| 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 |
| 18.0.111...771.1 |
$x^{18} - 8 x^{17} + 28 x^{16} - 54 x^{15} + 55 x^{14} - 8 x^{13} - 55 x^{12} + 69 x^{11} - 19 x^{10} - 37 x^{9} + 44 x^{8} - 16 x^{7} - 6 x^{6} + 15 x^{5} - 14 x^{4} + 3 x^{3} + 7 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,3^{4}\cdot 11^{5}\cdot 31^{8}$ |
$3$ |
$11.432207825$ |
$167.845280953044$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$8$ |
$80.526625464$ |
| 18.0.300...424.1 |
$x^{18} + 2 x^{16} - x^{12} - 2 x^{10} - 3 x^{8} + 3 x^{6} + 2 x^{4} - 2 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 11^{4}\cdot 23^{8}$ |
$3$ |
$13.7297605758$ |
|
|
|
✓ |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$8$ |
$416.592517002$ |
| 18.2.719...000.1 |
$x^{18} + x^{16} + 2 x^{14} - 2 x^{12} - 4 x^{11} - 6 x^{10} - 4 x^{9} - 6 x^{8} - 4 x^{7} - 2 x^{6} + 2 x^{4} + x^{2} + 1$ |
$18$ |
[2,8] |
$2^{16}\cdot 5^{5}\cdot 37^{8}$ |
$3$ |
$14.4118288828$ |
$106.22054246852501$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$9$ |
$1469.89353922$ |
| 18.2.270...353.1 |
$x^{18} - x^{17} + x^{16} - 3 x^{15} - 8 x^{14} + 5 x^{13} + 8 x^{12} + 18 x^{11} + 25 x^{10} - 34 x^{9} - 49 x^{8} + 6 x^{7} + 16 x^{6} + 10 x^{5} + 7 x^{4} - 7 x^{3} - 6 x^{2} + x + 1$ |
$18$ |
[2,8] |
$3^{9}\cdot 11^{5}\cdot 31^{8}$ |
$3$ |
$15.5118570101$ |
$167.845280953044$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$9$ |
$2751.63626644$ |
| 18.2.310...109.1 |
$x^{18} - 6 x^{17} + 20 x^{16} - 45 x^{15} + 68 x^{14} - 71 x^{13} + 52 x^{12} - 53 x^{11} + 123 x^{10} - 205 x^{9} + 218 x^{8} - 156 x^{7} + 48 x^{6} - 26 x^{5} + 43 x^{4} - 20 x^{3} - x + 1$ |
$18$ |
[2,8] |
$3^{6}\cdot 11^{5}\cdot 31^{9}$ |
$3$ |
$15.6313688455$ |
$167.845280953044$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$9$ |
$2687.87073054$ |
| 18.6.115...000.1 |
$x^{18} - 2 x^{17} - 2 x^{15} + 8 x^{14} - 6 x^{13} + 4 x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 34 x^{8} - 50 x^{7} - 76 x^{6} + 108 x^{5} + 32 x^{4} - 54 x^{3} + 4 x^{2} + 8 x - 2$ |
$18$ |
[6,6] |
$2^{20}\cdot 5^{5}\cdot 37^{8}$ |
$3$ |
$16.8118169052$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$11$ |
$20973.5724461$ |
| 18.2.266...000.1 |
$x^{18} - 4 x^{17} + 7 x^{16} - 2 x^{15} - 16 x^{14} + 44 x^{13} - 72 x^{12} + 94 x^{11} - 104 x^{10} + 108 x^{9} - 104 x^{8} + 94 x^{7} - 72 x^{6} + 44 x^{5} - 16 x^{4} - 2 x^{3} + 7 x^{2} - 4 x + 1$ |
$18$ |
[2,8] |
$2^{16}\cdot 5^{5}\cdot 37^{9}$ |
$3$ |
$17.6133276845$ |
$106.22054246852501$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$9$ |
$29796.8327747$ |
| 18.8.147...000.1 |
$x^{18} + x^{16} - 12 x^{14} + 24 x^{12} - 6 x^{10} - 66 x^{8} + 44 x^{6} + 44 x^{4} - 27 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{26}\cdot 5^{4}\cdot 37^{8}$ |
$3$ |
$19.3698526292$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$12$ |
$99742.4024554$ |
| 18.10.425...000.1 |
