| 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 |
| 18.0.168...552.1 |
$x^{18} - 4 x^{17} + 8 x^{16} - 11 x^{15} + 16 x^{14} - 20 x^{13} + 14 x^{12} - 8 x^{10} + 13 x^{9} - 20 x^{8} + 18 x^{7} - 2 x^{6} - 14 x^{5} + 20 x^{4} - 17 x^{3} + 10 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 11^{6}$ |
$4$ |
$11.6970819572$ |
$33.36893354677306$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$332.401225936$ |
| 18.0.137...747.1 |
$x^{18} - x^{17} + x^{16} + 2 x^{15} - 9 x^{14} + 6 x^{13} + 3 x^{12} - 21 x^{11} + 32 x^{10} - 24 x^{9} + 14 x^{8} - 5 x^{7} + 13 x^{6} - 14 x^{5} + 6 x^{4} - 3 x^{3} - x^{2} + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 19^{6}\cdot 23^{6}$ |
$3$ |
$13.1438049703$ |
$59.14621341619825$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$955.275046862$ |
| 18.0.494...968.1 |
$x^{18} - 3 x^{17} + 7 x^{16} - 9 x^{15} + 6 x^{14} + 4 x^{13} + 11 x^{12} - 54 x^{11} + 121 x^{10} - 152 x^{9} + 100 x^{8} + 14 x^{7} - 89 x^{6} + 83 x^{5} - 4 x^{4} - 50 x^{3} + 36 x^{2} - 10 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 19^{10}$ |
$3$ |
$14.1145149587$ |
$31.979766758139565$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$2261.196159404121$ |
| 18.0.316...952.1 |
$x^{18} - 4 x^{17} + 20 x^{15} - 29 x^{14} + 37 x^{13} - 145 x^{12} + 234 x^{11} + 137 x^{10} - 1107 x^{9} + 2430 x^{8} - 4388 x^{7} + 7497 x^{6} - 10621 x^{5} + 11285 x^{4} - 8627 x^{3} + 4555 x^{2} - 1479 x + 223$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 19^{10}$ |
$3$ |
$17.7831745055$ |
$56.98146642250715$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$17725.017305991136$ |
| 18.0.414...208.1 |
$x^{18} - 3 x^{17} - 6 x^{16} + 27 x^{15} + 18 x^{14} - 129 x^{13} - 3 x^{12} + 354 x^{11} - 162 x^{10} - 464 x^{9} + 426 x^{8} + 150 x^{7} - 390 x^{6} + 252 x^{5} + 84 x^{4} - 216 x^{3} + 132 x^{2} - 36 x + 4$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{31}$ |
$2$ |
$18.0521915206$ |
$25.64126624149289$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$42016.82501482997$ |
| 18.6.490...000.1 |
$x^{18} - 2 x^{17} - 6 x^{16} + 17 x^{15} + 30 x^{14} - 76 x^{13} - 72 x^{12} + 210 x^{11} + 106 x^{10} - 303 x^{9} - 118 x^{8} + 262 x^{7} + 102 x^{6} - 142 x^{5} - 68 x^{4} + 25 x^{3} + 16 x^{2} - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 5^{9}\cdot 19^{10}$ |
$3$ |
$18.2217604582$ |
$41.28570135662403$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$2$ |
$11$ |
$20286.0811613$ |
| 18.0.182...088.1 |
$x^{18} - 7 x^{17} + 23 x^{16} - 58 x^{15} + 132 x^{14} - 232 x^{13} + 286 x^{12} - 260 x^{11} + 147 x^{10} + 123 x^{9} - 425 x^{8} + 390 x^{7} - 314 x^{5} + 322 x^{4} - 174 x^{3} + 57 x^{2} - 11 x + 1$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{9}\cdot 13^{10}$ |
$3$ |
$19.5992363498$ |
$52.328113687220636$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$52047.91633001975$ |
| 18.0.297...888.1 |
$x^{18} - 9 x^{17} + 42 x^{16} - 129 x^{15} + 264 x^{14} - 324 x^{13} + 126 x^{12} + 369 x^{11} - 819 x^{10} + 711 x^{9} + 162 x^{8} - 1215 x^{7} + 1608 x^{6} - 1269 x^{5} + 729 x^{4} - 333 x^{3} + 117 x^{2} - 27 x + 3$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{31}\cdot 7^{6}$ |
$3$ |
$20.141640401$ |
$30.219468835479$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$145692.568555$ |
