| 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 |
| 20.4.760...072.1 |
$x^{20} - 6 x^{19} + 9 x^{18} - 12 x^{17} + 41 x^{16} - 26 x^{15} - 48 x^{14} + 84 x^{13} + 573 x^{12} - 2970 x^{11} - 210 x^{10} + 6948 x^{9} + 6410 x^{8} - 13776 x^{7} - 12312 x^{6} - 3128 x^{5} - 24311 x^{4} - 40006 x^{3} - 24063 x^{2} - 5134 x - 23$ |
$20$ |
(4, 8) |
$2^{20}\cdot 3^{15}\cdot 11^{17}$ |
$3$ |
$34.9989261272$ |
|
|
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
trivial |
$[2]$ |
$2$ |
$11$ |
$25071652.0074$ |
$3$ |
| 20.8.760...072.1 |
$x^{20} - 4 x^{19} - 2 x^{18} + 36 x^{17} - 109 x^{16} + 214 x^{15} - 237 x^{14} + 154 x^{13} + 626 x^{12} - 4576 x^{11} + 12363 x^{10} - 19092 x^{9} + 12308 x^{8} + 16680 x^{7} - 40479 x^{6} + 27996 x^{5} - 1165 x^{4} - 6902 x^{3} + 2120 x^{2} + 620 x - 23$ |
$20$ |
(8, 6) |
$2^{20}\cdot 3^{15}\cdot 11^{17}$ |
$3$ |
$34.9989261272$ |
$75.5683560168568$ |
|
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
trivial |
$[2]$ |
$2$ |
$13$ |
$108742418.631$ |
$7$ |
| 20.0.760...072.1 |
$x^{20} - 2 x^{19} + 11 x^{18} - 14 x^{17} + 115 x^{16} - 324 x^{15} + 1262 x^{14} - 2476 x^{13} + 5321 x^{12} - 7326 x^{11} + 13023 x^{10} - 18742 x^{9} + 32370 x^{8} - 41502 x^{7} + 49419 x^{6} - 42674 x^{5} + 36481 x^{4} - 25324 x^{3} + 20073 x^{2} - 10650 x + 4597$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{15}\cdot 11^{17}$ |
$3$ |
$34.9989261272$ |
$75.5683560168568$ |
|
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$7541288.46705$ |
$0$ |
| 20.4.760...072.2 |
$x^{20} - 2 x^{19} - 13 x^{18} - 14 x^{17} + 70 x^{16} + 150 x^{15} - 97 x^{14} - 244 x^{13} + 83 x^{12} - 132 x^{11} - 1992 x^{10} - 448 x^{9} + 2940 x^{8} + 978 x^{7} - 3555 x^{6} - 512 x^{5} + 11221 x^{4} - 1564 x^{3} - 6942 x^{2} - 3162 x - 617$ |
$20$ |
(4, 8) |
$2^{20}\cdot 3^{15}\cdot 11^{17}$ |
$3$ |
$34.9989261272$ |
|
|
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
trivial |
$[2]$ |
$2$ |
$11$ |
$32746856.351$ |
$3$ |
| 20.4.760...072.3 |
$x^{20} - 2 x^{19} + 2 x^{18} + 40 x^{17} - 140 x^{16} + 258 x^{15} - 382 x^{14} - 94 x^{13} + 830 x^{12} - 1572 x^{11} + 1044 x^{10} + 2996 x^{9} - 8643 x^{8} + 14400 x^{7} - 16161 x^{6} + 11632 x^{5} - 6203 x^{4} + 398 x^{3} + 282 x^{2} - 6 x + 1$ |
$20$ |
(4, 8) |
$2^{20}\cdot 3^{15}\cdot 11^{17}$ |
$3$ |
$34.9989261272$ |
|
|
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
trivial |
$[2]$ |
$2$ |
$11$ |
$35301761.581$ |
$3$ |
| 20.0.112...000.1 |
$x^{20} - 15 x^{17} - 25 x^{16} - 19 x^{15} + 135 x^{14} + 360 x^{13} + 195 x^{12} - 345 x^{11} - 1749 x^{10} - 795 x^{9} + 305 x^{8} + 2655 x^{7} + 3465 x^{6} - 574 x^{5} + 3760 x^{4} - 2315 x^{3} + 6165 x^{2} - 920 x + 2116$ |
$20$ |
(0, 10) |
$2^{19}\cdot 3^{15}\cdot 5^{26}$ |
$3$ |
$35.6845679206$ |
|
|
|
|
$D_5^2\wr C_2$ (as 20T486) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$82936900.7397$ |
$0$ |
| 20.8.706...408.1 |
$x^{20} - 8 x^{19} + 18 x^{18} - 32 x^{17} + 114 x^{16} - 68 x^{15} + 60 x^{14} - 580 x^{13} - 257 x^{12} + 306 x^{11} + 3570 x^{10} - 4440 x^{9} - 13642 x^{8} - 12022 x^{7} + 7998 x^{6} + 27772 x^{5} - 14092 x^{4} - 2680 x^{3} + 1380 x^{2} + 278 x + 13$ |
$20$ |
(8, 6) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
|
|
|
? |
$C_2^9.(C_5\times D_{10})$ (as 20T647) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$637726535.732$ |
$6$ |
| 20.20.706...408.1 |
