| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.18.12.2 |
$18$ |
$x^{18} + 12 x^{16} - 4 x^{15} + 72 x^{14} - 16 x^{13} + 276 x^{12} + 24 x^{11} + 664 x^{10} + 280 x^{9} + 864 x^{8} + 720 x^{7} + 384 x^{6} + 480 x^{5} - 128 x^{4} - 288 x^{3} + 192 x^{2} + 256 x + 64$ |
$2$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{3} + \left(2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 2 t^{2}$ |
$[0]$ |
$[1]$ |
| 5.18.12.2 |
$18$ |
$x^{18} - 10 x^{15} + 75 x^{12} + 1250 x^{9} + 3125 x^{6} - 12500 x^{3} + 62500$ |
$5$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ |
$x^{3} + 5 t^{2}$ |
$[0]$ |
$[1]$ |
| 11.18.12.2 |
$18$ |
$x^{18} - 66 x^{15} + 2541 x^{12} - 31944 x^{9} - 117128 x^{6} + 4026275 x^{3} + 7086244$ |
$11$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 3 t^{4} + 4 t^{3} + 6 t^{2} + 7 t + 2$ |
$x^{3} + 11 t^{2}$ |
$[0]$ |
$[1]$ |
| 17.18.12.2 |
$18$ |
$x^{18} - 68 x^{15} + 6936 x^{12} - 225998 x^{9} + 9354352 x^{6} - 72412707 x^{3} + 217238121$ |
$17$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ |
$x^{3} + 17 t^{2}$ |
$[0]$ |
$[1]$ |
| 23.18.12.2 |
$18$ |
$x^{18} - 46 x^{15} + 10051 x^{12} + 644851 x^{9} + 20428393 x^{6} - 572834527 x^{3} + 3700897225$ |
$23$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 9 t^{3} + 9 t^{2} + t + 5$ |
$x^{3} + 23 t^{2}$ |
$[0]$ |
$[1]$ |
| 29.18.12.2 |
$18$ |
$x^{18} - 58 x^{15} + 29435 x^{12} + 14316343 x^{9} - 252499317 x^{6} + 2071626049 x^{3} + 2379293284$ |
$29$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 25 t^{3} + 17 t^{2} + 13 t + 2$ |
$x^{3} + 29 t^{2}$ |
$[0]$ |
$[1]$ |
| 41.18.12.2 |
$18$ |
$x^{18} + 6724 x^{12} - 2274393 x^{9} + 110204679 x^{6} - 695137206 x^{3} + 28500625446$ |
$41$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 4 t^{4} + 33 t^{3} + 39 t^{2} + 6 t + 6$ |
$x^{3} + 41 t$ |
$[0]$ |
$[1]$ |
| 47.18.12.2 |
$18$ |
$x^{18} - 188 x^{15} + 48598 x^{12} + 122407317 x^{9} - 13511836689 x^{6} + 364887906137 x^{3} + 269480383225$ |
$47$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 35 t^{3} + 9 t^{2} + 41 t + 5$ |
$x^{3} + 47 t^{2}$ |
$[0]$ |
$[1]$ |
| 53.18.12.2 |
$18$ |
$x^{18} + 2809 x^{12} - 1042139 x^{9} + 31561924 x^{6} - 18818797185 x^{3} + 44328722258$ |
$53$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 7 t^{3} + 4 t^{2} + 45 t + 2$ |
$x^{3} + 53 t$ |
$[0]$ |
$[1]$ |
| 59.18.12.2 |
$18$ |
$x^{18} + 6962 x^{12} - 3696822 x^{9} + 460459718 x^{6} + 84361067282$ |
$59$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 18 t^{3} + 38 t^{2} + 2$ |
$x^{3} + 59 t$ |
$[0]$ |
$[1]$ |
| 71.18.12.2 |
$18$ |
$x^{18} + 5041 x^{12} - 3579110 x^{9} + 330351853 x^{6} - 52322651179 x^{3} + 896701987447$ |
$71$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 10 t^{3} + 13 t^{2} + 29 t + 7$ |
$x^{3} + 71 t$ |
$[0]$ |
$[1]$ |
| 83.18.12.2 |
$18$ |
$x^{18} + 6889 x^{12} - 43455812 x^{9} + 1518666272 x^{6} - 66963690931 x^{3} + 653880746738$ |
$83$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 76 t^{3} + 32 t^{2} + 17 t + 2$ |
$x^{3} + 83 t$ |
$[0]$ |
$[1]$ |
| 89.18.12.2 |
$18$ |
$x^{18} - 178 x^{15} + 1275281 x^{12} + 4623186702 x^{9} + 247580882986 x^{6} - 1423935159495 x^{3} + 4472831618649$ |