| 18.0.355...000.1 |
$x^{18} - 3 x^{17} + 15 x^{16} - 18 x^{15} + 33 x^{14} - 21 x^{13} + 75 x^{12} + 69 x^{11} + 132 x^{10} + 214 x^{9} + 309 x^{8} + 507 x^{7} + 567 x^{6} + 543 x^{5} + 381 x^{4} + 195 x^{3} + 75 x^{2} + 12 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 5^{6}$ |
$3$ |
$20.3422489782$ |
$28.856010107204362$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$119253.839734$ |
| 18.0.387...232.1 |
$x^{18} - 3 x^{17} + x^{16} + 9 x^{15} - 22 x^{14} - 20 x^{13} + 45 x^{12} + 16 x^{11} + 73 x^{10} + 70 x^{9} + 20 x^{8} + 50 x^{7} + 25 x^{6} + 23 x^{5} + 122 x^{4} + 138 x^{3} + 68 x^{2} + 14 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 37^{10}$ |
$3$ |
$20.4395095766$ |
$55.72910407292727$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$65819.9777767664$ |
| 18.6.666...000.1 |
$x^{18} - 2 x^{17} + 10 x^{16} - 15 x^{15} + 26 x^{14} - 34 x^{13} - 10 x^{12} + 14 x^{11} - 112 x^{10} + 111 x^{9} - 70 x^{8} + 88 x^{7} + 28 x^{6} + 10 x^{5} + 16 x^{4} - 19 x^{3} - 8 x^{2} - 4 x - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 5^{9}\cdot 11^{6}\cdot 19^{6}$ |
$4$ |
$21.0646264186$ |
$83.82439143954362$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$2$ |
$11$ |
$80091.8197007$ |
| 18.0.138...000.1 |
$x^{18} - 4 x^{17} + 5 x^{16} - 16 x^{15} + 69 x^{14} - 82 x^{13} - 86 x^{12} + 196 x^{11} + 72 x^{10} - 294 x^{9} + 127 x^{8} - 204 x^{7} + 759 x^{6} - 1052 x^{5} + 769 x^{4} - 336 x^{3} + 90 x^{2} - 14 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{14}\cdot 7^{10}$ |
$4$ |
$28.3393274252$ |
$53.20723141420387$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$560964.0932099912$ |
| 18.0.303...000.1 |
$x^{18} - 2 x^{17} + 8 x^{16} - x^{15} + 58 x^{14} - 55 x^{13} + 123 x^{12} + 9 x^{11} + 70 x^{10} - 12 x^{9} + 49 x^{8} + 204 x^{7} + 37 x^{6} + 175 x^{5} + 118 x^{4} + 90 x^{3} + 264 x^{2} + 208 x + 64$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 5^{12}\cdot 7^{15}$ |
$3$ |
$29.5977273519$ |
$41.857507436411844$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[18]$ |
$2$ |
$8$ |
$1994143.01875251$ |
| 18.0.714...088.1 |
$x^{18} - 3 x^{17} - 6 x^{16} + 3 x^{15} + 90 x^{14} - 66 x^{13} - 198 x^{12} - 231 x^{11} + 891 x^{10} + 55 x^{9} - 276 x^{8} - 1461 x^{7} + 2190 x^{6} - 1323 x^{5} + 21 x^{4} - 2289 x^{3} + 3759 x^{2} - 1449 x + 1393$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{31}\cdot 7^{10}$ |
$3$ |
$31.038048146$ |
$57.8077642622062$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$1566158.489890443$ |
| 18.0.781...712.1 |
$x^{18} + 6 x^{16} - 24 x^{15} - 72 x^{14} + 132 x^{13} + 774 x^{12} + 828 x^{11} - 102 x^{10} - 416 x^{9} - 324 x^{8} - 1752 x^{7} - 1515 x^{6} + 1476 x^{5} + 1632 x^{4} - 576 x^{3} - 288 x^{2} + 192 x + 64$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{31}\cdot 13^{6}$ |
$3$ |
$31.1927219529$ |
$112.51878599744718$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$18999317.186917692$ |
| 18.18.965...000.1 |
$x^{18} - 2 x^{17} - 22 x^{16} + 35 x^{15} + 174 x^{14} - 218 x^{13} - 650 x^{12} + 630 x^{11} + 1268 x^{10} - 931 x^{9} - 1322 x^{8} + 732 x^{7} + 728 x^{6} - 302 x^{5} - 200 x^{4} + 59 x^{3} + 24 x^{2} - 4 x - 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 5^{9}\cdot 19^{6}\cdot 37^{6}$ |
$4$ |
$31.5614374187$ |
