cdot 3^{8}\cdot 401^{10}$ |
$3$ |
$87.89530584951883$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
$[2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$15$ |
$1708854559346.0479$ |
| 20.16.757...264.1 |
$x^{20} - 2 x^{19} - 48 x^{18} - 114 x^{17} + 547 x^{16} + 4978 x^{15} + 12200 x^{14} - 9412 x^{13} - 112239 x^{12} - 239872 x^{11} + 48802 x^{10} + 1191586 x^{9} + 1415295 x^{8} - 1444892 x^{7} - 3231810 x^{6} - 340186 x^{5} + 1686180 x^{4} + 414342 x^{3} - 334384 x^{2} - 62082 x + 23379$ |
$20$ |
[16,2] |
$2^{30}\cdot 3^{8}\cdot 401^{10}$ |
$3$ |
$87.89530584951883$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
$[2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$4092525998755.5376$ |
| 20.8.757...264.4 |
$x^{20} - 2 x^{19} + 2 x^{18} + 156 x^{17} - 525 x^{16} + 2924 x^{15} - 1104 x^{14} - 18960 x^{13} + 29328 x^{12} + 69930 x^{11} - 286588 x^{10} + 187396 x^{9} + 556841 x^{8} - 1222008 x^{7} + 1557528 x^{6} - 1950012 x^{5} - 704947 x^{4} + 2766854 x^{3} - 133362 x^{2} - 346622 x - 16069$ |
$20$ |
[8,6] |
$2^{30}\cdot 3^{8}\cdot 401^{10}$ |
$3$ |
$87.89530584951883$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
$[2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$13$ |
$837755930652.2653$ |
| 20.8.757...264.5 |
$x^{20} - 4 x^{19} + 56 x^{18} - 42 x^{17} + 905 x^{16} + 1216 x^{15} - 2082 x^{14} + 42582 x^{13} - 113373 x^{12} + 547824 x^{11} - 633076 x^{10} - 1904514 x^{9} + 10423417 x^{8} - 14796050 x^{7} - 22693956 x^{6} + 61978488 x^{5} - 57158070 x^{4} - 135705214 x^{3} + 62516666 x^{2} + 43755378 x - 4525393$ |
$20$ |
[8,6] |
$2^{30}\cdot 3^{8}\cdot 401^{10}$ |
$3$ |
$87.89530584951883$ |
|
|
|
? |
$C_2^5.C_2^8:D_5$ (as 20T746) |
$[2, 2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$13$ |
$302663194693.51843$ |
| 20.20.150...944.1 |
$x^{20} - 4 x^{19} - 182 x^{18} + 876 x^{17} + 12914 x^{16} - 72376 x^{15} - 456694 x^{14} + 2993870 x^{13} + 8687123 x^{12} - 69841932 x^{11} - 86159290 x^{10} + 963595578 x^{9} + 331132958 x^{8} - 7864666092 x^{7} + 978376974 x^{6} + 36167748580 x^{5} - 11784340896 x^{4} - 81825138434 x^{3} + 29385368446 x^{2} + 59380528964 x - 24460069591$ |
$20$ |
[20,0] |
$2^{30}\cdot 3^{4}\cdot 401^{12}$ |
$3$ |
$128.48601747075244$ |
|
|
|
? |
$C_2^8:D_5$ (as 20T240) |
$[4]$ |
$[2, 2, 2, 2, 4]$ |
$2$ |
$19$ |
$144583945819215.8$ |
