| 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 |
| 18.8.107...168.1 |
$x^{18} - 10 x^{16} + 38 x^{14} - 5 x^{13} - 69 x^{12} + 36 x^{11} + 60 x^{10} - 90 x^{9} - 21 x^{8} + 106 x^{7} - 9 x^{6} - 64 x^{5} + 16 x^{4} + 21 x^{3} - 7 x^{2} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 163$ |
$5$ |
$14.7387736216$ |
$3471.5060116812047$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$3724.18995854$ |
| 18.8.253...723.1 |
$x^{18} - 9 x^{16} - 4 x^{15} + 24 x^{14} + 21 x^{13} - 18 x^{12} - 27 x^{11} + 9 x^{10} + 33 x^{9} + 9 x^{8} - 27 x^{7} - 18 x^{6} + 21 x^{5} + 24 x^{4} - 4 x^{3} - 9 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,3^{3}\cdot 9685993193^{2}$ |
$2$ |
$15.4558104315$ |
$170464.01256276938$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$12$ |
$5901.27218098$ |
| 18.8.290...719.1 |
$x^{18} - 9 x^{17} + 31 x^{16} - 41 x^{15} - 36 x^{14} + 217 x^{13} - 323 x^{12} + 108 x^{11} + 361 x^{10} - 641 x^{9} + 423 x^{8} + 68 x^{7} - 358 x^{6} + 294 x^{5} - 94 x^{4} - 20 x^{3} + 28 x^{2} - 9 x + 1$ |
$18$ |
[8,5] |
$-\,31\cdot 9685993193^{2}$ |
$2$ |
$15.5748904533$ |
$547965.1348242878$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$12$ |
$6377.29560563$ |
| 18.8.307...727.1 |
$x^{18} - 5 x^{17} + 4 x^{16} + 18 x^{15} - 42 x^{14} + 40 x^{13} - 48 x^{12} + 70 x^{11} - 69 x^{10} + 89 x^{9} - 67 x^{8} - 96 x^{7} + 187 x^{6} - 65 x^{5} - 54 x^{4} + 47 x^{3} - 3 x^{2} - 7 x + 1$ |
$18$ |
[8,5] |
$-\,7^{15}\cdot 41^{3}\cdot 97^{2}$ |
$3$ |
$15.6242108461$ |
$319.1730121130693$ |
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$12$ |
$6722.94980486$ |
| 18.8.471...019.1 |
$x^{18} - x^{17} - 8 x^{16} + 5 x^{15} + 28 x^{14} - 18 x^{13} - 64 x^{12} + 44 x^{11} + 86 x^{10} - 56 x^{9} - 56 x^{8} + 38 x^{7} + 23 x^{6} - 16 x^{5} - 17 x^{4} + 6 x^{3} + 8 x^{2} - x - 1$ |
$18$ |
[8,5] |
$-\,19\cdot 37^{2}\cdot 89\cdot 757^{2}\cdot 59617^{2}$ |
$5$ |
$15.998606972$ |
$1680372.883357441$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$12$ |
$8750.45510087$ |
| 18.8.692...544.1 |
$x^{18} - 5 x^{16} + x^{14} + 36 x^{12} - 88 x^{10} + 99 x^{8} - 69 x^{6} + 35 x^{4} - 10 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 37^{6}\cdot 401^{2}$ |
$3$ |
$16.3435162508$ |
|
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$12$ |
$10951.7579597$ |
| 18.8.728...159.1 |
$x^{18} + x^{16} - 5 x^{15} - 13 x^{14} + 11 x^{13} - 2 x^{12} + 41 x^{11} + 6 x^{10} - 68 x^{9} + 53 x^{8} - 63 x^{7} + x^{6} + 50 x^{5} - 28 x^{4} + 24 x^{3} - 5 x^{2} - 4 x + 1$ |
$18$ |
[8,5] |
$-\,7^{15}\cdot 41^{2}\cdot 97^{3}$ |
$3$ |
$16.3898581681$ |
$319.1730121130693$ |
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$12$ |
$11002.0590961$ |
| 18.8.181...227.1 |
$x^{18} - 4 x^{17} - x^{16} + 20 x^{15} - 21 x^{14} - 22 x^{13} + 73 x^{12} - 38 x^{11} - 94 x^{10} + 88 x^{9} + 26 x^{8} - 48 x^{7} + 42 x^{6} - 7 x^{5} - 33 x^{4} + 13 x^{3} + 8 x^{2} - 3 x - 1$ |
$18$ |
[8,5] |
$-\,37^{4}\cdot 67\cdot 229^{6}$ |
