| 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 |
Max $p$ |
| 20.0.779...625.1 |
$x^{20} + 35 x^{18} + 560 x^{16} - 119 x^{15} + 5075 x^{14} - 4515 x^{13} + 30625 x^{12} - 58170 x^{11} + 119035 x^{10} - 221725 x^{9} + 502985 x^{8} + 282975 x^{7} + 5120500 x^{6} + 5110798 x^{5} + 24667825 x^{4} + 21049420 x^{3} + 44559375 x^{2} + 11605160 x + 29901760$ |
$20$ |
(0, 10) |
$3^{15}\cdot 5^{21}\cdot 7^{19}$ |
$3$ |
$78.45174058792101$ |
|
✓ |
|
|
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 270]$ |
$[2, 2, 270]$ |
$2$ |
$9$ |
$224767289.30957106$ |
$0$ |
$7$ |
| 20.0.389...125.1 |
$x^{20} + 35 x^{18} - 35 x^{17} + 560 x^{16} - 644 x^{15} + 3500 x^{14} - 7980 x^{13} + 4900 x^{12} - 81165 x^{11} - 60326 x^{10} - 364070 x^{9} + 44415 x^{8} + 216755 x^{7} + 3244640 x^{6} + 6448680 x^{5} + 13887370 x^{4} + 18300310 x^{3} + 23635780 x^{2} + 19930925 x + 9992605$ |
$20$ |
(0, 10) |
$3^{15}\cdot 5^{22}\cdot 7^{19}$ |
$3$ |
$85.02586988569195$ |
|
✓ |
|
|
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 540]$ |
$[2, 2, 540]$ |
$2$ |
$9$ |
$632150489.6787821$ |
$0$ |
$7$ |
| 20.0.212...000.2 |
$x^{20} - 5 x^{19} - 15 x^{18} + 90 x^{17} + 275 x^{16} - 1533 x^{15} + 635 x^{14} + 3760 x^{13} + 2655 x^{12} - 43135 x^{11} + 214505 x^{10} - 540540 x^{9} + 1645640 x^{8} - 2620560 x^{7} + 9319680 x^{6} - 10183012 x^{5} + 37619320 x^{4} - 34850760 x^{3} + 90306000 x^{2} - 51284160 x + 73459824$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{15}\cdot 5^{21}\cdot 7^{15}$ |
$4$ |
$92.55651036041739$ |
|
✓ |
|
|
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 10, 410]$ |
$[2, 2, 10, 410]$ |
$2$ |
$9$ |
$63728758.83290176$ |
$0$ |
$7$ |
| 20.0.106...000.2 |
$x^{20} - 10 x^{19} + 60 x^{18} - 255 x^{17} + 1100 x^{16} - 4272 x^{15} + 12470 x^{14} - 28900 x^{13} + 38820 x^{12} + 88030 x^{11} - 928048 x^{10} + 2547660 x^{9} - 2979955 x^{8} + 3898470 x^{7} + 27800820 x^{6} - 113056091 x^{5} - 5438420 x^{4} + 153976080 x^{3} + 139869420 x^{2} + 45065640 x + 14016234$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{15}\cdot 5^{22}\cdot 7^{15}$ |
$4$ |
$100.3125966103832$ |
|
✓ |
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 10, 820]$ |
$[2, 2, 10, 820]$ |
$2$ |
$9$ |
$179235004.46434572$ |
$0$ |
$7$ |
| 20.20.488...704.1 |
$x^{20} - 10 x^{19} - 116 x^{18} + 1313 x^{17} + 4736 x^{16} - 67464 x^{15} - 71774 x^{14} + 1744748 x^{13} - 126850 x^{12} - 24570618 x^{11} + 14939336 x^{10} + 193331394 x^{9} - 163802315 x^{8} - 826609978 x^{7} + 787082462 x^{6} + 1707884929 x^{5} - 1813914636 x^{4} - 1179787402 x^{3} + 1644305872 x^{2} - 315124556 x - 58612856$ |
