| 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 |
| 12.2.368947264000000.1 |
$x^{12} + 5 x^{10} + 3 x^{8} - 16 x^{6} - 24 x^{4} - 9 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 5^{6}\cdot 7^{8}$ |
$3$ |
$16.364912636128995$ |
$32.02849260844362$ |
|
|
✓ |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$2$ |
$6$ |
$167.51743110979632$ |
| 12.10.564668382613504.1 |
$x^{12} - 4 x^{10} - 2 x^{8} + 22 x^{6} - 24 x^{4} + 9 x^{2} - 1$ |
$12$ |
[10,1] |
$-\,2^{12}\cdot 13^{10}$ |
$2$ |
$16.9557155647$ |
$33.18477908865881$ |
|
|
✓ |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$2$ |
$10$ |
$1229.06437826$ |
| 14.12.633...744.1 |
$x^{14} - 24 x^{12} + 194 x^{10} - 607 x^{8} + 531 x^{6} + 127 x^{4} - 55 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$50.1304371652$ |
$188.39724552501244$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
trivial |
$2$ |
$12$ |
$126296523.288$ |
| 16.4.101...000.3 |
$x^{16} - 8 x^{14} + 22 x^{12} - 17 x^{10} - 27 x^{8} + 58 x^{6} - 33 x^{4} + 2 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{8}\cdot 251^{4}$ |
$3$ |
$17.8005502824$ |
|
|
|
? |
$C_2^7.(C_2\times S_4)$ (as 16T1665) |
trivial |
trivial |
$2$ |
$9$ |
$4515.97134747$ |
| 16.10.187...944.1 |
$x^{16} - 15 x^{14} + 67 x^{12} - 97 x^{10} + x^{8} + 77 x^{6} - 17 x^{4} - 15 x^{2} - 1$ |
$16$ |
[10,3] |
$-\,2^{12}\cdot 2777^{6}$ |
$2$ |
$32.8937548696$ |
$206.27222054362778$ |
|
|
|
$C_2^8.\GL(2,3)$ (as 16T1761) |
trivial |
trivial |
$2$ |
$12$ |
$4019809.15757$ |
| 16.6.187...944.3 |
$x^{16} - 4 x^{14} - 19 x^{12} + 16 x^{10} + 78 x^{8} + 31 x^{6} - 38 x^{4} - 23 x^{2} - 1$ |
$16$ |
[6,5] |
$-\,2^{12}\cdot 2777^{6}$ |
$2$ |
$32.8937548696$ |
$206.27222054362778$ |
|
|
|
$C_2^8.\GL(2,3)$ (as 16T1761) |
trivial |
trivial |
$2$ |
$10$ |
$1613154.93252$ |
| 16.4.161...000.1 |
$x^{16} + 20 x^{14} + 134 x^{12} + 335 x^{10} + 109 x^{8} - 650 x^{6} - 505 x^{4} + 250 x^{2} + 25$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4}$ |
$4$ |
$37.6267504013$ |
|
|
|
? |
$C_2^7.(C_2\times S_4)$ (as 16T1665) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$863171.587527$ |
| 16.0.125...248.1 |
$x^{16} + 20 x^{14} + 164 x^{12} + 710 x^{10} + 1742 x^{8} + 2420 x^{6} + 1800 x^{4} + 625 x^{2} + 67$ |
$16$ |
[0,8] |
$2^{12}\cdot 67\cdot 2777^{6}$ |
$3$ |
$42.7802311503$ |
$1688.410892187069$ |
✓ |
|
? |
$C_2^8.\GL(2,3)$ (as 16T1761) |
$[44]$ |
$[44]$ |
$2$ |
$7$ |
$37704.042506$ |
| 16.0.582...024.1 |
$x^{16} - 43 x^{14} + 661 x^{12} - 5221 x^{10} + 30965 x^{8} - 123197 x^{6} + 672259 x^{4} - 409091 x^{2} + 97969$ |
$16$ |
[0,8] |
$2^{16}\cdot 13^{12}\cdot 79^{4}\cdot 313^{2}$ |
$4$ |
$83.721562482$ |
|
|
|
? |
$Q_8^2.C_2^3:A_4$ (as 16T1671) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$7$ |
$181375562.908$ |
| 18.12.110...176.3 |
$x^{18} - 6 x^{16} + 4 x^{14} + 43 x^{12} - 114 x^{10} + 96 x^{8} - 6 x^{6} - 22 x^{4} + 4 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$657.7159307568076$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$[2]$ |
$2$ |
$14$ |
$372335.492177$ |
| 18.8.125...184.4 |
$x^{18} - 7 x^{16} + 82 x^{12} - 126 x^{10} - 70 x^{8} + 83 x^{6} + 63 x^{4} + 14 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$21.81945910030794$ |