$3$ |
$17.2404937578$ |
$1375.3808036986495$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$12$ |
$16324.6540383$ |
| 18.8.181...227.2 |
$x^{18} - 5 x^{17} + 4 x^{16} + 23 x^{15} - 74 x^{14} + 100 x^{13} - 53 x^{12} - 48 x^{11} + 139 x^{10} - 173 x^{9} + 139 x^{8} - 48 x^{7} - 53 x^{6} + 100 x^{5} - 74 x^{4} + 23 x^{3} + 4 x^{2} - 5 x + 1$ |
$18$ |
[8,5] |
$-\,37^{4}\cdot 67\cdot 229^{6}$ |
$3$ |
$17.2404937578$ |
$1375.3808036986495$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$12$ |
$19964.5117589$ |
| 18.8.193...039.1 |
$x^{18} - 5 x^{17} - x^{16} + 38 x^{15} - 29 x^{14} - 110 x^{13} + 108 x^{12} + 172 x^{11} - 126 x^{10} - 215 x^{9} + 30 x^{8} + 215 x^{7} + 49 x^{6} - 105 x^{5} - 81 x^{4} + 44 x^{3} + 23 x^{2} - 8 x - 1$ |
$18$ |
[8,5] |
$-\,2791^{3}\cdot 944497^{2}$ |
$2$ |
$17.3063101268$ |
$373181.55393164273$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$12$ |
$17218.9925183$ |
| 18.8.217...959.1 |
$x^{18} - x^{17} - 7 x^{16} - 4 x^{15} + 13 x^{14} + 36 x^{13} + 35 x^{12} - 5 x^{11} - 60 x^{10} - 87 x^{9} - 60 x^{8} - 5 x^{7} + 35 x^{6} + 36 x^{5} + 13 x^{4} - 4 x^{3} - 7 x^{2} - x + 1$ |
$18$ |
[8,5] |
$-\,7^{12}\cdot 53^{6}\cdot 71$ |
$3$ |
$17.4182693716$ |
$224.473874393898$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$12$ |
$22237.1088021$ |
| 18.8.217...959.2 |
$x^{18} - 3 x^{17} - 3 x^{16} + 15 x^{15} - 8 x^{14} - 15 x^{13} + 17 x^{12} - 3 x^{11} + 11 x^{10} - 23 x^{9} + 11 x^{8} - 3 x^{7} + 17 x^{6} - 15 x^{5} - 8 x^{4} + 15 x^{3} - 3 x^{2} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,7^{12}\cdot 53^{6}\cdot 71$ |
$3$ |
$17.4182693716$ |
$224.473874393898$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$12$ |
$17680.4804353$ |
| 18.8.269...272.1 |
$x^{18} - x^{17} - 5 x^{16} - 7 x^{15} + 22 x^{14} + 38 x^{13} - 23 x^{12} - 74 x^{11} - 83 x^{10} + 128 x^{9} + 108 x^{8} + 8 x^{7} - 143 x^{6} - 83 x^{5} + 114 x^{4} + 24 x^{3} - 16 x^{2} - 6 x - 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 3^{3}\cdot 101^{6}\cdot 479^{2}$ |
$4$ |
$17.6249971134$ |
$604.7498018496447$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$12$ |
$21960.1479175$ |
| 18.8.270...056.1 |
$x^{18} - x^{16} + x^{14} - 8 x^{12} + 4 x^{10} + 3 x^{8} + 11 x^{6} - 9 x^{4} - 2 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}$ |
$4$ |
$17.6298533946$ |
|
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$12$ |
$22854.8709158$ |
| 18.8.285...147.1 |
$x^{18} - 12 x^{16} - 6 x^{15} + 58 x^{14} + 60 x^{13} - 127 x^{12} - 232 x^{11} + 60 x^{10} + 406 x^{9} + 241 x^{8} - 240 x^{7} - 388 x^{6} - 125 x^{5} + 120 x^{4} + 136 x^{3} + 58 x^{2} + 12 x + 1$ |
$18$ |
[8,5] |
$-\,197^{3}\cdot 397\cdot 479^{3}\cdot 85733$ |
$4$ |
$17.6837616472$ |
$1792132.5738803477$ |
|
|
? |
$C_3^6.(C_2^6.S_6)$ (as 18T962) |
trivial |
$2$ |
$12$ |
$23704.9683661$ |
| 18.8.338...647.1 |
