| 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 |
| 20.0.232...912.1 |
$x^{20} - 3 x^{18} + 6 x^{16} - 9 x^{14} + 12 x^{12} - 15 x^{10} + 18 x^{8} - 18 x^{6} + 15 x^{4} - 9 x^{2} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 11^{4}\cdot 19^{4}$ |
$4$ |
$16.5319637708$ |
|
|
|
✓ |
$D_4\times C_2^4:S_5$ (as 20T466) |
trivial |
trivial |
$6$ |
$9$ |
$25463.2665762$ |
$0$ |
| 20.0.301...472.1 |
$x^{20} - 3 x^{18} + 3 x^{14} + 3 x^{10} + 3 x^{8} + 6 x^{6} + 15 x^{4} + 12 x^{2} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{4}$ |
$3$ |
$16.7477380789$ |
$119.9396057655822$ |
|
|
? |
$D_4\times S_5$ (as 20T174) |
trivial |
trivial |
$6$ |
$9$ |
$27746.6029727$ |
$0$ |
| 20.0.301...472.2 |
$x^{20} + 9 x^{16} + 27 x^{12} + 36 x^{8} + 33 x^{4} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{4}$ |
$3$ |
$16.7477380789$ |
|
|
|
? |
$D_4\times C_2^4:S_5$ (as 20T466) |
trivial |
trivial |
$6$ |
$9$ |
$27813.4519941$ |
$0$ |
| 20.0.301...472.3 |
$x^{20} - 6 x^{18} + 15 x^{16} - 18 x^{14} + 12 x^{12} - 6 x^{10} + 6 x^{8} - 9 x^{6} + 12 x^{4} - 9 x^{2} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{4}$ |
$3$ |
$16.7477380789$ |
|
|
|
? |
$D_4\times C_2^4:S_5$ (as 20T466) |
trivial |
trivial |
$6$ |
$9$ |
$34500.6707287$ |
$0$ |
| 20.0.301...472.4 |
$x^{20} + 6 x^{16} + 15 x^{12} + 21 x^{8} + 15 x^{4} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{4}$ |
$3$ |
$16.7477380789$ |
|
|
|
? |
$D_4\times C_2^4:S_5$ (as 20T466) |
trivial |
trivial |
$6$ |
$9$ |
$36831.7755448$ |
$0$ |
| 20.0.318...949.1 |
$x^{20} - 5 x^{19} + 19 x^{18} - 48 x^{17} + 108 x^{16} - 180 x^{15} + 243 x^{14} - 219 x^{13} + 153 x^{12} - 50 x^{11} - 377 x^{10} + 973 x^{9} - 1023 x^{8} + 222 x^{7} + 1050 x^{6} - 1107 x^{5} - 396 x^{4} + 696 x^{3} + 268 x^{2} - 434 x + 109$ |
$20$ |
(0, 10) |
$3^{19}\cdot 223^{7}$ |
$2$ |
$18.8439478664$ |
$42.40505428484215$ |
|
|
? |
$C_4:S_5$ (as 20T120) |
trivial |
trivial |
$6$ |
$9$ |
$119850.009202$ |
$0$ |
| 20.0.761...000.1 |
$x^{20} - 12 x^{18} + 39 x^{16} - 12 x^{14} - 30 x^{12} - 12 x^{10} + 6 x^{8} + 12 x^{6} + 45 x^{4} - 24 x^{2} + 3$ |
$20$ |
(0, 10) |
$2^{28}\cdot 3^{19}\cdot 5^{12}$ |
$3$ |
$19.6829046449$ |
$30.849184495989267$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
trivial |
$6$ |
$9$ |
$251749.70025$ |
$0$ |
| 20.0.201...824.1 |
$x^{20} - 5 x^{19} + 10 x^{18} + 6 x^{17} - 60 x^{16} + 117 x^{15} - 48 x^{14} - 162 x^{13} + 396 x^{12} - 365 x^{11} + 190 x^{10} + 88 x^{9} - 42 x^{8} + 99 x^{7} + 30 x^{6} + 162 x^{5} + 138 x^{4} + 75 x^{3} + 34 x^{2} + 4 x + 1$ |
$20$ |
(0, 10) |
$2^{32}\cdot 3^{19}\cdot 7^{9}$ |
$3$ |
$20.6636626508$ |
$92.5610808200751$ |
|
|
? |
$D_{10}^2.C_2^2$ (as 20T214) |
trivial |
trivial |
$6$ |
$9$ |
$382203.363804$ |
$0$ |
| 20.0.672...256.1 |
$x^{20} - 9 x^{18} + 27 x^{16} - 9 x^{14} - 120 x^{12} + 288 x^{10} - 276 x^{8} - 159 x^{6} + 1065 x^{4} - 1338 x^{2} + 669$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{5}$ |
$3$ |
$21.946809978$ |
|
|
|
? |
$C_2^9.(C_2\times S_5)$ (as 20T796) |
trivial |
trivial |
$6$ |
$9$ |
$355938.753131$ |
$0$ |
| 20.0.672...256.2 |
$x^{20} - 18 x^{18} + 135 x^{16} - 534 x^{14} + 1152 x^{12} - 1245 x^{10} + 621 x^{8} - 828 x^{6} + 1722 x^{4} - 1338 x^{2} + 669$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{5}$ |