$89$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 82 t^{3} + 80 t^{2} + 15 t + 3$ |
$x^{3} + 89 t^{2}$ |
$[0]$ |
$[1]$ |
| 101.18.12.2 |
$18$ |
$x^{18} + 20402 x^{12} - 92727090 x^{9} + 2081208020 x^{6} - 704176733567 x^{3} + 2123040301202$ |
$101$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 90 t^{3} + 20 t^{2} + 67 t + 2$ |
$x^{3} + 101 t$ |
$[0]$ |
$[1]$ |
| 107.18.12.2 |
$18$ |
$x^{18} - 214 x^{15} + 515205 x^{12} + 3253714208 x^{9} - 1012983156528 x^{6} + 86299007989971 x^{3} + 6002921407396$ |
$107$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 52 t^{3} + 22 t^{2} + 79 t + 2$ |
$x^{3} + 107 t^{2}$ |
$[0]$ |
$[1]$ |
| 113.18.12.2 |
$18$ |
$x^{18} - 226 x^{15} + 778909 x^{12} + 4927493255 x^{9} - 1218289881392 x^{6} + 89560774065773 x^{3} + 18737565773481$ |
$113$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 59 t^{3} + 30 t^{2} + 71 t + 3$ |
$x^{3} + 113 t^{2}$ |
$[0]$ |
$[1]$ |
| 131.18.12.2 |
$18$ |
$x^{18} + 34322 x^{12} - 148374006 x^{9} + 1177999684 x^{6} - 848748772322 x^{3} + 10107826288562$ |
$131$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 66 t^{3} + 4 t^{2} + 22 t + 2$ |
$x^{3} + 131 t$ |
$[0]$ |
$[1]$ |
| 137.18.12.2 |
$18$ |
$x^{18} - 274 x^{15} + 3847645 x^{12} + 34060141838 x^{9} + 3422002856754 x^{6} - 29101819847571 x^{3} + 59506706255481$ |
$137$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 116 t^{3} + 102 t^{2} + 3 t + 3$ |
$x^{3} + 137 t^{2}$ |
$[0]$ |
$[1]$ |
| 149.18.12.2 |
$18$ |
$x^{18} - 298 x^{15} + 1487467 x^{12} + 36238581295 x^{9} - 5154092181257 x^{6} + 212461271241857 x^{3} + 43770106346404$ |
$149$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 105 t^{3} + 33 t^{2} + 55 t + 2$ |
$x^{3} + 149 t^{2}$ |
$[0]$ |
$[1]$ |
| 167.18.12.2 |
$18$ |
$x^{18} + 55778 x^{12} - 349309725 x^{9} + 29556260198 x^{6} - 259783971214 x^{3} + 108459807981845$ |
$167$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 2 t^{4} + 75 t^{3} + 38 t^{2} + 2 t + 5$ |
$x^{3} + 167 t$ |
$[0]$ |
$[1]$ |
| 173.18.12.2 |
$18$ |
$x^{18} - 346 x^{15} + 8050901 x^{12} + 2366216669 x^{9} + 10911966089462 x^{6} + 1691120954410909 x^{3} + 107235013328356$ |
$173$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 27 t^{3} + 134 t^{2} + 107 t + 2$ |
$x^{3} + 173 t^{2}$ |
$[0]$ |
$[1]$ |
| 179.18.12.2 |
$18$ |
$x^{18} + 224287 x^{12} - 521915849 x^{9} + 56464412455 x^{6} - 20030493661991 x^{3} + 65788226889842$ |
$179$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + 7 t^{4} + 91 t^{3} + 55 t^{2} + 109 t + 2$ |
$x^{3} + 179 t$ |
$[0]$ |
$[1]$ |
| 191.18.12.2 |
$18$ |
$x^{18} + 36481 x^{12} - 766465810 x^{9} + 13308633610 x^{6} - 2541949019510 x^{3} + 922473299180179$ |
$191$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 110 t^{3} + 10 t^{2} + 10 t + 19$ |
$x^{3} + 191 t$ |
$[0]$ |
$[1]$ |
| 197.18.12.2 |
$18$ |
$x^{18} + 38809 x^{12} - 948026252 x^{9} + 118984939999 x^{6} - 51330705570961 x^{3} + 116903456618258$ |
$197$ |
$3$ |
$6$ |
$12$ |
$C_9\times S_3$ (as 18T16) |
$18$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{18}$ |
$t^{6} + t^{4} + 124 t^{3} + 79 t^{2} + 173 t + 2$ |
$x^{3} + 197 t$ |
$[0]$ |
$[1]$ |