$104.27721702727186$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$[2]$ |
$2$ |
$12$ |
$179862.80469616404$ |
| 18.2.161...304.2 |
$x^{18} - 9 x^{16} + 27 x^{14} - 21 x^{12} - 18 x^{10} - 9 x^{8} + 39 x^{6} - 27 x^{4} + 36 x^{2} - 25$ |
$18$ |
[2,8] |
$2^{14}\cdot 3^{44}$ |
$2$ |
$25.1437958292$ |
$68.9397038608126$ |
|
|
|
$C_2^2:A_4^2.S_4$ (as 18T593) |
trivial |
trivial |
$2$ |
$9$ |
$1703151.21832$ |
| 18.0.484...912.1 |
$x^{18} - 9 x^{14} + 72 x^{10} + 108 x^{8} - 162 x^{6} + 54 x^{4} + 27 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,2^{14}\cdot 3^{45}$ |
$2$ |
$26.7262223901$ |
|
|
|
|
$C_2^2:A_4^2.S_4$ (as 18T590) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$543136.70788$ |
| 18.6.804...776.5 |
$x^{18} - 28 x^{14} - 54 x^{12} + 49 x^{10} + 189 x^{8} + 132 x^{6} + 7 x^{4} - 14 x^{2} - 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
$104.27721702727186$ |
|
|
? |
$C_2^4:(C_3\times S_4)$ (as 18T269) |
trivial |
$[2]$ |
$2$ |
$11$ |
$698332.566263$ |
| 18.0.351...832.3 |
$x^{18} + 15 x^{16} + 87 x^{14} + 277 x^{12} + 576 x^{10} + 831 x^{8} + 851 x^{6} + 633 x^{4} + 321 x^{2} + 107$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{6}\cdot 107^{9}$ |
$3$ |
$29.8374911188$ |
$225.5543797844839$ |
|
|
? |
$C_2^4.S_4^2$ (as 18T546) |
trivial |
trivial |
$2$ |
$8$ |
$776442.124776$ |
| 18.6.375...024.2 |
$x^{18} - 16 x^{16} + 113 x^{14} - 507 x^{12} + 1654 x^{10} - 4262 x^{8} + 8576 x^{6} - 12626 x^{4} + 15515 x^{2} - 11449$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{6}\cdot 107^{10}$ |
$3$ |
$38.68172614678416$ |
$225.5543797844839$ |
|
|
? |
$C_2^4.S_4^2$ (as 18T545) |
trivial |
$[2]$ |
$2$ |
$11$ |
$19604741.04012131$ |
| 18.18.141...064.2 |
$x^{18} - 20 x^{16} + 153 x^{14} - 573 x^{12} + 1136 x^{10} - 1219 x^{8} + 707 x^{6} - 211 x^{4} + 28 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 257^{6}\cdot 43237^{2}$ |
$3$ |
$41.6328458223$ |
$13048.095961157862$ |
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$587034867.509$ |
| 18.10.101...904.1 |
$x^{18} - 14 x^{16} - 99 x^{14} + 722 x^{12} + 3601 x^{10} - 4105 x^{8} - 26677 x^{6} - 20108 x^{4} + 4304 x^{2} - 64$ |
$18$ |
[10,4] |
$2^{14}\cdot 13^{8}\cdot 229^{8}$ |
$3$ |
$59.9840997604$ |
$327.49105830340295$ |
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T588) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$7900091512.89$ |
| 18.10.101...904.2 |
$x^{18} - 17 x^{16} - 193 x^{14} + 960 x^{12} + 1559 x^{10} - 5383 x^{8} - 4006 x^{6} + 1129 x^{4} + 591 x^{2} - 49$ |
$18$ |
[10,4] |
$2^{14}\cdot 13^{8}\cdot 229^{8}$ |
$3$ |
$59.9840997604$ |
$327.49105830340295$ |
|
|
|
$C_2^2:A_4^2.S_4$ (as 18T588) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$10025070758.2$ |
| 18.16.174...000.1 |
$x^{18} - 26 x^{16} + 163 x^{14} + 565 x^{12} - 8221 x^{10} + 27766 x^{8} - 38974 x^{6} + 21878 x^{4} - 4485 x^{2} + 245$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6}$ |
$4$ |
$61.8328482965$ |
$4929.353384853861$ |
|
|
? |
$A_4^3.(C_2^2\times S_4)$ (as 18T835) |
trivial |
$[2]$ |
$2$ |
$16$ |
$26124025175.4$ |
| 18.18.404...616.1 |
$x^{18} - 30 x^{16} + 298 x^{14} - 1453 x^{12} + 3945 x^{10} - 6162 x^{8} + 5379 x^{6} - 2364 x^{4} + 397 x^{2} - 4$ |
$18$ |
[18,0] |
$2^{16}\cdot 13^{8}\cdot 229^{8}$ |