$x^{18} - 2 x^{17} - 10 x^{16} + 26 x^{15} - 8 x^{14} - 53 x^{13} + 95 x^{12} - 43 x^{11} - 80 x^{10} + 147 x^{9} - 80 x^{8} - 43 x^{7} + 95 x^{6} - 53 x^{5} - 8 x^{4} + 26 x^{3} - 10 x^{2} - 2 x + 1$ |
$18$ |
[8,5] |
$-\,7^{13}\cdot 769^{4}$ |
$2$ |
$17.8511232641$ |
$424.81442954934494$ |
|
|
? |
$A_4^3:C_6$ (as 18T552) |
trivial |
$2$ |
$12$ |
$31484.8298754$ |
| 18.8.364...147.1 |
$x^{18} - 3 x^{17} - 8 x^{16} + 26 x^{15} + 13 x^{14} - 60 x^{13} - 20 x^{12} + 93 x^{11} + 7 x^{10} - 99 x^{9} + 7 x^{8} + 93 x^{7} - 20 x^{6} - 60 x^{5} + 13 x^{4} + 26 x^{3} - 8 x^{2} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,3^{3}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4}$ |
$4$ |
$17.9248223348$ |
$430.0977718087684$ |
|
|
? |
$A_4^3:C_6$ (as 18T552) |
trivial |
$2$ |
$12$ |
$27674.6767779$ |
| 18.8.426...131.1 |
$x^{18} - 4 x^{17} + 3 x^{16} + x^{15} + 7 x^{14} - 23 x^{13} + 39 x^{12} - 7 x^{11} - 20 x^{10} - 42 x^{9} - 50 x^{8} + 196 x^{7} - 176 x^{6} + 257 x^{5} - 294 x^{4} + 78 x^{3} + 128 x^{2} - 134 x + 41$ |
$18$ |
[8,5] |
$-\,7^{12}\cdot 53^{6}\cdot 139$ |
$3$ |
$18.0806356374$ |
$314.08270911399967$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$12$ |
$31755.5776286$ |
| 18.8.435...831.1 |
$x^{18} - 2 x^{17} - 5 x^{16} + 8 x^{15} + 7 x^{14} - 14 x^{13} - x^{12} - x^{11} + 23 x^{10} + 34 x^{9} - 64 x^{8} - 9 x^{7} + 11 x^{6} - 13 x^{5} + 48 x^{4} - 20 x^{3} - 10 x^{2} + 7 x - 1$ |
$18$ |
[8,5] |
$-\,19^{16}\cdot 151$ |
$2$ |
$18.1018992065$ |
$168.3287665780357$ |
|
|
? |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$12$ |
$29307.0525763$ |
| 18.8.443...464.1 |
$x^{18} - 3 x^{17} + 3 x^{16} - 12 x^{15} + 15 x^{14} - 6 x^{13} + 39 x^{12} + 42 x^{11} - 60 x^{10} - 2 x^{9} - 213 x^{8} - 3 x^{7} + 282 x^{6} - 15 x^{5} - 102 x^{4} - 12 x^{3} + 12 x^{2} + 6 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 3^{27}\cdot 17^{5}$ |
$3$ |
$18.1200717452$ |
|
|
|
? |
$C_6^3:A_4$ (as 18T400) |
trivial |
$2$ |
$12$ |
$29639.4320916$ |
| 18.8.516...871.1 |
$x^{18} - x^{17} - 9 x^{16} + 12 x^{15} + 18 x^{14} - 58 x^{13} + 15 x^{12} + 122 x^{11} - 38 x^{10} - 31 x^{9} + 54 x^{8} - 37 x^{7} - 15 x^{6} + 9 x^{5} + 2 x^{4} + 8 x^{3} + 7 x^{2} + 4 x + 1$ |
$18$ |
[8,5] |
$-\,37^{4}\cdot 191\cdot 229^{6}$ |
$3$ |
$18.2736446529$ |
$2322.2140099608105$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$12$ |
$35300.0991607$ |
| 18.8.539...576.1 |
$x^{18} - 4 x^{16} + 5 x^{14} - 6 x^{12} + 12 x^{10} - x^{8} - 23 x^{6} + 22 x^{4} - 8 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 453771377^{2}$ |
$2$ |
$18.3189587332$ |
|
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$12$ |
$31027.3310386$ |
| 18.8.550...071.1 |
$x^{18} - 2 x^{17} - 4 x^{16} + 21 x^{15} - 42 x^{14} + 47 x^{13} - 17 x^{12} - 45 x^{11} + 110 x^{10} - 137 x^{9} + 110 x^{8} - 45 x^{7} - 17 x^{6} + 47 x^{5} - 42 x^{4} + 21 x^{3} - 4 x^{2} - 2 x + 1$ |
$18$ |
[8,5] |
$-\,19^{16}\cdot 191$ |
$2$ |
$18.3397724752$ |
$189.31566492031587$ |
|
|
? |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$12$ |
