| 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 |
| 18.0.103...863.1 |
$x^{18} - 4 x^{17} + 11 x^{16} - 22 x^{15} + 36 x^{14} - 53 x^{13} + 80 x^{12} - 116 x^{11} + 154 x^{10} - 173 x^{9} + 154 x^{8} - 116 x^{7} + 80 x^{6} - 53 x^{5} + 36 x^{4} - 22 x^{3} + 11 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,7^{8}\cdot 23^{9}$ |
$2$ |
$11.3884087646$ |
$17.5494136775664$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$2$ |
$8$ |
$77.8161636269$ |
| 18.0.244...591.1 |
$x^{18} - 5 x^{17} + 12 x^{16} - 12 x^{15} - 13 x^{14} + 66 x^{13} - 110 x^{12} + 88 x^{11} + 15 x^{10} - 143 x^{9} + 225 x^{8} - 238 x^{7} + 205 x^{6} - 155 x^{5} + 102 x^{4} - 54 x^{3} + 22 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,31^{13}$ |
$1$ |
$11.9424809353$ |
$17.490467246468523$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$2$ |
$8$ |
$142.219936396$ |
| 18.0.364...328.1 |
$x^{18} - 6 x^{12} - 4 x^{9} + 36 x^{6} + 12 x^{3} + 4$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{33}$ |
$2$ |
$13.8772853557$ |
$17.00827646581399$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$6$ |
$8$ |
$2731.7820309155923$ |
| 18.0.193...723.2 |
$x^{18} + 3$ |
$18$ |
[0,9] |
$-\,3^{53}$ |
$1$ |
$25.4013634055$ |
$28.699246901098466$ |
|
|
|
$C_9:C_6$ (as 18T18) |
trivial |
$6$ |
$8$ |
$1116779.19466$ |
| 18.18.281...457.1 |
$x^{18} - 33 x^{16} - 11 x^{15} + 387 x^{14} + 144 x^{13} - 2216 x^{12} - 623 x^{11} + 6888 x^{10} + 821 x^{9} - 11951 x^{8} + 859 x^{7} + 11003 x^{6} - 2794 x^{5} - 4431 x^{4} + 1723 x^{3} + 391 x^{2} - 150 x - 9$ |
$18$ |
[18,0] |
$7^{8}\cdot 257^{9}$ |
$2$ |
$38.0684934929$ |
$58.66313320823844$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$2$ |
$17$ |
$290535844.764$ |
| 18.18.144...152.1 |
$x^{18} - 9 x^{17} + 3 x^{16} + 180 x^{15} - 362 x^{14} - 1330 x^{13} + 3998 x^{12} + 4144 x^{11} - 19161 x^{10} - 2623 x^{9} + 45321 x^{8} - 13752 x^{7} - 49858 x^{6} + 29002 x^{5} + 18518 x^{4} - 16692 x^{3} + 1755 x^{2} + 865 x - 137$ |
$18$ |
[18,0] |
$2^{16}\cdot 19^{8}\cdot 37^{9}$ |
$3$ |
$41.6886675209$ |
$80.20205218853394$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$2$ |
$17$ |
$698998807.188$ |
| 18.0.175...128.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 414 x^{14} - 882 x^{13} + 1554 x^{12} - 2304 x^{11} + 2907 x^{10} + 107993 x^{9} - 497187 x^{8} - 2002680 x^{7} + 9336642 x^{6} - 7002198 x^{5} - 7000902 x^{4} + 9334932 x^{3} - 2000331 x^{2} - 500103 x + 3087691489$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 7^{12}$ |
$3$ |
$172.122616565$ |
$194.46946178413242$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3]$ |
$6$ |
$8$ |
$157565908237.57254$ |
| 18.0.175...128.2 |
$x^{18} + 114354828$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 7^{12}$ |
$3$ |
$172.122616565$ |
$194.46946178413242$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 6, 6]$ |
$6$ |
$8$ |
$205037314981.65656$ |
| 18.0.769...000.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 108 x^{15} + 234 x^{14} - 462 x^{13} - 4710 x^{12} + 32004 x^{11} - 33261 x^{10} - 132499 x^{9} + 4397733 x^{8} - 16434924 x^{7} - 77689590 x^{6} + 289673118 x^{5} + 666797838 x^{4} - 1835112552 x^{3} - 3082794183 x^{2} + 4051301331 x + 6652087267$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{33}\cdot 5^{16}\cdot 7^{12}$ |
$4$ |
$212.329277786$ |
$260.23497865795395$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$30369487687.174183$ |
| 18.0.769...000.2 |
$x^{18} + 3 x^{16} - 36 x^{14} - 5628 x^{12} - 31914 x^{10} + 1031922 x^{8} + 14934396 x^{6} + 76305348 x^{4} + 153013329 x^{2} + 52743747$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{33}\cdot 5^{16}\cdot 7^{12}$ |
$4$ |
$212.329277786$ |
$260.23497865795395$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 9, 36, 36]$ |
$6$ |
$8$ |
$252123542.90200993$ |
| 18.0.295...968.1 |
$x^{18} + 18766633392$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 13^{12}$ |
$3$ |
$260.056760145$ |
$293.8201799857405$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3]$ |
$6$ |
$8$ |
$34046594837036.125$ |