$3$ |
$64.7864111249$ |
|
|
|
|
$C_2^2:A_4^2.S_4$ (as 18T588) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$72756672849.4$ |
| 18.14.228...976.1 |
$x^{18} - 14 x^{16} + 60 x^{14} - 52 x^{12} - 206 x^{10} + 434 x^{8} - 245 x^{6} + 25 x^{4} + 10 x^{2} - 1$ |
$18$ |
[14,2] |
$2^{20}\cdot 3^{12}\cdot 503^{8}$ |
$3$ |
$71.3272518776$ |
$318.5766854539171$ |
|
|
? |
$A_4^3.S_4$ (as 18T719) |
trivial |
$[2]$ |
$2$ |
$15$ |
$112925066556$ |
| 18.18.610...168.2 |
$x^{18} - 71 x^{16} + 2030 x^{14} - 29960 x^{12} + 243661 x^{10} - 1085986 x^{8} + 2511168 x^{6} - 2558163 x^{4} + 635860 x^{2} - 43237$ |
$18$ |
[18,0] |
$2^{18}\cdot 257^{6}\cdot 43237^{3}$ |
$3$ |
$75.3327165902$ |
$13048.095961157862$ |
|
|
? |
$S_4^3.S_4$ (as 18T885) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$17$ |
$77283035472.6$ |
| 18.18.409...064.1 |
$x^{18} - 54 x^{16} + 1203 x^{14} - 14349 x^{12} + 99573 x^{10} - 409398 x^{8} + 972425 x^{6} - 1238373 x^{4} + 722274 x^{2} - 142129$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{18}\cdot 7^{14}\cdot 29^{6}$ |
$4$ |
$83.7366775519$ |
|
|
|
? |
$A_4^3:(C_2\times A_4)$ (as 18T701) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$458673138470$ |
| 18.18.200...136.2 |
$x^{18} - 105 x^{16} + 4536 x^{14} - 105014 x^{12} + 1420839 x^{10} - 11417007 x^{8} + 52263162 x^{6} - 119427945 x^{4} + 92681883 x^{2} - 6964321$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{18}\cdot 7^{16}\cdot 29^{6}$ |
$4$ |
$103.94784914334778$ |
$1772.7986604582713$ |
|
|
? |
$A_4^3:(C_2\times A_4)$ (as 18T701) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$2820691242954.3164$ |
| 18.18.239...952.2 |
$x^{18} - 103 x^{16} + 4170 x^{14} - 88068 x^{12} + 1065425 x^{10} - 7547378 x^{8} + 30446048 x^{6} - 63809759 x^{4} + 56537944 x^{2} - 16974593$ |
$18$ |
[18,0] |
$2^{18}\cdot 257^{9}\cdot 43237^{2}$ |
$3$ |
$104.976386345$ |
$13048.095961157862$ |
|
|
? |
$S_4^3.S_4$ (as 18T884) |
$[2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$1174071788510$ |
| 18.14.344...784.1 |
$x^{18} - 158 x^{14} + 413 x^{12} + 5716 x^{10} - 34136 x^{8} + 70159 x^{6} - 62388 x^{4} + 21750 x^{2} - 1509$ |
$18$ |
[14,2] |
$2^{20}\cdot 3^{13}\cdot 503^{9}$ |
$3$ |
$107.11476475629891$ |
$318.5766854539171$ |
|
|
? |
$A_4^3.S_4$ (as 18T717) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$15$ |
$2210665239370.801$ |
| 18.18.774...096.2 |
$x^{18} - 114 x^{16} + 3807 x^{14} - 53640 x^{12} + 355131 x^{10} - 1210293 x^{8} + 2188746 x^{6} - 2060856 x^{4} + 931770 x^{2} - 158949$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{21}\cdot 7^{15}\cdot 29^{6}$ |
$4$ |
$112.04328295$ |
|
|
|
? |
$A_4^3:(C_2\times A_4)$ (as 18T710) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$6849681897570$ |
| 18.18.103...624.1 |
$x^{18} - 431 x^{16} + 74548 x^{14} - 6618234 x^{12} + 320089753 x^{10} - 8252893775 x^{8} + 102979471316 x^{6} - 495920101143 x^{4} + 1006835962877 x^{2} - 733930477541$ |
$18$ |
[18,0] |
$2^{18}\cdot 257^{9}\cdot 43237^{3}$ |
$3$ |
$189.949935081$ |
$13048.095961157862$ |
|
|
? |
$S_4^3.S_4$ (as 18T880) |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$147516465652000$ |
| 18.6.148...000.1 |