$30327.9632735$ |
| 18.8.573...376.1 |
$x^{18} - 10 x^{16} + 39 x^{14} - 75 x^{12} + 66 x^{10} + x^{8} - 52 x^{6} + 42 x^{4} - 12 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$12$ |
$31568.7152852$ |
| 18.8.573...376.2 |
$x^{18} - 6 x^{16} + 16 x^{14} - 12 x^{12} - 15 x^{10} + 4 x^{8} + 18 x^{6} - 6 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$12$ |
$32092.4415918$ |
| 18.8.573...376.3 |
$x^{18} - 3 x^{14} - x^{12} - 4 x^{10} + 2 x^{8} + 11 x^{6} - x^{4} - 5 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$12$ |
$31182.2092318$ |
| 18.8.573...376.4 |
$x^{18} - 9 x^{16} + 34 x^{14} - 73 x^{12} + 101 x^{10} - 106 x^{8} + 73 x^{6} - 23 x^{4} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$12$ |
$33844.3438865$ |
| 18.8.573...376.5 |
$x^{18} - 4 x^{16} - 2 x^{14} + 22 x^{12} - 35 x^{10} + 48 x^{8} - 64 x^{6} + 44 x^{4} - 12 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.381430657322177$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$12$ |
$33223.470269528996$ |
| 18.8.573...376.6 |
$x^{18} - 3 x^{16} - 4 x^{14} + 25 x^{12} - 38 x^{10} + 26 x^{8} - 15 x^{6} + 15 x^{4} - 7 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.381430657322177$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$12$ |
$31797.506877630192$ |
| 18.8.581...123.1 |
$x^{18} - 4 x^{17} + 6 x^{16} + 5 x^{15} - 35 x^{14} + 77 x^{13} - 114 x^{12} + 119 x^{11} - 52 x^{10} - 90 x^{9} + 173 x^{8} - 163 x^{7} + 142 x^{6} - 187 x^{5} + 147 x^{4} + 13 x^{3} - 50 x^{2} + 14 x - 1$ |
$18$ |
[8,5] |
$-\,7^{12}\cdot 13^{4}\cdot 43^{5}$ |
$3$ |
$18.3942844514$ |
$464.7841483677139$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$12$ |
$34380.6983555$ |
| 18.8.668...375.1 |
$x^{18} - 3 x^{17} + x^{15} + 3 x^{14} + 3 x^{13} + 3 x^{12} + 6 x^{11} - 15 x^{10} - 3 x^{9} - 15 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + x^{3} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,3^{15}\cdot 5^{9}\cdot 13^{4}\cdot 17^{4}$ |
$4$ |
$18.5379671649$ |
$642.7936760178231$ |
|
|
? |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$12$ |
$46678.2467071$ |
| 18.8.759...088.1 |
$x^{18} - 4 x^{17} + 2 x^{16} + 7 x^{15} - 12 x^{14} + 12 x^{13} + 6 x^{12} - 8 x^{11} + 10 x^{10} - x^{9} + 10 x^{8} - 8 x^{7} + 6 x^{6} + 12 x^{5} - 12 x^{4} + 7 x^{3} + 2 x^{2} - 4 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2}$ |
$4$ |
$18.6698949697$ |
$2139.2083026220857$ |
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
$2$ |
$12$ |
$40202.4399869$ |
| 18.8.759...088.2 |
$x^{18} - 2 x^{17} - 9 x^{16} + 19 x^{15} + 29 x^{14} - 55 x^{13} - 81 x^{12} + 101 x^{11} + 145 x^{10} - 94 x^{9} - 152 x^{8} - 13 x^{7} + 99 x^{6} + 89 x^{5} - 33 x^{4} - 52 x^{3} + 3 x^{2} + 7 x - 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2}$ |
$4$ |
$18.6698949697$ |
$2139.2083026220857$ |
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
$2$ |
$12$ |
$34838.2865675$ |
| 18.8.120...992.1 |