$153.73577043029613$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$2$ |
$17$ |
$37555765.5049$ |
| 18.0.360...312.1 |
$x^{18} - 6 x^{17} + 15 x^{16} + 21 x^{15} - 189 x^{14} + 447 x^{13} - 277 x^{12} - 819 x^{11} + 2771 x^{10} - 6116 x^{9} + 8916 x^{8} - 5025 x^{7} + 13003 x^{6} - 24345 x^{5} + 9437 x^{4} - 22214 x^{3} + 36967 x^{2} + 19033 x + 93919$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 11^{14}$ |
$4$ |
$33.9561721168$ |
$74.21184385155381$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$1305071.139073367$ |
| 18.0.650...928.1 |
$x^{18} - 25 x^{15} + 252 x^{12} - 1245 x^{9} + 2786 x^{6} - 1715 x^{3} + 343$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 7^{6}\cdot 11^{6}$ |
$4$ |
$35.0912458715$ |
$127.78813364145171$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$2374820.8449431765$ |
| 18.0.214...112.1 |
$x^{18} - 6 x^{17} + 3 x^{16} + 36 x^{15} - 72 x^{14} + 24 x^{13} + 677 x^{12} - 2154 x^{11} + 650 x^{10} - 12520 x^{9} + 93111 x^{8} - 184794 x^{7} + 51751 x^{6} + 253950 x^{5} - 276628 x^{4} - 32494 x^{3} + 217588 x^{2} - 143080 x + 34300$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{9}\cdot 7^{6}\cdot 13^{10}$ |
$4$ |
$37.4919903721$ |
$138.44717539350094$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$21541865.688527487$ |
| 18.0.376...192.1 |
$x^{18} - 5 x^{16} - 16 x^{15} - 20 x^{14} + 152 x^{13} + 370 x^{12} + 32 x^{11} - 2786 x^{10} - 3960 x^{9} + 13300 x^{8} + 14472 x^{7} - 12096 x^{6} - 79632 x^{5} + 22194 x^{4} + 192240 x^{3} - 108675 x^{2} - 139320 x + 106677$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{9}\cdot 67^{10}$ |
$3$ |
$38.6833789156$ |
$145.0985114774686$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$306761663.9033038$ |
| 18.0.457...632.1 |
$x^{18} - 3 x^{17} + 21 x^{16} - 42 x^{15} + 189 x^{14} - 237 x^{13} + 963 x^{12} - 438 x^{11} + 3060 x^{10} + 1234 x^{9} + 7878 x^{8} + 8448 x^{7} + 16185 x^{6} + 21609 x^{5} + 25599 x^{4} + 24864 x^{3} + 19005 x^{2} + 10773 x + 2779$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{31}\cdot 7^{10}$ |
$3$ |
$39.1054902068$ |
$103.00172615951683$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$118048197.30834381$ |
| 18.0.137...000.1 |
$x^{18} - 5 x^{15} + 76 x^{12} - 715 x^{9} + 2632 x^{6} - 1785 x^{3} + 343$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 5^{6}\cdot 7^{10}$ |
$4$ |
$41.5774125159$ |
$119.15955157499168$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$13242502.889658673$ |
| 18.0.182...528.1 |
$x^{18} - 6 x^{17} + 6 x^{16} + 78 x^{15} - 48 x^{14} - 720 x^{13} + 27 x^{12} + 3312 x^{11} + 2754 x^{10} - 7740 x^{9} - 13158 x^{8} - 5742 x^{7} + 11037 x^{6} + 43218 x^{5} + 76230 x^{4} + 77742 x^{3} + 51030 x^{2} + 21546 x + 5061$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{31}\cdot 7^{10}$ |
$3$ |
$42.236265542$ |
$84.59223933509352$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3, 3]$ |
$6$ |
$8$ |
$12168177.008988433$ |
| 18.0.191...352.1 |
$x^{18} - 5 x^{15} + 40 x^{12} + x^{9} + 608 x^{6} + 3819 x^{3} + 6859$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 19^{10}$ |
$3$ |
$42.343544876$ |
$95.9393002744187$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$24473773.67715159$ |
| 18.0.195...008.1 |