$3$ |
$21.946809978$ |
|
|
|
? |
$C_2^9.(C_2\times S_5)$ (as 20T796) |
trivial |
trivial |
$6$ |
$9$ |
$385674.914901$ |
$0$ |
| 20.0.672...256.3 |
$x^{20} - 9 x^{18} + 21 x^{16} + 69 x^{14} - 375 x^{12} + 39 x^{10} + 2691 x^{8} - 6432 x^{6} + 6672 x^{4} - 3345 x^{2} + 669$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{5}$ |
$3$ |
$21.946809977967536$ |
|
|
|
? |
$C_2^9.(C_2\times S_5)$ (as 20T796) |
trivial |
trivial |
$6$ |
$9$ |
$518714.726494947$ |
$0$ |
| 20.0.186...125.1 |
$x^{20} - 6 x^{15} + 12 x^{10} - 9 x^{5} + 3$ |
$20$ |
(0, 10) |
$3^{19}\cdot 5^{20}\cdot 7^{5}$ |
$3$ |
$23.0945607384$ |
|
|
|
✓ |
$D_5^3.C_2^2$ (as 20T292) |
trivial |
trivial |
$6$ |
$9$ |
$1173510.59419$ |
$0$ |
| 20.0.186...125.2 |
$x^{20} - 3 x^{15} + 3 x^{10} - 3 x^{5} + 3$ |
$20$ |
(0, 10) |
$3^{19}\cdot 5^{20}\cdot 7^{5}$ |
$3$ |
$23.0945607384$ |
$54.393539143070406$ |
|
|
✓ |
$D_5^3.C_2^2$ (as 20T292) |
trivial |
trivial |
$6$ |
$9$ |
$957028.046637$ |
$0$ |
| 20.0.322...184.1 |
$x^{20} - 6 x^{19} + 9 x^{18} + 12 x^{17} - 54 x^{16} + 126 x^{15} - 165 x^{14} - 204 x^{13} + 945 x^{12} - 1128 x^{11} + 546 x^{10} - 108 x^{9} - 18 x^{8} + 252 x^{7} - 342 x^{6} + 108 x^{5} + 81 x^{4} - 90 x^{3} + 63 x^{2} - 36 x + 9$ |
$20$ |
(0, 10) |
$2^{36}\cdot 3^{19}\cdot 7^{9}$ |
$3$ |
$23.7363152952$ |
$92.5610808200751$ |
|
|
? |
$D_{10}^2.C_2^2$ (as 20T214) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$1258186.91302$ |
$0$ |
| 20.0.116...000.1 |
$x^{20} - 3 x^{10} + 3$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$28.3965246792$ |
$51.124101742197034$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
trivial |
$6$ |
$9$ |
$11115433.2713$ |
$0$ |
| 20.0.158...821.1 |
$x^{20} - 10 x^{19} + 31 x^{18} - 30 x^{17} + 204 x^{16} - 1356 x^{15} + 1788 x^{14} + 5046 x^{13} - 7719 x^{12} - 22606 x^{11} + 6799 x^{10} + 135932 x^{9} + 30141 x^{8} - 628017 x^{7} + 36765 x^{6} + 1558050 x^{5} - 209409 x^{4} - 2238513 x^{3} + 177178 x^{2} + 1358483 x + 600301$ |
$20$ |
(0, 10) |
$3^{19}\cdot 223^{9}$ |
$2$ |
$32.3595430542$ |
$163.86788154685044$ |
|
|
? |
$(C_2^4\times C_4):S_5$ (as 20T375) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$10213662.9228$ |
$0$ |
| 20.0.334...624.1 |
$x^{20} - 15 x^{18} - 177 x^{16} + 459 x^{14} + 25977 x^{12} + 114117 x^{10} + 186858 x^{8} + 950139 x^{6} + 7627938 x^{4} + 6415041 x^{2} + 33268701$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{7}$ |
$3$ |
$37.6878957328$ |
|
|
|
? |
$(C_2^4\times C_4):S_5$ (as 20T375) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$52533635.8157$ |
$0$ |
| 20.0.334...624.2 |
$x^{20} + 3 x^{18} - 75 x^{16} - 378 x^{14} + 4140 x^{12} + 28782 x^{10} - 76851 x^{8} - 843600 x^{6} + 433512 x^{4} + 15217074 x^{2} + 33268701$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{7}$ |
$3$ |
$37.6878957328$ |
|
|
|
? |
$(C_2^4\times C_4):S_5$ (as 20T375) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$49298099.3039$ |
$0$ |
| 20.0.334...624.3 |
$x^{20} - 21 x^{18} + 120 x^{16} + 1530 x^{14} - 17268 x^{12} - 61185 x^{10} + 1963395 x^{8} - 12188478 x^{6} + 35870442 x^{4} - 52812198 x^{2} + 33268701$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 223^{7}$ |
