| 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 |
Max $p$ |
| 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 |
$[2]$ |
$2$ |
$12$ |
$6722.94980486$ |
$7$ |
$97$ |
| 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 |
$[2]$ |
$2$ |
$12$ |
$11002.0590961$ |
$7$ |
$97$ |
| 18.6.194...000.1 |
$x^{18} - 6 x^{17} + 11 x^{16} + 6 x^{15} - 60 x^{14} + 122 x^{13} - 141 x^{12} + 74 x^{11} + 54 x^{10} - 122 x^{9} + 71 x^{8} + 36 x^{7} - 70 x^{6} + 16 x^{5} + 33 x^{4} - 10 x^{3} - 11 x^{2} - 4 x + 1$ |
$18$ |
(6, 6) |
$2^{18}\cdot 5^{6}\cdot 7^{15}$ |
$3$ |
$17.3088559575$ |
$22.634106993721137$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$13385.82469770262$ |
$5$ |
$7$ |
| 18.0.379...000.2 |
$x^{18} + x^{16} - 16 x^{15} + 8 x^{14} - 53 x^{13} + 110 x^{12} - 62 x^{11} + 188 x^{10} - 65 x^{9} + 109 x^{8} - 70 x^{7} + 57 x^{6} - 71 x^{5} + 49 x^{4} - 31 x^{3} + 16 x^{2} - 3 x + 1$ |
$18$ |
(0, 9) |
$-\,2^{12}\cdot 5^{9}\cdot 7^{15}$ |
$3$ |
$17.9647026261$ |
$22.634106993721137$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$3652.277942285766$ |
$0$ |
$7$ |
| 18.6.580...552.1 |
$x^{18} - 4 x^{17} + 4 x^{16} - 20 x^{15} + 51 x^{14} + 24 x^{13} + 3 x^{12} - 162 x^{11} - 195 x^{10} + 90 x^{9} + 324 x^{8} + 372 x^{7} - 74 x^{6} - 184 x^{5} - 215 x^{4} - 28 x^{3} - 25 x^{2} + 10 x + 1$ |
$18$ |
(6, 6) |
$2^{24}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$18.393404106$ |
$22.08931872239049$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$25505.791722934875$ |
$5$ |
$7$ |
| 18.0.156...904.1 |
$x^{18} + 10 x^{16} - 20 x^{15} + 79 x^{14} - 204 x^{13} + 399 x^{12} - 820 x^{11} + 1371 x^{10} - 1886 x^{9} + 3412 x^{8} - 2978 x^{7} + 4318 x^{6} - 4122 x^{5} + 3141 x^{4} - 2700 x^{3} + 2025 x^{2} - 486 x + 729$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$22.0893187224$ |
$22.08931872239049$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$6959.170810461739$ |
$0$ |
$7$ |
| 18.8.225...128.1 |
$x^{18} - x^{17} - 12 x^{16} + 8 x^{15} + 46 x^{14} - 16 x^{13} - 39 x^{12} - 9 x^{11} - 94 x^{10} + 48 x^{9} + 81 x^{8} - 17 x^{7} + 136 x^{6} - 88 x^{5} - 55 x^{4} + 91 x^{3} - 120 x^{2} - 16 x + 64$ |
$18$ |
(8, 5) |
$-\,2^{12}\cdot 7^{15}\cdot 41^{5}$ |
$3$ |
$22.5387873569$ |
$316.06754812716173$ |
|
|
? |
$A_4^3.C_2^3:A_4$ (as 18T839) |
trivial |
$[2]$ |
$2$ |
$12$ |
$304198.198516$ |
$7$ |
$41$ |
| 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 |
$[2]$ |
$2$ |
$11$ |
$163825.939612$ |
$5$ |
$1399$ |
| 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 |
$[2]$ |
$2$ |
$11$ |
$111936.796178$ |
$5$ |
$1511$ |
| 18.6.371...328.1 |
$x^{18} - 7 x^{16} - 28 x^{14} - 63 x^{12} + 147 x^{10} - 539 x^{8} + 1715 x^{6} - 2058 x^{4} + 1372 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{30}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$23.1742370124$ |