$x^{18} - 3 x^{17} - 21 x^{16} + 54 x^{15} + 228 x^{14} - 504 x^{13} - 1012 x^{12} + 2040 x^{11} + 4523 x^{10} - 6703 x^{9} - 1497 x^{8} + 252 x^{7} + 34702 x^{6} - 21324 x^{5} + 57104 x^{4} - 90118 x^{3} + 127507 x^{2} + 22997 x + 160003$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{9}\cdot 79^{10}$ |
$3$ |
$42.3911963506$ |
$166.45232445421618$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$24722362.03581395$ |
| 18.0.200...152.1 |
$x^{18} - 3 x^{17} - 25 x^{16} + 97 x^{15} + 324 x^{14} - 1424 x^{13} - 2893 x^{12} + 12134 x^{11} + 25059 x^{10} - 36958 x^{9} - 87068 x^{8} + 95416 x^{7} + 313237 x^{6} + 151945 x^{5} - 220562 x^{4} - 362142 x^{3} - 140268 x^{2} + 158994 x + 138087$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 7^{10}\cdot 13^{10}$ |
$4$ |
$42.456770097$ |
$210.20358299362027$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$187527338.95768923$ |
| 18.0.200...152.2 |
$x^{18} - 3 x^{17} + 10 x^{16} - 9 x^{15} - 7 x^{14} + 118 x^{13} + 42 x^{12} - 536 x^{11} + 2032 x^{10} - 3800 x^{9} + 4088 x^{8} + 1616 x^{7} - 9680 x^{6} + 16256 x^{5} - 2176 x^{4} - 33024 x^{3} + 44288 x^{2} - 22528 x + 4096$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 7^{10}\cdot 13^{10}$ |
$4$ |
$42.456770097$ |
$210.20358299362027$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$297602831.7716659$ |
| 18.0.204...368.1 |
$x^{18} - 3 x^{17} + 9 x^{16} - 57 x^{15} + 143 x^{14} - 3 x^{13} + 1674 x^{12} + 1233 x^{11} + 5724 x^{10} + 2007 x^{9} + 10875 x^{8} + 1305 x^{7} + 10340 x^{6} + 858 x^{5} + 5358 x^{4} + 381 x^{3} + 1558 x^{2} + 165 x + 183$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 43^{10}$ |
$4$ |
$42.5039324927$ |
$231.1371199229907$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$55890127.22994664$ |
| 18.0.217...368.1 |
$x^{18} + 11 x^{16} - 18 x^{15} + 68 x^{14} + 70 x^{13} + 533 x^{12} + 1100 x^{11} + 580 x^{10} + 7210 x^{9} + 16613 x^{8} + 59948 x^{7} + 60667 x^{6} + 137522 x^{5} + 142906 x^{4} + 494826 x^{3} + 675168 x^{2} - 1634408 x + 1185076$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 139^{10}$ |
$3$ |
$42.6393984453$ |
$167.9163394069419$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3, 3]$ |
$6$ |
$8$ |
$9350988.404859575$ |
| 18.0.275...672.1 |
$x^{18} - 8 x^{15} + 43 x^{12} - 148 x^{9} + 559 x^{6} + 2652 x^{3} + 2197$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{27}\cdot 13^{10}$ |
$3$ |
$43.2085105283$ |
$159.0522979201057$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$311678005.927199$ |
| 18.0.520...152.1 |
$x^{18} - 30 x^{15} + 360 x^{12} - 1672 x^{9} + 6720 x^{6} - 6048 x^{3} + 21952$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{37}\cdot 7^{10}$ |
$3$ |
$44.7646116017$ |
$76.8571500447917$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$36855368.88515014$ |
| 18.0.520...152.2 |
$x^{18} - 12 x^{15} + 87 x^{12} - 848 x^{9} + 7392 x^{6} - 18816 x^{3} + 21952$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{37}\cdot 7^{10}$ |
$3$ |
$44.7646116017$ |
$118.68160094629725$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$174512587.28025168$ |
| 18.0.569...048.2 |
$x^{18} - 57 x^{15} + 954 x^{12} - 3931 x^{9} + 6396 x^{6} - 4563 x^{3} + 2197$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{37}\cdot 13^{6}$ |
$3$ |
$44.9876898333$ |
$149.59708836062785$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$81283585.10862277$ |
