| 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 |
| 18.2.160...016.1 |
$x^{18} - 8 x^{16} + 24 x^{14} - 20 x^{12} - 14 x^{10} + 28 x^{8} + 48 x^{6} + 4 x^{4} + 5 x^{2} - 4$ |
$18$ |
[2,8] |
$2^{36}\cdot 13^{12}$ |
$2$ |
$22.1150992547$ |
|
|
|
? |
$C_2^8:\SL(2,8)$ (as 18T802) |
trivial |
$2$ |
$9$ |
$191488.574096$ |
| 18.2.256...256.1 |
$x^{18} + 8 x^{14} + 16 x^{12} + 54 x^{10} - 12 x^{8} + 64 x^{6} - 40 x^{4} + 29 x^{2} - 4$ |
$18$ |
[2,8] |
$2^{40}\cdot 13^{12}$ |
$2$ |
$25.7979054937$ |
|
|
|
? |
$C_2^8:\SL(2,8)$ (as 18T802) |
trivial |
$2$ |
$9$ |
$596706.465633$ |
| 18.14.266...481.1 |
$x^{18} - 9 x^{17} - 5174 x^{16} + 41596 x^{15} + 4869892 x^{14} - 34817888 x^{13} + 15448024979 x^{12} - 92233622060 x^{11} - 37069802271238 x^{10} + 186193651434593 x^{9} + 27543488615884655 x^{8} - 111292129510493812 x^{7} - 7043899323057397236 x^{6} + 21522003448861623419 x^{5} + 148074184270976385603 x^{4} - 332148588001646325015 x^{3} + 74509939668051066534948 x^{2} - 74340259768852339867254 x - 1916536067788781293227657$ |
$18$ |
[14,2] |
$3^{8}\cdot 37^{12}\cdot 2977717^{8}$ |
$3$ |
$13639.6500292$ |
|
|
|
|
$C_2^8:\SL(2,8)$ (as 18T802) |
$[21]$ |
$2$ |
$15$ |
$104543282491000000000000000000000$ |
| 18.10.240...329.1 |
$x^{18} - 9 x^{17} + 3104 x^{16} - 24628 x^{15} - 13605605 x^{14} + 95669511 x^{13} + 8194134628 x^{12} - 50409629333 x^{11} + 4323861179975 x^{10} - 21154934580100 x^{9} - 3869367851828095 x^{8} + 15603842594817993 x^{7} + 450744223413333883 x^{6} - 1406934411431367586 x^{5} + 86436303926292745097 x^{4} - 170509470653298726280 x^{3} - 4575685716288915179964 x^{2} + 4660703355602403057408 x - 311308150973639204626416$ |
$18$ |
[10,4] |
$3^{10}\cdot 37^{12}\cdot 2977717^{8}$ |
$3$ |
$15410.4989399$ |
|
|
|
|
$C_2^8:\SL(2,8)$ (as 18T802) |
$[42]$ |
$2$ |
$13$ |
$71573314169600000000000000000000$ |
| 18.14.240...329.1 |
$x^{18} - 9097 x^{16} + 21918784 x^{14} - 8722330342 x^{12} - 13442398479722 x^{10} + 8439306339453536 x^{8} + 1882836967318101 x^{6} - 314874705862769661 x^{4} + 759018943953897696 x^{2} - 232463222451360000$ |
$18$ |
[14,2] |
$3^{10}\cdot 37^{12}\cdot 2977717^{8}$ |
$3$ |
$15410.4989399$ |
|
|
|
|
$C_2^8:\SL(2,8)$ (as 18T802) |
$[21]$ |
$2$ |
$15$ |
$235897989389000000000000000000000$ |
| 18.6.240...329.1 |
$x^{18} - 9 x^{17} + 9730 x^{16} - 77636 x^{15} + 30549542 x^{14} - 212488878 x^{13} + 29435749890 x^{12} - 173855673712 x^{11} - 9137095413055 x^{10} + 47274099000373 x^{9} - 19233394569589884 x^{8} + 76648029936995248 x^{7} - 277364572766295287 x^{6} + 564026068049490119 x^{5} + 3802107430731006610371 x^{4} - 7605065577706978424229 x^{3} + 143444061378545111720408 x^{2} - 139641447345692192162992 x - 241556296179995152654604808$ |
$18$ |
[6,6] |
$3^{10}\cdot 37^{12}\cdot 2977717^{8}$ |
$3$ |
$15410.4989399$ |
|
|
|
|
$C_2^8:\SL(2,8)$ (as 18T802) |
$[2, 210]$ |
$2$ |
$11$ |
$1636803091270000000000000000000$ |