$x^{18} - 3 x^{17} - x^{16} + 10 x^{15} - 10 x^{14} + 4 x^{13} - 8 x^{11} + 21 x^{10} - 27 x^{9} + 21 x^{8} - 8 x^{7} + 4 x^{5} - 10 x^{4} + 10 x^{3} - x^{2} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 37^{6}\cdot 43\cdot 16361^{2}$ |
$4$ |
$19.1588709967$ |
$8098.911922110533$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$48078.3122261$ |
| 18.8.124...176.1 |
$x^{18} + 3 x^{14} - 6 x^{12} - 9 x^{10} - 12 x^{8} + 29 x^{6} + 9 x^{4} - 15 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 3^{24}\cdot 1297^{2}$ |
$3$ |
$19.189951989231883$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$12$ |
$51430.002503910466$ |
| 18.8.126...872.1 |
$x^{18} - 3 x^{17} - 4 x^{16} + 8 x^{15} + 27 x^{14} - 39 x^{13} - 18 x^{12} + 39 x^{11} - 56 x^{10} + 91 x^{9} - 109 x^{7} + 94 x^{6} - 13 x^{5} - 49 x^{4} + 34 x^{3} - 5 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 101^{6}\cdot 127\cdot 479^{2}$ |
$4$ |
$19.2082071151$ |
$3934.7484036603246$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$69593.6579676$ |
| 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 |
$2$ |
$12$ |
$99742.4024554$ |
| 18.8.162...568.1 |
$x^{18} - 4 x^{17} - x^{16} + 28 x^{15} - 53 x^{14} + 32 x^{13} + 22 x^{12} - 72 x^{11} + 174 x^{10} - 456 x^{9} + 817 x^{8} - 696 x^{7} - 177 x^{6} + 1028 x^{5} - 1053 x^{4} + 540 x^{3} - 148 x^{2} + 20 x - 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 101^{6}\cdot 163\cdot 479^{2}$ |
$4$ |
$19.4763762947$ |
$4457.680212190382$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$74368.5676062$ |
| 18.8.165...896.1 |
$x^{18} - 8 x^{17} + 23 x^{16} - 17 x^{15} - 59 x^{14} + 169 x^{13} - 149 x^{12} - 99 x^{11} + 385 x^{10} - 386 x^{9} + 64 x^{8} + 275 x^{7} - 347 x^{6} + 189 x^{5} - 19 x^{4} - 44 x^{3} + 31 x^{2} - 9 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2}$ |
$4$ |
$19.4985507404$ |
$9486.771800045728$ |
|
|
✓ |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$62237.6710679$ |
| 18.8.171...247.1 |
$x^{18} - 5 x^{17} - x^{16} + 46 x^{15} - 73 x^{14} - 72 x^{13} + 294 x^{12} - 197 x^{11} - 206 x^{10} + 343 x^{9} - 52 x^{8} - 160 x^{7} + 82 x^{6} + 3 x^{5} - 4 x^{4} - x^{3} + 2 x^{2} + 2 x - 1$ |
$18$ |
[8,5] |
$-\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 127$ |
$4$ |
$19.5349648963$ |
$2798.3911956091342$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$12$ |
$58551.281415$ |
| 18.8.173...504.1 |
$x^{18} - 4 x^{16} + 4 x^{14} + x^{12} - 12 x^{10} + 18 x^{8} + 6 x^{6} - 16 x^{4} + 2 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 7^{12}\cdot 55243^{2}$ |
$3$ |
$19.5436219068$ |
$2432.665042802672$ |
|
|
? |
$S_4^3.C_6$ (as 18T768) |
trivial |
$2$ |
$12$ |
$68586.9064216$ |
| 18.8.178...544.1 |
$x^{18} - x^{17} - 11 x^{16} + 13 x^{15} + 40 x^{14} - 68 x^{13} - 75 x^{12} + 176 x^{11} + 99 x^{10} - 296 x^{9} - 132 x^{8} + 398 x^{7} + 155 x^{6} - 413 x^{5} - 96 x^{4} + 312 x^{3} + 50 x^{2} - 140 x - 49$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2}$ |