| 18.0.143...392.1 |
$x^{18} - 9 x^{17} + 63 x^{16} - 279 x^{15} + 1026 x^{14} - 3024 x^{13} + 8037 x^{12} - 18900 x^{11} + 38367 x^{10} - 63180 x^{9} + 86670 x^{8} - 99792 x^{7} + 70551 x^{6} + 84807 x^{5} - 319788 x^{4} + 302292 x^{3} + 122472 x^{2} - 418446 x + 226233$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{31}\cdot 7^{6}\cdot 13^{6}$ |
$4$ |
$47.3597377425$ |
$167.0766381803499$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$246972334.17984632$ |
| 18.0.297...003.1 |
$x^{18} - 6 x^{17} + 39 x^{16} - 150 x^{15} + 669 x^{14} - 1584 x^{13} + 4191 x^{12} - 10746 x^{11} + 16053 x^{10} - 31018 x^{9} + 54399 x^{8} - 57408 x^{7} + 104028 x^{6} - 119904 x^{5} + 49968 x^{4} - 132864 x^{3} + 112896 x^{2} + 43008 x + 4096$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 37^{10}$ |
$2$ |
$49.3096599564$ |
$134.44467252061932$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$810773555.0000257$ |
| 18.18.445...000.1 |
$x^{18} - 42 x^{16} - 6 x^{15} + 621 x^{14} + 174 x^{13} - 4243 x^{12} - 1224 x^{11} + 14907 x^{10} + 2716 x^{9} - 27504 x^{8} - 90 x^{7} + 24358 x^{6} - 4302 x^{5} - 7317 x^{4} + 1174 x^{3} + 657 x^{2} + 42 x - 1$ |
$18$ |
[18,0] |
$2^{33}\cdot 3^{24}\cdot 5^{6}\cdot 7^{6}$ |
$4$ |
$50.4358502357$ |
$126.16348990930013$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$2$ |
$17$ |
$3927677460.06$ |
| 18.0.521...000.1 |
$x^{18} - 9 x^{17} + 33 x^{16} - 27 x^{15} - 189 x^{14} + 717 x^{13} - 1142 x^{12} + 597 x^{11} + 1758 x^{10} - 7263 x^{9} + 16119 x^{8} - 23991 x^{7} + 28780 x^{6} - 25590 x^{5} + 9324 x^{4} - 4725 x^{3} + 8820 x^{2} + 17199 x + 9261$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 7^{6}\cdot 181^{6}$ |
$5$ |
$50.8740326311$ |
$520.4755864719621$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$1263791154.7914963$ |
| 18.0.563...448.1 |
$x^{18} - 3 x^{17} - 2 x^{16} + 27 x^{15} - 63 x^{14} - 182 x^{13} + 326 x^{12} + 24 x^{11} + 1072 x^{10} + 3160 x^{9} + 1576 x^{8} + 3344 x^{7} + 7792 x^{6} + 7808 x^{5} + 30080 x^{4} + 60160 x^{3} + 60672 x^{2} + 26624 x + 4096$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 127^{10}$ |
$3$ |
$51.0940663937$ |
$277.50792385820444$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[2]$ |
$6$ |
$8$ |
$621058194.3189892$ |
| 18.0.753...968.1 |
$x^{18} - 2 x^{17} + 3 x^{16} - 58 x^{15} + 197 x^{14} - 42 x^{13} - 644 x^{12} + 370 x^{11} + 2172 x^{10} - 4392 x^{9} + 3635 x^{8} - 2080 x^{7} + 1995 x^{6} - 2114 x^{5} + 1387 x^{4} - 534 x^{3} + 122 x^{2} - 16 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{14}\cdot 13^{10}$ |
$4$ |
$51.9281899384$ |
$117.97277216449416$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3, 3]$ |
$6$ |
$8$ |
$35319007.470736034$ |
| 18.0.101...083.1 |
$x^{18} - 3 x^{17} - 27 x^{16} + 54 x^{15} + 354 x^{14} - 426 x^{13} - 2956 x^{12} + 1716 x^{11} + 18452 x^{10} + 7658 x^{9} - 32814 x^{8} - 114078 x^{7} + 30115 x^{6} + 394695 x^{5} + 97727 x^{4} - 771736 x^{3} + 26068 x^{2} + 309680 x + 134848$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 7^{10}\cdot 67^{10}$ |
$3$ |
$52.7892558523$ |
$291.43250970131453$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[9]$ |
$6$ |
$8$ |
$448034530.39626753$ |
| 18.0.122...528.1 |
$x^{18} - 16 x^{15} + 649 x^{12} + 5872 x^{9} + 19627 x^{6} - 1824 x^{3} + 6859$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{27}\cdot 19^{10}$ |