$20$ |
(20, 0) |
$2^{16}\cdot 17^{15}\cdot 53^{13}$ |
$3$ |
$192.504108489$ |
$328.90735776316194$ |
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$293289608829000000$ |
$17$ |
$53$ |
| 20.0.781...264.1 |
$x^{20} - 4 x^{19} + 96 x^{18} + 122 x^{17} + 4620 x^{16} + 18596 x^{15} + 184045 x^{14} + 728624 x^{13} + 6000753 x^{12} + 13556428 x^{11} + 139124895 x^{10} + 136683460 x^{9} + 2117576320 x^{8} - 289614572 x^{7} + 18977386826 x^{6} - 37574492902 x^{5} + 70623059201 x^{4} - 324133328144 x^{3} + 72454618799 x^{2} - 66338130030 x + 1082598671174$ |
$20$ |
(0, 10) |
$2^{20}\cdot 17^{15}\cdot 53^{13}$ |
$3$ |
$221.129152751$ |
$328.90735776316194$ |
✓ |
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 2, 6, 6, 5562]$ |
$[2, 2, 2, 6, 6, 5562]$ |
$2$ |
$9$ |
$4097659676.87$ |
$0$ |
$53$ |
| 20.20.258...312.1 |
$x^{20} - 4 x^{19} - 211 x^{18} + 1138 x^{17} + 12703 x^{16} - 81202 x^{15} - 279760 x^{14} + 2366808 x^{13} + 1504150 x^{12} - 31913924 x^{11} + 22954298 x^{10} + 194714572 x^{9} - 295344111 x^{8} - 469380944 x^{7} + 1107126565 x^{6} + 182743098 x^{5} - 1481772709 x^{4} + 491417950 x^{3} + 577682706 x^{2} - 321816380 x + 25224604$ |
$20$ |
(20, 0) |
$2^{16}\cdot 17^{15}\cdot 53^{14}$ |
$3$ |
$234.776052566$ |
$328.90735776316194$ |
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[4]$ |
$[2, 2, 2, 8]$ |
$2$ |
$19$ |
$1146610929550000000$ |
$16$ |
$53$ |
| 20.0.393...944.1 |
$x^{20} - x^{19} + 55 x^{18} - 278 x^{17} + 2263 x^{16} - 11313 x^{15} + 79085 x^{14} - 392560 x^{13} + 1827617 x^{12} - 8550529 x^{11} + 37812683 x^{10} - 141163000 x^{9} + 484077264 x^{8} - 1681413400 x^{7} + 5243487620 x^{6} - 13458733172 x^{5} + 31389769344 x^{4} - 73483265336 x^{3} + 152848977996 x^{2} - 230279722452 x + 197469154012$ |
$20$ |
(0, 10) |
$2^{16}\cdot 7^{15}\cdot 11^{15}\cdot 13^{13}$ |
$4$ |
$239.74812502439644$ |
|
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[2, 4, 8]$ |
$[2, 4, 8]$ |
$2$ |
$9$ |
$152693517470566.22$ |
$0$ |
$13$ |
| 20.4.393...944.1 |
$x^{20} - 6 x^{19} - 169 x^{18} + 986 x^{17} + 11703 x^{16} - 65220 x^{15} - 419598 x^{14} + 2219948 x^{13} + 7818605 x^{12} - 40542306 x^{11} - 60740475 x^{10} + 364634002 x^{9} + 18475857 x^{8} - 1104174196 x^{7} - 466792714 x^{6} + 57248456 x^{5} + 6676113383 x^{4} + 312500410 x^{3} - 9802818353 x^{2} - 6711815042 x + 3619949909$ |
$20$ |
(4, 8) |
$2^{16}\cdot 7^{15}\cdot 11^{15}\cdot 13^{13}$ |
$4$ |
$239.74812502439644$ |
|
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[4]$ |
$[2, 2, 4]$ |
$2$ |
$11$ |
$4987918329401424.0$ |
$2$ |
$13$ |
| 20.0.414...992.1 |