$35.06460777718351$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$196769.60774758863$ |
$5$ |
$7$ |
| 18.6.600...728.1 |
$x^{18} - 4 x^{17} + 4 x^{16} + 8 x^{15} - 40 x^{14} + 66 x^{13} + 38 x^{12} - 274 x^{11} + 78 x^{10} - 8 x^{9} - 894 x^{8} - 342 x^{7} + 45 x^{6} - 702 x^{5} - 194 x^{4} + 644 x^{3} + 360 x^{2} - 18 x - 27$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 13^{6}$ |
$3$ |
$23.8008689519$ |
$36.496400897189325$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$219143.404293034$ |
$5$ |
$13$ |
| 18.0.276...000.2 |
$x^{18} - x^{17} + 5 x^{16} + 18 x^{15} - 39 x^{14} + 15 x^{13} + 7 x^{12} - 341 x^{11} + 1040 x^{10} + 102 x^{9} - 3301 x^{8} + 4433 x^{7} + 5347 x^{6} - 6273 x^{5} + 26465 x^{4} - 35883 x^{3} + 41441 x^{2} - 20184 x + 24389$ |
$18$ |
(0, 9) |
$-\,2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$25.9095846432$ |
$31.11577769126579$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[6]$ |
$[6]$ |
$2$ |
$8$ |
$28012.59863654079$ |
$0$ |
$7$ |
| 18.8.289...343.1 |
$x^{18} - 3 x^{17} + 9 x^{16} + 2 x^{15} - 58 x^{14} + 260 x^{13} - 456 x^{12} + 186 x^{11} + 1564 x^{10} - 4448 x^{9} + 4752 x^{8} - 274 x^{7} - 9044 x^{6} + 15315 x^{5} - 13459 x^{4} - 6698 x^{3} + 22326 x^{2} - 6125 x - 3569$ |
$18$ |
(8, 5) |
$-\,7^{15}\cdot 41^{3}\cdot 97^{4}$ |
$3$ |
$25.9746979475$ |
$319.1730121130693$ |
|
|
? |
$S_4^3.C_6$ (as 18T765) |
trivial |
$[2, 2]$ |
$2$ |
$12$ |
$753523.40911$ |
$6$ |
$97$ |
| 18.6.297...624.1 |
$x^{18} - 4 x^{17} - 4 x^{16} + 18 x^{15} + 19 x^{14} + 2 x^{13} - 91 x^{12} - 300 x^{11} + 988 x^{10} - 444 x^{9} - 1850 x^{8} + 4736 x^{7} - 6476 x^{6} + 5624 x^{5} - 2944 x^{4} + 832 x^{3} - 24 x^{2} - 48 x + 8$ |
$18$ |
(6, 6) |
$2^{33}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$26.0122015449$ |
$35.06460777718351$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$850112.0397633199$ |
$5$ |
$7$ |
| 18.6.297...624.2 |
$x^{18} - 56 x^{14} - 42 x^{12} + 784 x^{10} + 392 x^{8} - 3332 x^{6} + 5488 x^{2} - 2744$ |
$18$ |
(6, 6) |
$2^{33}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$26.0122015449$ |
$31.239014120786564$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$424908.3007113114$ |
$5$ |
$7$ |
| 18.10.858...312.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 34 x^{15} - 171 x^{14} + 177 x^{13} + 514 x^{12} - 1461 x^{11} + 438 x^{10} + 2633 x^{9} - 3090 x^{8} - 963 x^{7} + 3216 x^{6} - 801 x^{5} - 405 x^{4} + 567 x^{3} - 351 x^{2} - 243 x - 27$ |
$18$ |
(10, 4) |
$2^{6}\cdot 3^{24}\cdot 7^{15}$ |
$3$ |
$27.590106159$ |
$73.65674656366089$ |
|
|
|
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$[2]$ |
$2$ |
$13$ |
$2716594.14709$ |
$9$ |
$7$ |
| 18.0.100...856.1 |
