| 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 |
| 18.0.154...467.1 |
$x^{18} + 9 x^{16} - 9 x^{15} + 36 x^{14} - 63 x^{13} + 109 x^{12} - 189 x^{11} + 252 x^{10} - 335 x^{9} + 378 x^{8} - 378 x^{7} + 334 x^{6} - 243 x^{5} + 147 x^{4} - 67 x^{3} + 21 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 23^{6}$ |
$2$ |
$10.2459148551$ |
$22.05628309434856$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$78.7017437829$ |
| 18.0.928...243.1 |
$x^{18} - 9 x^{16} - 11 x^{15} + 21 x^{14} + 69 x^{13} + 54 x^{12} - 75 x^{11} - 219 x^{10} - 205 x^{9} - 6 x^{8} + 231 x^{7} + 342 x^{6} + 303 x^{5} + 201 x^{4} + 103 x^{3} + 39 x^{2} + 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 31^{6}$ |
$2$ |
$11.3178003472$ |
$25.606443093809357$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$296.277259881$ |
| 18.0.120...232.2 |
$x^{18} - x^{17} + 2 x^{16} - 11 x^{15} + 13 x^{14} - 21 x^{13} + 45 x^{12} - 52 x^{11} + 71 x^{10} - 81 x^{9} + 80 x^{8} - 74 x^{7} + 30 x^{6} - 39 x^{5} + 52 x^{4} + 24 x^{3} + 35 x^{2} + 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 107^{6}$ |
$3$ |
$13.0529462712$ |
$28.44062787690364$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$2135.41668653$ |
| 18.0.125...827.1 |
$x^{18} + 3 x^{16} - 9 x^{15} + 21 x^{14} - 39 x^{13} + 66 x^{12} - 84 x^{11} + 105 x^{10} - 112 x^{9} + 105 x^{8} - 84 x^{7} + 66 x^{6} - 39 x^{5} + 21 x^{4} - 9 x^{3} + 3 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,3^{25}\cdot 23^{6}$ |
$2$ |
$13.0790948109$ |
$22.05628309434856$ |
|
|
|
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$2115.40608662$ |
| 18.6.228...272.1 |
$x^{18} - 3 x^{17} - 7 x^{16} + 14 x^{15} + 32 x^{14} - 5 x^{13} - 108 x^{12} - 105 x^{11} + 225 x^{10} + 403 x^{9} - 218 x^{8} - 704 x^{7} + 2 x^{6} + 681 x^{5} + 232 x^{4} - 265 x^{3} - 136 x^{2} + 24 x + 9$ |
$18$ |
[6,6] |
$2^{12}\cdot 17^{9}\cdot 19^{6}$ |
$3$ |
$17.4647480494$ |
$28.52909038564125$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$2$ |
$11$ |
$19003.8461826$ |
| 18.6.228...272.2 |
$x^{18} - x^{17} - 8 x^{16} + 10 x^{15} + 13 x^{14} - 5 x^{13} - 24 x^{12} - 29 x^{11} + 62 x^{10} + 13 x^{9} - 18 x^{8} - 39 x^{7} + 18 x^{6} + 11 x^{5} - 13 x^{4} + 14 x^{3} - 8 x^{2} + x + 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 17^{9}\cdot 19^{6}$ |
$3$ |
$17.4647480494$ |
$28.52909038564125$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$2$ |
$11$ |
$17410.6119922$ |
| 18.18.418...981.2 |
$x^{18} - 4 x^{17} - 25 x^{16} + 112 x^{15} + 187 x^{14} - 1130 x^{13} - 175 x^{12} + 4953 x^{11} - 2796 x^{10} - 9129 x^{9} + 9114 x^{8} + 5568 x^{7} - 8480 x^{6} - 117 x^{5} + 2264 x^{4} - 220 x^{3} - 125 x^{2} + 1$ |
$18$ |
[18,0] |
$29^{9}\cdot 257^{6}$ |
$2$ |
$34.2381302738$ |
$86.33075929238663$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$2$ |
$17$ |
$95471510.8169$ |
| 18.18.418...981.3 |
$x^{18} - 9 x^{17} + 11 x^{16} + 116 x^{15} - 342 x^{14} - 350 x^{13} + 2199 x^{12} - 714 x^{11} - 5598 x^{10} + 5077 x^{9} + 5467 x^{8} - 7742 x^{7} - 998 x^{6} + 3767 x^{5} - 406 x^{4} - 497 x^{3} + 2 x^{2} + 16 x + 1$ |
$18$ |
[18,0] |
$29^{9}\cdot 257^{6}$ |
$2$ |
$34.2381302738$ |
$86.33075929238663$ |
|
|
|
$C_3^2:D_6$ (as 18T57) |
trivial |
$2$ |
$17$ |
$157717243.918$ |
