| 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 |
| 18.0.929...543.1 |
$x^{18} - 4 x^{17} + 10 x^{16} - 21 x^{15} + 37 x^{14} - 58 x^{13} + 80 x^{12} - 97 x^{11} + 107 x^{10} - 106 x^{9} + 92 x^{8} - 71 x^{7} + 52 x^{6} - 39 x^{5} + 30 x^{4} - 20 x^{3} + 11 x^{2} - 4 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 1399^{2}$ |
$2$ |
$11.3183642997$ |
$189.30288116733712$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$14$ |
$8$ |
$509.337225135$ |
$0$ |
| 18.0.108...103.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 6 x^{15} - 2 x^{14} + 21 x^{13} - 47 x^{12} + 61 x^{11} - 35 x^{10} - 37 x^{9} + 119 x^{8} - 155 x^{7} + 130 x^{6} - 79 x^{5} + 43 x^{4} - 27 x^{3} + 16 x^{2} - 6 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 1511^{2}$ |
$2$ |
$11.4156323582$ |
$196.7345330512998$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$14$ |
$8$ |
$524.185517787$ |
$0$ |
| 18.0.128...283.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 3 x^{14} + 18 x^{13} - 47 x^{12} + 90 x^{11} - 87 x^{10} + 43 x^{9} + 63 x^{8} - 186 x^{7} + 274 x^{6} - 270 x^{5} + 198 x^{4} - 106 x^{3} + 39 x^{2} - 9 x + 1$ |
$18$ |
(0, 9) |
$-\,3^{27}\cdot 1297^{2}$ |
$2$ |
$11.522961256$ |
$187.13364208500832$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$18$ |
$8$ |
$784.727413524$ |
$0$ |
| 18.0.750...847.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 7 x^{15} + 4 x^{14} + 7 x^{13} - 19 x^{12} + 33 x^{11} - 28 x^{10} + 17 x^{9} + 15 x^{8} - 33 x^{7} + 53 x^{6} - 44 x^{5} + 36 x^{4} - 17 x^{3} + 9 x^{2} - 2 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 41^{2}\cdot 97^{2}$ |
$3$ |
$12.7115639859$ |
$319.1730121130693$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$14$ |
$8$ |
$1446.90537804$ |
$0$ |
| 18.0.244...663.1 |
$x^{18} + 7 x^{16} - 4 x^{15} + 21 x^{14} - 14 x^{13} + 44 x^{12} - 42 x^{11} + 63 x^{10} - 29 x^{9} - 7 x^{8} - 14 x^{7} + 67 x^{6} - 112 x^{5} + 105 x^{4} - 65 x^{3} + 28 x^{2} - 7 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 22679^{2}$ |
$2$ |
$15.4243395755$ |
$762.1848590619448$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$14$ |
$8$ |
$8111.04910311$ |
$0$ |
| 18.0.132...463.1 |
$x^{18} - 3 x^{17} + 8 x^{16} - 9 x^{15} + 11 x^{14} - 12 x^{13} + 36 x^{12} - 59 x^{11} + 25 x^{10} - 11 x^{9} + 77 x^{8} - 221 x^{7} + 279 x^{6} - 210 x^{5} + 129 x^{4} - 49 x^{3} + 18 x^{2} - 4 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 52879^{2}$ |
$2$ |
$16.9456259147$ |
$1163.8311675162051$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$14$ |
$8$ |
$18327.0613213$ |
$0$ |
| 18.0.135...667.1 |
$x^{18} + 9 x^{16} - 2 x^{15} + 57 x^{14} - 12 x^{13} + 173 x^{12} - 30 x^{11} + 375 x^{10} - 30 x^{9} + 429 x^{8} + 63 x^{7} + 342 x^{6} + 60 x^{5} + 135 x^{4} + 44 x^{3} + 36 x^{2} + 6 x + 1$ |
$18$ |
(0, 9) |
$-\,3^{27}\cdot 73^{2}\cdot 577^{2}$ |
$3$ |
$16.9634845664$ |
$1066.4272127060524$ |
✓ |
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$18$ |
$8$ |
$26510.9946997$ |
$0$ |
| 18.0.904...183.1 |
$x^{18} - 2 x^{17} + 4 x^{16} + 5 x^{15} + 13 x^{14} - 16 x^{13} + 41 x^{12} - 37 x^{11} + 69 x^{10} - 186 x^{9} + 472 x^{8} - 593 x^{7} + 672 x^{6} - 521 x^{5} + 389 x^{4} - 176 x^{3} + 75 x^{2} - 14 x + 1$ |