$x^{20} - 4 x^{19} + 177 x^{18} - 4 x^{17} + 8449 x^{16} + 23822 x^{15} + 168540 x^{14} + 596526 x^{13} + 2612317 x^{12} + 7067238 x^{11} + 38130743 x^{10} + 75736410 x^{9} + 321304814 x^{8} + 864149074 x^{7} + 1787066994 x^{6} + 245640690 x^{5} + 6843858589 x^{4} - 4594563420 x^{3} + 14977761454 x^{2} - 24323038390 x + 15554125329$ |
$20$ |
(0, 10) |
$2^{20}\cdot 17^{15}\cdot 53^{14}$ |
$3$ |
$269.686865375$ |
$328.90735776316194$ |
✓ |
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 6, 12, 22248]$ |
$[2, 2, 6, 12, 22248]$ |
$2$ |
$9$ |
$8009866748.83$ |
$0$ |
$53$ |
| 20.4.511...272.1 |
$x^{20} - 3 x^{19} - 109 x^{18} + 874 x^{17} - 759 x^{16} - 15157 x^{15} - 135227 x^{14} + 1527264 x^{13} + 927943 x^{12} - 29902077 x^{11} + 15880149 x^{10} + 910761676 x^{9} - 3607945172 x^{8} - 25051446848 x^{7} + 47447295520 x^{6} + 579288476848 x^{5} + 469017755136 x^{4} - 4937110551040 x^{3} - 15529734627008 x^{2} - 9459350206144 x + 6774058131520$ |
$20$ |
(4, 8) |
$2^{16}\cdot 7^{15}\cdot 11^{15}\cdot 13^{14}$ |
$4$ |
$272.553891374306$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 4]$ |
$[2, 2, 2, 4]$ |
$2$ |
$11$ |
$33260752823462220$ |
$2$ |
$13$ |
| 20.0.511...272.1 |
$x^{20} - 6 x^{19} + 216 x^{18} - 1093 x^{17} + 19018 x^{16} - 81544 x^{15} + 888786 x^{14} - 3200544 x^{13} + 23877802 x^{12} - 70647150 x^{11} + 372810412 x^{10} - 881542622 x^{9} + 3311764471 x^{8} - 6211478090 x^{7} + 16546960658 x^{6} - 25919041653 x^{5} + 47528976126 x^{4} - 62448845622 x^{3} + 68366421642 x^{2} - 54399144116 x + 21376757978$ |
$20$ |
(0, 10) |
$2^{16}\cdot 7^{15}\cdot 11^{15}\cdot 13^{14}$ |
$4$ |
$272.553891374306$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 4, 16]$ |
$[2, 4, 16]$ |
$2$ |
$9$ |
$1018200581271943.9$ |
$0$ |
$13$ |
| 20.4.513...776.1 |
$x^{20} - 8 x^{19} + 170 x^{18} - 264 x^{17} + 9206 x^{16} + 39680 x^{15} + 448672 x^{14} + 3205056 x^{13} + 23901424 x^{12} + 156793344 x^{11} + 882147904 x^{10} + 5143483648 x^{9} + 23314586816 x^{8} + 100368147456 x^{7} + 353271460352 x^{6} + 1122667758080 x^{5} + 2969896724416 x^{4} + 5938321552896 x^{3} + 11551268406912 x^{2} + 8441222075904 x + 284662974336$ |
$20$ |
(4, 8) |
$2^{63}\cdot 3^{15}\cdot 53^{16}$ |
$3$ |
$484.7369468199184$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$24649276698462750000$ |
$3$ |
$53$ |
| 20.4.513...776.6 |
$x^{20} - 8 x^{19} + 170 x^{18} - 264 x^{17} + 5814 x^{16} + 83776 x^{15} - 182240 x^{14} + 7231360 x^{13} + 1466736 x^{12} + 182050176 x^{11} + 1563139392 x^{10} + 437884160 x^{9} + 73912168896 x^{8} + 75536428032 x^{7} + 1209918238208 x^{6} + 6926897485824 x^{5} + 8017404276672 x^{4} + 140593022798336 x^{3} + 224801039355520 x^{2} + 669435566788096 x + 3819758726037376$ |