$4$ |
$19.5779559553$ |
$4671.341555622468$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$65853.2938786$ |
| 18.8.178...544.2 |
$x^{18} - 3 x^{17} - 3 x^{16} + 13 x^{15} - 7 x^{14} + 7 x^{13} + 20 x^{12} - 103 x^{11} + 42 x^{10} + 171 x^{9} - 53 x^{8} - 251 x^{7} - 138 x^{6} + 436 x^{5} + 30 x^{4} - 175 x^{3} + 68 x^{2} - 13 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2}$ |
$4$ |
$19.5779559553$ |
$4671.341555622468$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$68183.3465869$ |
| 18.8.188...848.1 |
$x^{18} - 2 x^{17} - 8 x^{16} + 27 x^{15} - 26 x^{14} - 18 x^{13} + 66 x^{12} - 52 x^{11} - 16 x^{10} + 57 x^{9} - 16 x^{8} - 52 x^{7} + 66 x^{6} - 18 x^{5} - 26 x^{4} + 27 x^{3} - 8 x^{2} - 2 x + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 37^{6}\cdot 67\cdot 16361^{2}$ |
$4$ |
$19.6367796044$ |
$10109.504024340771$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$67015.0431188$ |
| 18.8.250...584.1 |
$x^{18} - 9 x^{17} + 27 x^{16} - 11 x^{15} - 99 x^{14} + 177 x^{13} - 38 x^{12} - 87 x^{11} + 48 x^{10} - 201 x^{9} + 288 x^{8} + 51 x^{7} - 186 x^{6} + 3 x^{5} + 39 x^{4} - 8 x^{3} + 9 x^{2} - 6 x + 1$ |
$18$ |
[8,5] |
$-\,2^{6}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$19.9481992835$ |
|
|
|
|
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$12$ |
$84349.8186411$ |
| 18.8.256...128.1 |
$x^{18} + 3 x^{16} - 13 x^{14} - 48 x^{12} + 38 x^{10} + 163 x^{8} + 23 x^{6} - 161 x^{4} - 56 x^{2} + 37$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 37^{7}\cdot 401^{2}$ |
$3$ |
$19.9741274742$ |
|
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$86122.6934234$ |
| 18.8.256...128.2 |
$x^{18} - 4 x^{16} + 21 x^{14} - 45 x^{12} + 55 x^{10} - 174 x^{8} + 274 x^{6} - 53 x^{4} - 111 x^{2} + 37$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 37^{7}\cdot 401^{2}$ |
$3$ |
$19.9741274742$ |
|
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$80102.3237016$ |
| 18.8.256...128.3 |
$x^{18} - 3 x^{16} - 9 x^{14} + 46 x^{12} - 38 x^{10} - 209 x^{8} + 599 x^{6} - 343 x^{4} - 148 x^{2} + 37$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 37^{7}\cdot 401^{2}$ |
$3$ |
$19.9741274742$ |
|
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$12$ |
$79410.3823865$ |
| 18.8.277...351.1 |
$x^{18} - 3 x^{17} - 9 x^{16} + 49 x^{15} - 63 x^{14} - 27 x^{13} + 152 x^{12} - 117 x^{11} - 99 x^{10} + 231 x^{9} - 99 x^{8} - 117 x^{7} + 152 x^{6} - 27 x^{5} - 63 x^{4} + 49 x^{3} - 9 x^{2} - 3 x + 1$ |
$18$ |
[8,5] |
$-\,3^{24}\cdot 7^{12}\cdot 71$ |
$3$ |
$20.0635626471$ |
$133.41035526120362$ |
|
|
? |
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$12$ |
$84491.1381717$ |
| 18.8.395...816.1 |
$x^{18} - 9 x^{16} + 24 x^{14} - 31 x^{12} + 39 x^{10} - 9 x^{8} - 9 x^{6} - 24 x^{4} + 1$ |
$18$ |
[8,5] |
$-\,2^{24}\cdot 3^{24}\cdot 17^{4}$ |
$3$ |
$20.4629429828$ |
$96.21957765640818$ |
|
|
? |
$C_2\times C_3^3:A_4$ (as 18T199) |
trivial |
$2$ |
$12$ |
$113523.737562$ |