$x^{18} - 4 x^{17} + 9 x^{16} - 4 x^{15} + 28 x^{14} - 76 x^{13} + 22 x^{12} - 308 x^{11} + 683 x^{10} + 184 x^{9} + 2225 x^{8} + 384 x^{7} + 3547 x^{6} - 1536 x^{5} + 6427 x^{4} - 5108 x^{3} + 7281 x^{2} - 3612 x + 1849$ |
$18$ |
(0, 9) |
$-\,2^{30}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$27.8307976362$ |
$35.06460777718351$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$63391.07407344074$ |
$0$ |
$7$ |
| 18.0.105...875.1 |
$x^{18} - 2 x^{17} + 7 x^{16} - 22 x^{15} + 55 x^{14} - 92 x^{13} + 169 x^{12} - 309 x^{11} + 504 x^{10} - 775 x^{9} + 1552 x^{8} - 3224 x^{7} + 5234 x^{6} - 6059 x^{5} + 5110 x^{4} - 3802 x^{3} + 3209 x^{2} - 2494 x + 1009$ |
$18$ |
(0, 9) |
$-\,3^{6}\cdot 5^{15}\cdot 7^{15}$ |
$3$ |
$27.9102539798$ |
$33.51845543269161$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$134923.2262128377$ |
$0$ |
$7$ |
| 18.0.206...944.2 |
$x^{18} + 16 x^{16} - 9 x^{15} + 81 x^{14} - 120 x^{13} + 327 x^{12} - 605 x^{11} + 1559 x^{10} - 3712 x^{9} + 8024 x^{8} - 16765 x^{7} + 31445 x^{6} - 50943 x^{5} + 64799 x^{4} - 62331 x^{3} + 42715 x^{2} - 18850 x + 4537$ |
$18$ |
(0, 9) |
$-\,2^{12}\cdot 7^{15}\cdot 13^{9}$ |
$3$ |
$28.9672125886$ |
$36.496400897189325$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$8$ |
$59792.552179039536$ |
$0$ |
$13$ |
| 18.0.382...000.1 |
$x^{18} - 6 x^{17} + 39 x^{16} - 162 x^{15} + 612 x^{14} - 1782 x^{13} + 4780 x^{12} - 10608 x^{11} + 21915 x^{10} - 37600 x^{9} + 60915 x^{8} - 80394 x^{7} + 100303 x^{6} - 92832 x^{5} + 77901 x^{4} - 39644 x^{3} + 9537 x^{2} - 1068 x + 757$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 3^{9}\cdot 5^{6}\cdot 7^{15}$ |
$4$ |
$29.9798179393$ |
$39.20342329707507$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$138539.55802600196$ |
$0$ |
$7$ |
| 18.18.431...112.1 |
$x^{18} - 5 x^{17} - 17 x^{16} + 116 x^{15} + 28 x^{14} - 898 x^{13} + 729 x^{12} + 2639 x^{11} - 3688 x^{10} - 2725 x^{9} + 6303 x^{8} - 110 x^{7} - 4279 x^{6} + 1433 x^{5} + 961 x^{4} - 464 x^{3} - 59 x^{2} + 35 x + 1$ |
$18$ |
(18, 0) |
$2^{12}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$30.1782223225$ |
$104.21525486870038$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$23947078.6456$ |
$16$ |
$53$ |
| 18.10.431...112.1 |
$x^{18} - 6 x^{17} + 8 x^{16} + 4 x^{15} + 59 x^{13} - 237 x^{12} + 77 x^{11} - 47 x^{10} - 128 x^{9} + 1174 x^{8} + 613 x^{7} + 2819 x^{6} + 1007 x^{5} - 6422 x^{4} - 3110 x^{3} + 2151 x^{2} + 1141 x + 127$ |
$18$ |
(10, 4) |
$2^{12}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$30.1782223225$ |
$135.1504647117669$ |
|
|
? |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$4210824.90408$ |
$8$ |
$53$ |
| 18.10.431...112.2 |
$x^{18} + 7 x^{16} - 63 x^{14} - 112 x^{12} + 1421 x^{10} - 2695 x^{8} - 98 x^{6} + 4116 x^{4} - 2401 x^{2} - 343$ |