$20$ |
(4, 8) |
$2^{63}\cdot 3^{15}\cdot 53^{16}$ |
$3$ |
$484.7369468199184$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$17127663543868910000$ |
$3$ |
$53$ |
| 20.4.102...552.5 |
$x^{20} - 4 x^{19} - 32 x^{18} - 152 x^{17} + 662 x^{16} + 12176 x^{15} + 16832 x^{14} + 97552 x^{13} - 629006 x^{12} + 779224 x^{11} + 3791408 x^{10} + 13608128 x^{9} + 71446532 x^{8} - 240943472 x^{7} - 200770880 x^{6} - 1354912048 x^{5} - 819494303 x^{4} + 18600090204 x^{3} - 10414044912 x^{2} - 27552270696 x + 17862528270$ |
$20$ |
(4, 8) |
$2^{64}\cdot 3^{15}\cdot 53^{16}$ |
$3$ |
$501.8311583326247$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$42907053192269430000$ |
$3$ |
$53$ |
| 20.4.102...552.10 |
$x^{20} - 8 x^{19} + 170 x^{18} - 264 x^{17} + 5799 x^{16} + 83872 x^{15} - 182168 x^{14} + 7254304 x^{13} + 1244202 x^{12} + 187691472 x^{11} + 1533824844 x^{10} + 742564688 x^{9} + 72767846382 x^{8} + 84464068512 x^{7} + 1164475428104 x^{6} + 7128978743328 x^{5} + 6876524892165 x^{4} + 142262695282424 x^{3} + 214027887688090 x^{2} + 671250282787960 x + 3796415961089083$ |
$20$ |
(4, 8) |
$2^{64}\cdot 3^{15}\cdot 53^{16}$ |
$3$ |
$501.8311583326247$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$29814163706552460000$ |
$3$ |
$53$ |
| 20.20.352...624.2 |
$x^{20} - 656 x^{18} - 16 x^{17} + 186368 x^{16} + 4448 x^{15} - 30148560 x^{14} - 160752 x^{13} + 3069374675 x^{12} - 76649328 x^{11} - 204944754828 x^{10} + 12627463952 x^{9} + 9055694844272 x^{8} - 895470287984 x^{7} - 260153771058852 x^{6} + 33505948247296 x^{5} + 4619658045471117 x^{4} - 637514610703920 x^{3} - 45414639474419396 x^{2} + 4737416779644064 x + 186129196859087782$ |
$20$ |
(20, 0) |
$2^{59}\cdot 31^{15}\cdot 53^{13}$ |
$3$ |
$1340.7230404184918$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
not computed |
not computed |
$2$ |
$19$ |
|
$15$ |
$53$ |
| 20.20.186...072.1 |
$x^{20} - 1276 x^{18} - 16 x^{17} + 658002 x^{16} + 8416 x^{15} - 174997424 x^{14} - 2239984 x^{13} + 25314437011 x^{12} + 628091280 x^{11} - 1921782848456 x^{10} - 102900137840 x^{9} + 68574729140642 x^{8} + 5077647112400 x^{7} - 1097427171073028 x^{6} + 52349328823712 x^{5} + 6801945730533617 x^{4} - 3019425270314576 x^{3} - 10867727001230072 x^{2} + 5179746228111552 x + 2300893286748984$ |
$20$ |
(20, 0) |
$2^{59}\cdot 31^{15}\cdot 53^{14}$ |
$3$ |
$1635.1321822921866$ |
|
|
|
? |
$C_{20}:C_4$ (as 20T18) |
not computed |
not computed |
$2$ |
$19$ |
|
$15$ |
$53$ |