$18$ |
(0, 9) |
$-\,7^{15}\cdot 138041^{2}$ |
$2$ |
$18.8521278962$ |
$1880.4094066508408$ |
✓ |
|
? |
$S_3^3:C_6$ (as 18T286) |
$[2]$ |
$[2]$ |
$14$ |
$8$ |
$22017.7641526$ |
$0$ |
| 18.10.427...125.1 |
$x^{18} - 2 x^{17} - x^{16} + 10 x^{15} - 22 x^{14} - 16 x^{13} + 27 x^{12} - 47 x^{11} - 41 x^{10} + 83 x^{9} + 135 x^{8} + 65 x^{7} - 52 x^{6} - 66 x^{5} - 20 x^{4} + 7 x^{3} + 10 x^{2} + x - 1$ |
$18$ |
(10, 4) |
$5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$20.5510642367$ |
$516.0140075482474$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$2$ |
$13$ |
$139386.821518$ |
$10$ |
| 18.6.243...192.1 |
$x^{18} + 14 x^{14} - 35 x^{12} + 49 x^{10} - 49 x^{8} - 294 x^{6} + 343 x^{4} + 343 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 1399^{2}$ |
$3$ |
$22.6367285994$ |
$378.60576233467424$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2]$ |
$2$ |
$11$ |
$163825.939612$ |
$5$ |
| 18.6.284...832.1 |
$x^{18} - 98 x^{10} - 147 x^{8} + 98 x^{6} + 343 x^{4} + 343 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 1511^{2}$ |
$3$ |
$22.8312647165$ |
$393.4690661025996$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2]$ |
$2$ |
$11$ |
$111936.796178$ |
$5$ |
| 18.10.336...752.1 |
$x^{18} - 36 x^{12} + 126 x^{10} - 351 x^{8} + 666 x^{6} - 621 x^{4} + 243 x^{2} - 27$ |
$18$ |
(10, 4) |
$2^{18}\cdot 3^{27}\cdot 1297^{2}$ |
$3$ |
$23.0459225119$ |
$374.26728417001664$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2]$ |
$2$ |
$13$ |
$385443.859761$ |
$9$ |
| 18.14.755...125.1 |
$x^{18} - 2 x^{17} - 19 x^{16} + 38 x^{15} + 118 x^{14} - 245 x^{13} - 329 x^{12} + 701 x^{11} + 606 x^{10} - 970 x^{9} - 800 x^{8} + 626 x^{7} + 622 x^{6} - 136 x^{5} - 224 x^{4} - 14 x^{3} + 25 x^{2} + 2 x - 1$ |
$18$ |
(14, 2) |
$5^{9}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$27.396365002$ |
$1881.5913691563694$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
trivial |
$2$ |
$15$ |
$4481033.63861$ |
$14$ |
| 18.14.242...448.1 |
$x^{18} - 15 x^{16} - 8 x^{15} + 15 x^{14} - 60 x^{13} + 225 x^{12} + 624 x^{11} - 540 x^{10} - 1296 x^{9} + 42 x^{8} + 612 x^{7} + 1016 x^{6} + 408 x^{5} - 1152 x^{4} - 232 x^{3} + 360 x^{2} - 8$ |
$18$ |
(14, 2) |
$2^{24}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$33.2210599357$ |
$61.40615581253971$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2]$ |
$2$ |
$15$ |
$38677859.9152$ |
$13$ |
| 18.18.354...048.1 |
$x^{18} - 24 x^{16} + 234 x^{14} - 1209 x^{12} + 3627 x^{10} - 6480 x^{8} + 6741 x^{6} - 3753 x^{4} + 891 x^{2} - 27$ |
$18$ |
(18, 0) |
$2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2}$ |
$4$ |
$33.9269691329$ |
$2132.854425412105$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2]$ |
$2$ |
$17$ |
$68517333.7785$ |
$17$ |
| 18.18.353...368.1 |
$x^{18} - 2 x^{17} - 35 x^{16} + 58 x^{15} + 469 x^{14} - 652 x^{13} - 3016 x^{12} + 3628 x^{11} + 9642 x^{10} - 10322 x^{9} - 14412 x^{8} + 13846 x^{7} + 8833 x^{6} - 6794 x^{5} - 2455 x^{4} + 1120 x^{3} + 231 x^{2} - 42 x - 1$ |
$18$ |
(18, 0) |
$2^{27}\cdot 7^{12}\cdot 138041^{2}$ |
$3$ |
$38.5527797834$ |
$3845.455014749317$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$207892546.294$ |
$16$ |