$18$ |
(10, 4) |
$2^{12}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$30.1782223225$ |
$144.2245210641738$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$3746929.3176$ |
$8$ |
$53$ |
| 18.2.535...232.1 |
$x^{18} - 10 x^{15} + 7 x^{14} - 96 x^{12} + 350 x^{11} - 539 x^{10} + 1128 x^{9} - 1092 x^{8} + 854 x^{7} + 165 x^{6} - 1344 x^{5} + 2394 x^{4} - 3330 x^{3} + 2268 x^{2} - 756 x + 162$ |
$18$ |
(2, 8) |
$2^{34}\cdot 3^{8}\cdot 7^{15}$ |
$3$ |
$30.5431954791$ |
$39.35869146874217$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$[6]$ |
$2$ |
$9$ |
$11927329.759810016$ |
$1$ |
$7$ |
| 18.6.637...000.1 |
$x^{18} - 14 x^{14} + 49 x^{10} - 784 x^{8} + 1813 x^{6} - 4116 x^{4} + 9604 x^{2} - 2744$ |
$18$ |
(6, 6) |
$2^{33}\cdot 5^{6}\cdot 7^{15}$ |
$3$ |
$30.8408751701$ |
$45.26821398744227$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$3501160.3686457397$ |
$5$ |
$7$ |
| 18.6.747...000.2 |
$x^{18} - 4 x^{17} - 9 x^{16} + 34 x^{15} + 63 x^{14} - 100 x^{13} - 492 x^{12} + 706 x^{11} + 1924 x^{10} - 7642 x^{9} + 441 x^{8} + 51712 x^{7} - 32185 x^{6} - 173014 x^{5} + 130693 x^{4} + 191344 x^{3} - 183596 x^{2} + 65694 x - 11171$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{9}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$31.1157776913$ |
$31.11577769126579$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$1722510.6678123942$ |
$5$ |
$7$ |
| 18.6.747...000.3 |
$x^{18} - 13 x^{16} - 47 x^{15} + 57 x^{14} + 438 x^{13} + 628 x^{12} - 1121 x^{11} - 4355 x^{10} - 3071 x^{9} + 6668 x^{8} + 17640 x^{7} + 4264 x^{6} - 19900 x^{5} - 26320 x^{4} - 3000 x^{3} + 34400 x^{2} + 4000 x - 8000$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{9}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$31.1157776913$ |
$39.20342329707507$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$2839625.480782971$ |
$5$ |
$7$ |
| 18.0.802...848.1 |
$x^{18} + 28 x^{16} + 336 x^{14} + 2226 x^{12} + 9212 x^{10} + 27440 x^{8} + 65464 x^{6} + 123480 x^{4} + 148176 x^{2} + 74088$ |
$18$ |
(0, 9) |
$-\,2^{33}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$31.2390141208$ |
$31.239014120786564$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$8$ |
$31684.521927615173$ |
$0$ |
$7$ |
| 18.0.802...848.2 |
$x^{18} - 8 x^{17} + 50 x^{16} - 214 x^{15} + 777 x^{14} - 2306 x^{13} + 5951 x^{12} - 13076 x^{11} + 25573 x^{10} - 42600 x^{9} + 65630 x^{8} - 85698 x^{7} + 110878 x^{6} - 123990 x^{5} + 146017 x^{4} - 124430 x^{3} + 112877 x^{2} - 54474 x + 17851$ |
$18$ |
(0, 9) |
$-\,2^{33}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$31.2390141208$ |
$35.06460777718351$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$8$ |
$53687.93588131197$ |
$0$ |
$7$ |