$x^{18} - 45 x^{16} - 120 x^{15} + 540 x^{14} + 3528 x^{13} - 766415 x^{12} - 14040 x^{11} + 23066160 x^{10} + 61515480 x^{9} - 104596947 x^{8} - 889672680 x^{7} + 71245892080 x^{6} - 3334779720 x^{5} - 1105895341185 x^{4} - 2942601049224 x^{3} - 3308995080765 x^{2} - 1764560251800 x - 987580732187625$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{29}\cdot 5^{18}\cdot 41^{4}\cdot 107^{7}\cdot 263^{4}$ |
$6$ |
$2844.88368043$ |
|
|
|
? |
$A_6^3.S_4$ (as 18T975) |
trivial |
$[2]$ |
$2$ |
$11$ |
$4819762159170000000000000$ |
| 20.2.124...000.1 |
$x^{20} + 8 x^{18} + 16 x^{16} - 21 x^{14} - 82 x^{12} - 32 x^{10} + 64 x^{8} + 34 x^{6} - 29 x^{4} - 25 x^{2} - 5$ |
$20$ |
[2,9] |
$-\,2^{12}\cdot 5^{11}\cdot 53^{8}$ |
$3$ |
$17.9788474569$ |
$184.67051214539345$ |
|
|
|
$C_2^8.(D_4\times A_5)$ (as 20T798) |
trivial |
trivial |
$2$ |
$10$ |
$42605.2154849$ |
| 20.6.626...696.1 |
$x^{20} + 3 x^{18} - 4 x^{16} - 28 x^{14} - 67 x^{12} - 83 x^{10} - 40 x^{8} + 17 x^{6} + 21 x^{4} + 2 x^{2} - 1$ |
$20$ |
[6,7] |
$-\,2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4}$ |
$4$ |
$21.8691164919$ |
|
|
|
? |
$C_2^{10}.C_2^4:S_5$ (as 20T992) |
trivial |
$[2]$ |
$2$ |
$12$ |
$336274.035854$ |
| 20.10.599...000.1 |
$x^{20} - 4 x^{18} + 11 x^{14} - x^{12} - 4 x^{10} - 9 x^{8} - 9 x^{6} + 10 x^{4} + 7 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{12}\cdot 5^{10}\cdot 29^{2}\cdot 13345751^{2}$ |
$4$ |
$24.4837029145$ |
$172190.15379250972$ |
|
|
? |
$C_2^8.S_5^2:D_4$ (as 20T1045) |
trivial |
trivial |
$2$ |
$14$ |
$2835601.07584$ |
| 21.1.193...664.1 |
$x^{21} - 7 x^{15} - 6 x^{14} + 343 x^{3} + 882 x^{2} + 756 x + 216$ |
$21$ |
[1,10] |
$2^{18}\cdot 3^{18}\cdot 7^{21}\cdot 23^{7}$ |
$4$ |
$92.4685621837$ |
|
|
|
? |
$A_7^3.D_6$ (as 21T157) |
trivial |
trivial |
$2$ |
$10$ |
$1981799132730$ |
| 21.9.183...776.1 |
$x^{21} - 63 x^{15} - 54 x^{14} + 1176 x^{9} + 2016 x^{8} + 864 x^{7} - 6517 x^{3} - 16758 x^{2} - 14364 x - 4104$ |
$21$ |
[9,6] |
$2^{18}\cdot 3^{47}\cdot 7^{21}\cdot 19^{6}$ |
$4$ |
$343.81492895$ |
|
|
|
? |
$A_7^3.C_6$ (as 21T154) |
trivial |
trivial |
$2$ |
$14$ |
$28289058281700000000$ |
| 22.6.261...704.1 |
$x^{22} - 6 x^{20} + 16 x^{18} - 18 x^{16} + 4 x^{14} - 6 x^{12} + 25 x^{10} - 3 x^{8} - 19 x^{6} + 4 x^{4} + 4 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$17.6294938054$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
trivial |
$2$ |
$13$ |
$107375.053215$ |
| 22.6.984...504.1 |
$x^{22} - 1256355480 x^{20} + 346321257364221748 x^{18} - 281369885833667927777292253 x^{16} + 211852233873305124874717191486598021 x^{14} - 51988958787642502292357344580089958853671609 x^{12} + 16164751063634090233408096678662142988343936090500554 x^{10} - 12944956884362741410715058367642423772239748398213938868430054 x^{8} + 2876793194724455010428571062539352506917449465867424287833700972460630 x^{6} - 30897186782318789777365615471712373496217555545254574233072653398519233478514 x^{4} + 15685554292006069651346777755707519381113345792414561710283876785994521259120839545704 x^{2} - 3765085538799951525236302125814989854461975604609828445625128934755165972532492439340389009701$ |
$22$ |
[6,8] |
$2^{22}\cdot 971^{11}\cdot 25709231^{11}$ |
$3$ |
$315997.8689864854$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T50) |
not computed |
not computed |
$2$ |
$13$ |
|