$x^{18} - 2 x^{17} - 7 x^{16} + 10 x^{15} + 18 x^{14} - 12 x^{13} - 10 x^{12} + 14 x^{11} - 52 x^{10} - 28 x^{9} + 52 x^{8} + 14 x^{7} + 10 x^{6} - 12 x^{5} - 18 x^{4} + 10 x^{3} + 7 x^{2} - 2 x - 1$ |
$18$ |
[10,4] |
$2^{20}\cdot 5^{5}\cdot 37^{9}$ |
$3$ |
$20.5464582276$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$13$ |
$291134.035196$ |
| 18.8.726...064.1 |
$x^{18} - 15 x^{16} + 88 x^{14} - 252 x^{12} + 334 x^{10} - 86 x^{8} - 208 x^{6} + 136 x^{4} + 5 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{26}\cdot 101^{8}$ |
$2$ |
$21.1656009743$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$12$ |
$215357.582685$ |
| 18.4.736...000.1 |
$x^{18} + x^{16} - 12 x^{14} - 12 x^{12} + 38 x^{10} + 30 x^{8} - 44 x^{6} + 45 x^{2} + 5$ |
$18$ |
[4,7] |
$-\,2^{26}\cdot 5^{5}\cdot 37^{8}$ |
$3$ |
$21.1815620058$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$10$ |
$120885.33855$ |
| 18.6.130...768.1 |
$x^{18} - 6 x^{16} - 8 x^{15} - 14 x^{14} - 14 x^{13} + 87 x^{12} + 218 x^{11} + 354 x^{10} + 302 x^{9} - 24 x^{8} - 246 x^{7} - 323 x^{6} - 260 x^{5} - 42 x^{4} + 96 x^{3} + 90 x^{2} + 32 x + 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 17^{5}\cdot 37^{8}$ |
$3$ |
$21.8675388487$ |
$357.04837085175126$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$11$ |
$278078.668259$ |
| 18.4.942...000.1 |
$x^{18} + 5 x^{16} + 6 x^{14} - 22 x^{12} - 106 x^{10} - 66 x^{8} + 146 x^{6} + 158 x^{4} + 25 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{32}\cdot 5^{4}\cdot 37^{8}$ |
$3$ |
$24.4044850609$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$10$ |
$414162.951181$ |
| 18.10.120...104.1 |
$x^{18} - 5 x^{17} + x^{16} + 28 x^{15} - 28 x^{14} - 48 x^{13} + 30 x^{12} + 112 x^{11} + 53 x^{10} - 337 x^{9} - 599 x^{8} + 2448 x^{7} - 1946 x^{6} - 1518 x^{5} + 3896 x^{4} - 3358 x^{3} + 1777 x^{2} - 595 x + 89$ |
$18$ |
[10,4] |
$2^{16}\cdot 17^{5}\cdot 37^{9}$ |
$3$ |
$24.7442586946$ |
$357.04837085175126$ |
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$13$ |
$1255251.03197$ |
| 18.0.272...000.1 |
$x^{18} - 4 x^{17} + 6 x^{16} + 12 x^{15} - 62 x^{14} + 50 x^{13} + 234 x^{12} - 714 x^{11} + 654 x^{10} + 630 x^{9} - 2146 x^{8} + 1700 x^{7} + 1804 x^{6} - 6128 x^{5} + 8338 x^{4} - 7064 x^{3} + 4052 x^{2} - 1468 x + 274$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 5^{5}\cdot 37^{9}$ |
$3$ |
$25.8869152217$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
$[2, 2]$ |
$2$ |
$8$ |
$60198.0710392$ |
| 18.0.471...000.1 |
$x^{18} + 6 x^{16} - 62 x^{12} - 108 x^{10} + 96 x^{8} + 428 x^{6} + 420 x^{4} + 160 x^{2} + 20$ |
$18$ |
[0,9] |
$-\,2^{32}\cdot 5^{5}\cdot 37^{8}$ |
$3$ |
$26.6870958408$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
$[2]$ |
$2$ |
$8$ |
$207356.920721$ |
| 18.12.266...123.1 |
$x^{18} - 2 x^{17} - 15 x^{16} + 12 x^{15} + 43 x^{14} - 18 x^{13} + 318 x^{12} + 704 x^{11} - 297 x^{10} - 1025 x^{9} - 1978 x^{8} - 5379 x^{7} - 1333 x^{6} + 9458 x^{5} + 7080 x^{4} - 3148 x^{3} - 3851 x^{2} - 642 x - 9$ |