| 18.2.907...000.2 |
$x^{18} - 7 x^{16} - 2 x^{15} + 42 x^{14} - 70 x^{13} + 116 x^{12} - 210 x^{11} - 56 x^{10} + 818 x^{9} - 966 x^{8} - 182 x^{7} + 1346 x^{6} - 1218 x^{5} + 392 x^{4} + 66 x^{3} - 77 x^{2} + 14 x + 1$ |
$18$ |
(2, 8) |
$2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 7^{15}$ |
$4$ |
$31.4522785988$ |
$49.39321823992395$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$[6]$ |
$2$ |
$9$ |
$1313648.1862367177$ |
$1$ |
$7$ |
| 18.0.160...696.1 |
$x^{18} - 6 x^{17} + 31 x^{16} - 126 x^{15} + 449 x^{14} - 1344 x^{13} + 3523 x^{12} - 8124 x^{11} + 16814 x^{10} - 30804 x^{9} + 50122 x^{8} - 71112 x^{7} + 87448 x^{6} - 89688 x^{5} + 73686 x^{4} - 45720 x^{3} + 20178 x^{2} - 5832 x + 918$ |
$18$ |
(0, 9) |
$-\,2^{34}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$32.4654336372$ |
$39.35869146874217$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$8$ |
$1486658.4572439173$ |
$0$ |
$7$ |
| 18.0.177...000.1 |
$x^{18} - 5 x^{17} + 33 x^{16} - 117 x^{15} + 444 x^{14} - 1134 x^{13} + 3154 x^{12} - 5743 x^{11} + 12731 x^{10} - 15916 x^{9} + 28249 x^{8} - 20200 x^{7} + 32454 x^{6} + 6574 x^{5} + 23195 x^{4} + 52174 x^{3} + 60501 x^{2} + 54675 x + 24921$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$32.644031086$ |
$55.442012918176914$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$650027.3886087111$ |
$0$ |
$7$ |
| 18.6.285...625.1 |
$x^{18} - 3 x^{17} - 4 x^{16} - 11 x^{15} + 40 x^{14} + 187 x^{13} - 21 x^{12} - 708 x^{11} - 972 x^{10} + 1445 x^{9} + 796 x^{8} - 2013 x^{7} + 2001 x^{6} - 1431 x^{5} + 535 x^{4} - 41 x^{3} - 17 x^{2} - x + 1$ |
$18$ |
(6, 6) |
$3^{9}\cdot 5^{15}\cdot 7^{15}$ |
$3$ |
$33.5184554327$ |
$33.51845543269161$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$2765502.045498877$ |
$5$ |
$7$ |
| 18.6.307...736.1 |
$x^{18} - 2 x^{17} + 3 x^{16} - 8 x^{15} - 4 x^{13} - 100 x^{12} + 206 x^{11} - 198 x^{10} + 548 x^{9} - 546 x^{8} + 104 x^{7} + 1429 x^{6} - 484 x^{5} - 1562 x^{4} - 344 x^{3} - 56 x^{2} - 352 x - 104$ |
$18$ |
(6, 6) |
$2^{27}\cdot 7^{15}\cdot 13^{6}$ |
$3$ |
$33.659511668$ |
$51.61370512661073$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$11500048.03513821$ |
$5$ |
$13$ |
| 18.2.428...856.1 |
$x^{18} - 4 x^{17} + 10 x^{16} - 110 x^{14} + 124 x^{13} + 248 x^{12} + 36 x^{11} - 950 x^{10} + 188 x^{9} + 1492 x^{8} - 1744 x^{7} + 794 x^{6} + 696 x^{5} - 2000 x^{4} + 1968 x^{3} - 192 x^{2} - 144 x + 36$ |
$18$ |
(2, 8) |
$2^{37}\cdot 3^{8}\cdot 7^{15}$ |
$3$ |
$34.2835777594$ |
$39.35869146874217$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$[6]$ |
$2$ |
$9$ |
$5411310.715793057$ |
$1$ |
$7$ |
| 18.0.708...000.1 |
$x^{18} - 12 x^{15} + 32 x^{12} + 8 x^{9} + 660 x^{6} + 32 x^{3} + 64$ |
$18$ |
(0, 9) |