$x^{20} - 8 x^{19} - 12 x^{18} + 226 x^{17} - 123 x^{16} - 2666 x^{15} + 3138 x^{14} + 17018 x^{13} - 24119 x^{12} - 63492 x^{11} + 92520 x^{10} + 138594 x^{9} - 188890 x^{8} - 165550 x^{7} + 196554 x^{6} + 91516 x^{5} - 90361 x^{4} - 14680 x^{3} + 11874 x^{2} - 1144 x + 1$ |
$20$ |
(20, 0) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
$298.8948611725355$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
trivial |
$[2, 2]$ |
$2$ |
$19$ |
$7244239011.09$ |
$18$ |
| 20.12.706...408.1 |
$x^{20} - 8 x^{19} + 18 x^{18} + 64 x^{17} - 456 x^{16} + 742 x^{15} + 1512 x^{14} - 8476 x^{13} + 11518 x^{12} + 12156 x^{11} - 66624 x^{10} + 87666 x^{9} + 23639 x^{8} - 200536 x^{7} + 233064 x^{6} - 106766 x^{5} - 10204 x^{4} + 37256 x^{3} - 18846 x^{2} + 4208 x - 359$ |
$20$ |
(12, 4) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
|
|
|
? |
$C_2^9.(C_5\times D_{10})$ (as 20T647) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$1594259308.02$ |
$10$ |
| 20.0.706...408.1 |
$x^{20} - 8 x^{19} + 48 x^{18} - 194 x^{17} + 657 x^{16} - 1808 x^{15} + 4398 x^{14} - 9430 x^{13} + 18493 x^{12} - 33000 x^{11} + 56352 x^{10} - 91110 x^{9} + 153485 x^{8} - 242326 x^{7} + 407778 x^{6} - 515444 x^{5} + 857558 x^{4} - 668326 x^{3} + 1079706 x^{2} - 137098 x + 8641$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
$298.8948611725355$ |
✓ |
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2, 82]$ |
$[2, 82]$ |
$2$ |
$9$ |
$528205.092142$ |
$0$ |
| 20.12.706...408.2 |
$x^{20} - 8 x^{19} + 18 x^{18} + 88 x^{17} - 828 x^{16} + 2794 x^{15} - 4056 x^{14} - 2026 x^{13} + 19048 x^{12} - 33756 x^{11} + 23208 x^{10} + 16374 x^{9} - 53929 x^{8} + 57422 x^{7} - 36024 x^{6} + 11338 x^{5} + 3974 x^{4} - 3442 x^{3} - 264 x^{2} + 128 x + 13$ |
$20$ |
(12, 4) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
|
|
|
? |
$C_2^9.(C_5\times D_{10})$ (as 20T647) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$1794901705.67$ |
$10$ |
| 20.8.706...408.2 |
$x^{20} - 8 x^{19} + 18 x^{18} - 56 x^{17} + 324 x^{16} - 356 x^{15} - 1572 x^{14} + 2528 x^{13} + 2818 x^{12} - 1914 x^{11} - 7776 x^{10} + 2496 x^{9} + 4883 x^{8} - 4924 x^{7} - 4056 x^{6} + 5314 x^{5} + 2774 x^{4} - 2944 x^{3} + 612 x^{2} + 962 x - 347$ |
$20$ |
(8, 6) |
$2^{30}\cdot 3^{15}\cdot 71^{9}$ |
$3$ |
$43.8987537813$ |
|
|
|
? |
$C_2^9.(C_5\times D_{10})$ (as 20T647) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$667852533.879$ |
$6$ |
| 20.0.717...000.1 |
$x^{20} + 10 x^{18} - 20 x^{17} + 80 x^{16} - 220 x^{15} + 415 x^{14} - 810 x^{13} + 1045 x^{12} - 1270 x^{11} + 953 x^{10} - 720 x^{9} + 300 x^{8} - 760 x^{7} + 2830 x^{6} - 800 x^{5} + 7615 x^{4} + 870 x^{3} + 7700 x^{2} + 1930 x + 691$ |
$20$ |
(0, 10) |
$2^{25}\cdot 3^{15}\cdot 5^{26}$ |
$3$ |
$43.9328564381$ |
|
|
|
|
$D_5^2\wr C_2$ (as 20T486) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$164413164.019$ |
$0$ |
| 20.10.509...288.1 |
$x^{20} - 4 x^{19} - 22 x^{18} + 67 x^{17} + 149 x^{16} - 36 x^{15} - 486 x^{14} - 1944 x^{13} + 2162 x^{12} - 1062 x^{11} + 2118 x^{10} + 14474 x^{9} - 11665 x^{8} - 4742 x^{7} + 1212 x^{6} - 5189 x^{5} + 7070 x^{4} - 2100 x^{3} + 1936 x^{2} - 1069 x - 5$ |
$20$ |
(10, 5) |
$-\,2^{16}\cdot 3^{15}\cdot 7^{10}\cdot 61^{8}$ |
$4$ |
$54.3683172739$ |
$281.4996282050667$ |
|
|
? |
$D_5^2:C_{10}$ (as 20T185) |
trivial |
$[2]$ |
$2$ |
$14$ |
$26040856698.6$ |
$9$ |
