Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
18.0.597...347.1 |
$x^{18} + 18 x^{16} - 13 x^{15} + 135 x^{14} - 195 x^{13} + 620 x^{12} - 1170 x^{11} + 2175 x^{10} - 3813 x^{9} + 5778 x^{8} - 7992 x^{7} + 10122 x^{6} - 11340 x^{5} + 10998 x^{4} - 9323 x^{3} + 6777 x^{2} - 3426 x + 991$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 23^{8}$ |
$2$ |
$20.9360262251$ |
$31.810664815402767$ |
|
|
? |
$S_3\times D_9$ (as 18T50) |
trivial |
$6$ |
$8$ |
$84776.5081683$ |
18.2.774...592.1 |
$x^{18} - 9 x^{12} - 4 x^{9} + 63 x^{6} - 36 x^{3} + 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 3^{45}$ |
$2$ |
$31.1769145362$ |
$39.797892808498275$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
trivial |
$2$ |
$9$ |
$10987730.3293$ |
18.2.773...792.1 |
$x^{18} - 12 x^{15} - 27 x^{14} - 72 x^{13} - 186 x^{12} - 108 x^{11} + 45 x^{10} + 336 x^{9} + 972 x^{8} + 2052 x^{7} + 3231 x^{6} + 2592 x^{5} + 1782 x^{4} - 252 x^{3} - 810 x^{2} - 216 x + 144$ |
$18$ |
[2,8] |
$2^{34}\cdot 3^{37}$ |
$2$ |
$35.4292092899$ |
$46.89915576842371$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
trivial |
$2$ |
$9$ |
$178921364.387$ |
18.0.378...000.1 |
$x^{18} + 18 x^{16} - 18 x^{15} + 243 x^{14} - 306 x^{13} + 1764 x^{12} - 2916 x^{11} + 11979 x^{10} - 15620 x^{9} + 36450 x^{8} - 41922 x^{7} + 55053 x^{6} - 52002 x^{5} + 46152 x^{4} - 28872 x^{3} + 19764 x^{2} - 7848 x + 2656$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{45}\cdot 5^{9}$ |
$3$ |
$64.5461521445$ |
$88.99079368105217$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
$[2]$ |
$2$ |
$8$ |
$369617552674$ |
18.0.332...875.1 |
$x^{18} + 342 x^{16} + 26163 x^{14} - 56772 x^{13} - 538365 x^{12} - 8094114 x^{11} + 47606400 x^{10} + 687285632 x^{9} + 3278237751 x^{8} + 738088326 x^{7} - 29706477732 x^{6} - 100211012352 x^{5} - 48798420480 x^{4} + 431541779712 x^{3} + 1408298336064 x^{2} + 1686750632064 x + 699473507584$ |
$18$ |
[0,9] |
$-\,3^{45}\cdot 5^{8}\cdot 19^{16}$ |
$3$ |
$436.642836493$ |
$517.9648892176996$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
$[3, 9, 9]$ |
$6$ |
$8$ |
$6840674555320000$ |
18.0.166...375.1 |
$x^{18} - 342 x^{15} + 430920 x^{12} + 3789702 x^{9} + 403028703 x^{6} - 2173425048 x^{3} + 6068404224$ |
$18$ |
[0,9] |
$-\,3^{45}\cdot 5^{9}\cdot 19^{16}$ |
$3$ |
$477.483101841$ |
$477.4831018408995$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
$[3, 9, 18]$ |
$2$ |
$8$ |
$5491590146240000$ |
18.18.101...336.1 |
$x^{18} - 318 x^{16} - 212 x^{15} + 36729 x^{14} + 34980 x^{13} - 2034564 x^{12} - 2583432 x^{11} + 58781664 x^{10} + 103129520 x^{9} - 889486704 x^{8} - 2128457952 x^{7} + 6135260496 x^{6} + 21082331520 x^{5} - 6285328512 x^{4} - 77451096320 x^{3} - 82190351232 x^{2} - 18643490304 x + 6047664640$ |
$18$ |
[18,0] |
$2^{35}\cdot 3^{27}\cdot 53^{16}$ |
$3$ |
$681.879519782$ |
$904.6039520510453$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
trivial |
$2$ |
$17$ |
$5212831613330000000000$ |
18.18.393...304.1 |
$x^{18} - 954 x^{16} + 296217 x^{14} - 286200 x^{13} - 36510216 x^{12} + 84108456 x^{11} + 1885287168 x^{10} - 6956743536 x^{9} - 38883795984 x^{8} + 211649296032 x^{7} + 191094022800 x^{6} - 2602305600192 x^{5} + 2974331897280 x^{4} + 9205791789312 x^{3} - 26694357563520 x^{2} + 24196212919296 x - 7334325786624$ |
$18$ |
[18,0] |
$2^{35}\cdot 3^{45}\cdot 53^{16}$ |
$3$ |
$2045.63855935$ |
$2125.9487459259076$ |
|
|
|
$S_3\times D_9$ (as 18T50) |
$[3]$ |
$2$ |
$17$ |
$35072364445100000000000000$ |