$3$ |
$37.6878957328$ |
|
|
|
? |
$(C_2^4\times C_4):S_5$ (as 20T375) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$53048248.7817$ |
$0$ |
| 20.0.119...000.1 |
$x^{20} - 96 x^{10} + 3072$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$40.1587503255937$ |
$72.30039804795702$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
trivial |
$6$ |
$9$ |
$418747824.9653931$ |
$0$ |
| 20.0.114...421.1 |
$x^{20} - 3 x + 3$ |
$20$ |
(0, 10) |
$3^{19}\cdot 7\cdot 43\cdot 53\cdot 6200861344763935261871$ |
$5$ |
$56.6278289107$ |
$28243101367273.344$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$2707228857.22$ |
$0$ |
| 20.2.723...504.1 |
$x^{20} - 6 x + 3$ |
$20$ |
(2, 9) |
$-\,2^{20}\cdot 3^{19}\cdot 71\cdot 4217\cdot 41161\cdot 481597793519831$ |
$6$ |
$98.3935897389$ |
|
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$2584613299170$ |
$1$ |
| 20.2.638...000.1 |
$x^{20} - 6$ |
$20$ |
(2, 9) |
$-\,2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.716939211$ |
$154.9792959172223$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
$[2]$ |
$2$ |
$10$ |
$10716506705700$ |
$1$ |
| 20.2.638...000.2 |
$x^{20} - 6144$ |
$20$ |
(2, 9) |
$-\,2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.71693921141936$ |
$154.9792959172223$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$[2]$ |
$2$ |
$10$ |
$7204063400163.169$ |
$1$ |
| 20.2.638...579.1 |
$x^{20} - 3 x - 6$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 47\cdot 503\cdot 506941\cdot 18877081\cdot 243003080027717$ |
$6$ |
$109.716939804$ |
$2.105475202725852e+16$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$11727997931100$ |
$1$ |
| 20.2.711...504.1 |
$x^{20} - 6 x - 6$ |
$20$ |
(2, 9) |
$-\,2^{20}\cdot 3^{19}\cdot 7027\cdot 324673\cdot 69280069\cdot 369250463$ |
$6$ |
$110.306844737$ |
|
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$7575898015650$ |
$1$ |
| 20.2.240...179.1 |
$x^{20} - 9 x + 3$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 469793\cdot 119120711\cdot 369803439913457535719$ |
$4$ |
$147.590508906$ |
$4.0850518618016506e+17$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$94391849803100$ |
$1$ |
| 20.2.241...179.1 |
$x^{20} - 9 x - 6$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 7907\cdot 26\!\cdots\!91$ |
$3$ |
$147.610087744$ |
$4.090474184207663e+17$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$251909078200000$ |
$1$ |
| 20.0.420...000.1 |
$x^{20} + 75 x^{12} - 120 x^{11} + 48 x^{10} + 300000 x^{4} - 960000 x^{3} + 1152000 x^{2} - 614400 x + 122880$ |
$20$ |
(0, 10) |
$2^{47}\cdot 3^{19}\cdot 5^{29}\cdot 13^{10}$ |
$4$ |
$538.472916131$ |
|
|
|
|
$A_5^4.D_4$ (as 20T1058) |
$[8]$ |
$[8]$ |
$2$ |
$9$ |
$16426600675400000000$ |
$0$ |
| 21.1.789...469.1 |
$x^{21} - 6 x - 9$ |
$21$ |
(1, 10) |
$3^{19}\cdot 40993\cdot 16\!\cdots\!99$ |
$3$ |
$153.313675513$ |
$7.399675492503949e+18$ |
|
|
? |
$S_{21}$ (as 21T164) |
trivial |
trivial |
$2$ |
$10$ |
$2786329095580000$ |
$1$ |
| 21.1.789...469.1 |
$x^{21} + 3 x - 9$ |
$21$ |
(1, 10) |
$3^{19}\cdot 39642567892885679\cdot 171296011336035585833$ |
$3$ |
$153.313911936$ |
$7.399795308341263e+18$ |
|
|
? |
$S_{21}$ (as 21T164) |
trivial |
trivial |
$2$ |
$10$ |
$611100974052000$ |
$1$ |