$18$ |
[12,3] |
$-\,3^{9}\cdot 53^{4}\cdot 107^{8}$ |
$3$ |
$33.3949954374$ |
$1070.0301643596565$ |
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$14$ |
$38854135.6506$ |
| 18.6.471...173.1 |
$x^{18} + 22 x^{16} + 67 x^{14} - 210 x^{12} - 1195 x^{10} - 1564 x^{8} - 228 x^{6} + 583 x^{4} + 106 x^{2} - 53$ |
$18$ |
[6,6] |
$3^{8}\cdot 53^{5}\cdot 107^{8}$ |
$3$ |
$39.1712793449$ |
$2073.8404080758137$ |
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$11$ |
$53050622.2612$ |
| 18.12.826...808.1 |
$x^{18} - 9 x^{17} + 21 x^{16} + 24 x^{15} - 159 x^{14} + 99 x^{13} + 468 x^{12} - 135 x^{11} - 2133 x^{10} + 468 x^{9} + 5247 x^{8} - 3717 x^{7} - 8925 x^{6} + 7686 x^{5} + 17712 x^{4} + 9000 x^{3} + 756 x^{2} - 540 x - 108$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 3^{25}\cdot 47^{8}$ |
$3$ |
$40.4119378709$ |
|
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$14$ |
$444070120.072$ |
| 18.6.381...013.1 |
$x^{18} - 9 x^{17} + 8 x^{16} + 91 x^{15} - 23 x^{14} - 541 x^{13} - 884 x^{12} + 265 x^{11} + 2354 x^{10} + 3168 x^{9} + 2578 x^{8} + 2307 x^{7} + 2622 x^{6} + 1593 x^{5} + 321 x^{4} + 54 x^{3} + 126 x^{2} + 81 x + 9$ |
$18$ |
[6,6] |
$3^{12}\cdot 53^{5}\cdot 107^{8}$ |
$3$ |
$50.0028434413$ |
$2073.8404080758137$ |
|
|
|
$C_6^3:S_4$ (as 18T485) |
$[2]$ |
$2$ |
$11$ |
$578806742.984$ |
| 18.0.322...631.1 |
$x^{18} - 6 x^{17} + 44 x^{16} - 206 x^{15} + 853 x^{14} - 2814 x^{13} + 8031 x^{12} - 19591 x^{11} + 41483 x^{10} - 76594 x^{9} + 121349 x^{8} - 164625 x^{7} + 190250 x^{6} - 187745 x^{5} + 173615 x^{4} - 162870 x^{3} + 152400 x^{2} - 128943 x + 61821$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 107^{8}\cdot 157^{5}$ |
$3$ |
$56.2964615556$ |
$5126.195337882163$ |
✓ |
|
? |
$C_6^3:S_4$ (as 18T485) |
$[2, 20]$ |
$2$ |
$8$ |
$13012269.2615$ |
| 18.0.699...712.1 |
$x^{18} + 44 x^{16} + 647 x^{14} + 3767 x^{12} + 10055 x^{10} + 13535 x^{8} + 9568 x^{6} + 3447 x^{4} + 552 x^{2} + 27$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{8}$ |
$4$ |
$66.7899908747$ |
|
✓ |
|
|
$C_6^3:S_4$ (as 18T485) |
$[606]$ |
$2$ |
$8$ |
$3975042.09289$ |
| 18.18.699...712.1 |
$x^{18} - 44 x^{16} + 647 x^{14} - 3767 x^{12} + 10055 x^{10} - 13535 x^{8} + 9568 x^{6} - 3447 x^{4} + 552 x^{2} - 27$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{8}$ |
$4$ |
$66.7899908747$ |
|
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$17$ |
$280370083041$ |
| 18.18.871...037.1 |
$x^{18} - 65 x^{16} - 43 x^{15} + 1612 x^{14} + 1847 x^{13} - 19451 x^{12} - 29194 x^{11} + 121396 x^{10} + 218343 x^{9} - 376478 x^{8} - 806649 x^{7} + 469788 x^{6} + 1370574 x^{5} - 17907 x^{4} - 858897 x^{3} - 203157 x^{2} + 93150 x + 19953$ |
$18$ |
[18,0] |
$3^{12}\cdot 107^{8}\cdot 157^{5}$ |
$3$ |
$67.6085011277$ |
$5126.195337882163$ |
|
|
|
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$17$ |
$243556388943$ |