| 18.0.295...968.2 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 414 x^{14} - 882 x^{13} + 1554 x^{12} - 2304 x^{11} + 2907 x^{10} + 418685 x^{9} - 1895301 x^{8} - 7595136 x^{7} + 35434770 x^{6} - 26575794 x^{5} - 26574498 x^{4} + 35433060 x^{3} - 7592787 x^{2} - 1898217 x + 44484293569$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 13^{12}$ |
$3$ |
$260.056760145$ |
$293.8201799857405$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3]$ |
$6$ |
$8$ |
$13089556510972.09$ |
| 18.0.167...288.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 108 x^{15} + 207 x^{14} - 273 x^{13} - 2436 x^{12} + 15903 x^{11} - 106503 x^{10} + 385808 x^{9} - 162243 x^{8} - 1489695 x^{7} + 36908697 x^{6} - 104067936 x^{5} + 573490734 x^{4} - 975956418 x^{3} + 3278636388 x^{2} - 2807652156 x + 5898348532$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 7^{16}\cdot 19^{12}$ |
$4$ |
$477.64982451$ |
$585.4171086702478$ |
|
|
|
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$3161751653565.267$ |
| 18.0.167...000.1 |
$x^{18} + 903544320000$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{53}\cdot 5^{16}\cdot 7^{12}$ |
$4$ |
$616.948702814$ |
$697.047747583028$ |
|
|
|
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 3, 6, 6]$ |
$6$ |
$8$ |
$301210541098340.0$ |
| 18.0.167...000.2 |
$x^{18} + 658683809280000$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{53}\cdot 5^{16}\cdot 7^{12}$ |
$4$ |
$616.948702814$ |
$697.047747583028$ |
|
|
|
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 3, 6, 6]$ |
$6$ |
$8$ |
$277106388929839.0$ |
| 18.0.181...568.1 |
$x^{18} + 29056171447488$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{53}\cdot 73^{12}$ |
$3$ |
$704.302016194$ |
$795.7422258401564$ |
|
|
|
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 3, 3, 9]$ |
$6$ |
$8$ |
$572293837606309.1$ |
| 18.0.429...000.1 |
$x^{18} + 17862732942187500$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 19^{12}$ |
$4$ |
$1400.38779587$ |
$1582.2014932526486$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 9, 9, 9]$ |
$6$ |
$8$ |
$78819973054704270$ |
| 18.0.429...000.2 |
$x^{18} + 73165754131200$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 19^{12}$ |
$4$ |
$1400.38779587$ |
$1582.2014932526486$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 9, 18, 18]$ |
$6$ |
$8$ |
$18795714135381332$ |
| 18.0.152...000.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 414 x^{14} - 882 x^{13} + 1554 x^{12} - 2304 x^{11} + 2907 x^{10} + 223429361 x^{9} - 1005443343 x^{8} - 4021787304 x^{7} + 18768331554 x^{6} - 14076248382 x^{5} - 14076247086 x^{4} + 18768329844 x^{3} - 4021784955 x^{2} - 1005446259 x + 12480520737495001$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 31^{12}$ |
$4$ |
$1940.82798586$ |
$2192.807554047981$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
not computed |
$6$ |
$8$ |
|
| 18.0.152...000.2 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 414 x^{14} - 882 x^{13} + 1554 x^{12} - 2304 x^{11} + 2907 x^{10} + 386088221 x^{9} - 1737408213 x^{8} - 6949646784 x^{7} + 32431675794 x^{6} - 24323756562 x^{5} - 24323755266 x^{4} + 32431674084 x^{3} - 6949644435 x^{2} - 1737411129 x + 37266634952753761$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 31^{12}$ |
$4$ |
$1940.82798586$ |
$2192.807554047981$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
$[3, 3, 3, 3, 3, 3, 9]$ |
$6$ |
$8$ |
$28127663525441974000$ |
| 18.0.168...528.1 |
$x^{18} + 1233198609603674112$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 7^{16}\cdot 43^{12}$ |
$4$ |
$3255.49081469$ |
$3678.1543251612748$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
not computed |
$6$ |
$8$ |
|
| 18.0.345...008.1 |
$x^{18} + 6257694863834800428$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 7^{16}\cdot 67^{12}$ |
$4$ |
$4375.42965283$ |
$4943.4959021731665$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
not computed |
$6$ |
$8$ |
|
| 18.0.832...728.1 |
$x^{18} + 110960891811846912$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 3^{53}\cdot 11^{16}\cdot 103^{12}$ |
$4$ |
$8709.89894265$ |
$9840.713517927445$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
not computed |
$6$ |
$8$ |
|