$-\,2^{20}\cdot 3^{6}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$35.2575036911$ |
$49.39321823992395$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 6]$ |
$[3, 6]$ |
$2$ |
$8$ |
$411004.99346778373$ |
$0$ |
$7$ |
| 18.0.128...568.1 |
$x^{18} - 21 x^{14} + 168 x^{12} - 245 x^{10} - 294 x^{8} + 3381 x^{6} + 4116 x^{4} - 6860 x^{2} + 2058$ |
$18$ |
(0, 9) |
$-\,2^{37}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$36.4412171396$ |
$39.35869146874217$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$8$ |
$4611850.95536467$ |
$0$ |
$7$ |
| 18.0.131...416.1 |
$x^{18} - x^{17} + 17 x^{16} - 13 x^{15} + 118 x^{14} - 70 x^{13} + 445 x^{12} - 268 x^{11} + 1053 x^{10} - 928 x^{9} + 1664 x^{8} - 2312 x^{7} + 1927 x^{6} - 3581 x^{5} + 3396 x^{4} - 3588 x^{3} + 6198 x^{2} - 2434 x + 3277$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 7^{15}\cdot 13^{9}$ |
$3$ |
$36.4964008972$ |
$51.61370512661073$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$8$ |
$857534.4928023067$ |
$0$ |
$13$ |
| 18.0.244...000.2 |
$x^{18} + 3 x^{16} - 8 x^{15} + 37 x^{14} - 62 x^{13} + 77 x^{12} - 244 x^{11} + 188 x^{10} - 270 x^{9} + 192 x^{8} + 108 x^{7} + 6 x^{6} + 860 x^{5} + 68 x^{4} + 544 x^{3} + 520 x^{2} + 80 x + 400$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{9}\cdot 5^{6}\cdot 7^{15}$ |
$4$ |
$37.7722036938$ |
$49.39321823992395$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$8$ |
$7705550.9580970425$ |
$0$ |
$7$ |
| 18.6.246...888.1 |
$x^{18} - 2 x^{17} + 26 x^{16} - 44 x^{15} + 269 x^{14} - 378 x^{13} + 1166 x^{12} - 1208 x^{11} + 1342 x^{10} - 1192 x^{9} - 1620 x^{8} + 3008 x^{7} - 3631 x^{6} + 2162 x^{5} + 550 x^{4} - 724 x^{3} + 336 x^{2} - 96 x + 8$ |
$18$ |
(6, 6) |
$2^{30}\cdot 7^{15}\cdot 13^{6}$ |
$3$ |
$37.7815244119$ |
$72.99280179437865$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$23690932.632656835$ |
$5$ |
$13$ |
| 18.6.275...168.1 |
$x^{18} + 7 x^{16} - 70 x^{14} - 504 x^{12} + 931 x^{10} + 8722 x^{8} + 6860 x^{6} - 6517 x^{4} - 3430 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$38.0221775525$ |
$135.1504647117669$ |
|
|
? |
$A_4^2:C_2^2$ (as 18T176) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$6733353.96589$ |
$4$ |
$53$ |
| 18.6.275...168.2 |
$x^{18} - 84 x^{14} - 133 x^{12} + 1470 x^{10} + 3626 x^{8} + 98 x^{6} - 3430 x^{4} - 2058 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$38.0221775525$ |
|
|
|
? |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
$[3]$ |
$[2, 2, 6]$ |
$2$ |
$11$ |
$4692184.11043$ |
$3$ |
$53$ |
| 18.6.308...432.1 |
$x^{18} - 52 x^{15} + 324 x^{12} - 300 x^{9} - 836 x^{6} + 72 x^{3} + 8$ |
$18$ |
(6, 6) |
$2^{24}\cdot 3^{18}\cdot 7^{15}$ |
$3$ |
$38.2598223318$ |
$45.94763453668202$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$[2]$ |
$2$ |
$11$ |
$20582578.44895166$ |
$5$ |
$7$ |
| 18.6.334...192.1 |
$x^{18} - 3 x^{17} - 56 x^{16} + 141 x^{15} + 1384 x^{14} - 2656 x^{13} - 19886 x^{12} + 25447 x^{11} + 176463 x^{10} - 121459 x^{9} - 956008 x^{8} + 215581 x^{7} + 2966304 x^{6} + 66795 x^{5} - 4938409 x^{4} - 116479 x^{3} + 4397847 x^{2} - 260805 x - 1538039$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{6}\cdot 7^{15}\cdot 11^{9}$ |
$4$ |
$38.4301244864$ |
$46.152156687754065$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$7074477.941544473$ |
$5$ |
$11$ |
| 18.6.357...408.1 |
$x^{18} + 14 x^{16} + 7 x^{14} - 693 x^{12} - 3479 x^{10} - 4067 x^{8} + 6762 x^{6} + 13377 x^{4} + 2058 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 169457^{2}$ |
$3$ |
$38.5731383512$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$17627829.429$ |
$4$ |
$169457$ |
| 18.18.357...408.1 |
$x^{18} - 35 x^{16} + 441 x^{14} - 2723 x^{12} + 9212 x^{10} - 17885 x^{8} + 19894 x^{6} - 12005 x^{4} + 3430 x^{2} - 343$ |
$18$ |
(18, 0) |
$2^{18}\cdot 7^{15}\cdot 169457^{2}$ |
$3$ |
$38.5731383512$ |
|
|
|
? |
$S_4^3.C_6$ (as 18T768) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$272527985.673$ |
$16$ |
$169457$ |
| 18.6.357...408.2 |
$x^{18} - 119 x^{14} - 196 x^{12} + 2989 x^{10} + 7546 x^{8} + 3283 x^{6} - 3087 x^{4} - 2401 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{15}\cdot 169457^{2}$ |
$3$ |
$38.5731383512$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$16366060.7115$ |
$4$ |
$169457$ |
| 18.6.478...000.1 |
$x^{18} - 8 x^{17} + 13 x^{16} + 76 x^{15} - 546 x^{14} + 1560 x^{13} - 1136 x^{12} - 6946 x^{11} + 33547 x^{10} - 80862 x^{9} + 94675 x^{8} - 730 x^{7} - 197469 x^{6} + 854612 x^{5} - 3338939 x^{4} + 8315292 x^{3} - 11925585 x^{2} + 9050590 x - 2815721$ |
$18$ |
(6, 6) |
$2^{18}\cdot 3^{9}\cdot 5^{9}\cdot 7^{15}$ |
$4$ |
$39.2034232971$ |
$55.442012918176914$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$23621285.338625655$ |
$5$ |
$7$ |
| 18.0.796...000.2 |
$x^{18} + 28 x^{16} + 294 x^{14} + 2660 x^{12} + 15533 x^{10} + 49392 x^{8} + 126861 x^{6} + 253820 x^{4} + 240100 x^{2} + 343000$ |
$18$ |
(0, 9) |
$-\,2^{33}\cdot 5^{9}\cdot 7^{15}$ |
$3$ |
$40.3293938139$ |
$45.26821398744227$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$8$ |
$261074.19480096793$ |
$0$ |
$7$ |
| 18.0.118...224.1 |
$x^{18} - 4 x^{17} + 18 x^{16} - 76 x^{15} + 219 x^{14} - 830 x^{13} + 3664 x^{12} - 6028 x^{11} + 21568 x^{10} - 53670 x^{9} + 78836 x^{8} - 187718 x^{7} + 310341 x^{6} - 344234 x^{5} + 528250 x^{4} - 599004 x^{3} + 342240 x^{2} - 152352 x + 97336$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 13^{6}$ |
$4$ |
$41.2243142889$ |
$63.21362064733427$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$2122866.2679582797$ |
$0$ |
$13$ |