$3$ |
$53.3495235165$ |
$170.94439926752142$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$550424662.0359514$ |
| 18.0.186...032.1 |
$x^{18} - 2 x^{17} + 16 x^{16} - 114 x^{15} + 486 x^{14} - 1617 x^{13} + 5983 x^{12} - 21824 x^{11} + 61120 x^{10} - 124458 x^{9} + 193737 x^{8} - 252336 x^{7} + 307981 x^{6} - 344420 x^{5} + 321958 x^{4} - 236085 x^{3} + 139299 x^{2} - 130761 x + 126963$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{10}\cdot 31^{10}$ |
$4$ |
$54.6110436956$ |
$243.38682724932116$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$4121877351.3792276$ |
| 18.0.517...288.1 |
$x^{18} - 6 x^{17} + 24 x^{16} - 78 x^{15} + 216 x^{14} - 714 x^{13} + 2135 x^{12} - 5022 x^{11} + 7298 x^{10} - 686 x^{9} - 15438 x^{8} + 30174 x^{7} + 19897 x^{6} - 100260 x^{5} + 3110 x^{4} + 71956 x^{3} + 25906 x^{2} + 1900 x + 703$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{9}\cdot 19^{6}\cdot 97^{6}$ |
$4$ |
$57.7949879181$ |
$567.9894155463887$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$511066585.49785817$ |
| 18.0.683...848.1 |
$x^{18} - 6 x^{17} + 7 x^{16} + 5 x^{15} - 123 x^{14} + 2007 x^{13} - 10303 x^{12} + 16857 x^{11} + 45543 x^{10} - 311864 x^{9} + 844354 x^{8} - 1438355 x^{7} + 1685627 x^{6} - 1365187 x^{5} + 739367 x^{4} - 280422 x^{3} + 121521 x^{2} - 68391 x + 19363$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 163^{10}$ |
$3$ |
$58.6926524368$ |
$341.6609083592211$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[2]$ |
$6$ |
$8$ |
$272590163.0199287$ |
| 18.0.761...000.1 |
$x^{18} - 6 x^{16} - 12 x^{15} - 45 x^{14} - 48 x^{13} + 660 x^{12} + 6267 x^{10} - 1024 x^{9} + 19710 x^{8} - 9060 x^{7} + 11553 x^{6} - 13680 x^{5} - 65244 x^{4} + 29136 x^{3} - 73008 x^{2} + 32448 x + 140608$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{31}\cdot 5^{6}\cdot 7^{6}$ |
$4$ |
$59.0499155081$ |
$193.41085663551166$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3, 3]$ |
$6$ |
$8$ |
$292071104.75417435$ |
| 18.0.126...512.1 |
$x^{18} - 6 x^{17} + 26 x^{16} - 82 x^{15} + 172 x^{14} - 156 x^{13} - 2102 x^{12} + 10416 x^{11} - 12604 x^{10} - 17892 x^{9} + 56416 x^{8} - 53392 x^{7} + 52964 x^{6} - 115936 x^{5} + 291840 x^{4} - 625664 x^{3} + 892928 x^{2} - 655360 x + 262144$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 47^{6}$ |
$5$ |
$60.7320792965$ |
$437.6841356646234$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$1209162608.4915006$ |
| 18.0.127...408.1 |
$x^{18} - 3 x^{17} + 10 x^{16} + 91 x^{15} + 151 x^{14} + 34 x^{13} + 3415 x^{12} + 14395 x^{11} + 29125 x^{10} - 21192 x^{9} - 97073 x^{8} - 90513 x^{7} + 153009 x^{6} + 344700 x^{5} - 49059 x^{4} - 421497 x^{3} - 92718 x^{2} + 222021 x + 111051$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{9}\cdot 151^{10}$ |
$3$ |
$60.7548773995$ |
$285.5933413976806$ |
|
|
|
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$45444000566.5836$ |
| 18.0.150...448.1 |
$x^{18} - 7 x^{15} + 226 x^{12} + 445 x^{9} + 7252 x^{6} + 17427 x^{3} + 50653$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 37^{10}$ |
$3$ |
$61.3185287299$ |
$167.1873122187818$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$430430077.0591191$ |
| 18.0.154...000.1 |
$x^{18} - 11 x^{16} - 75 x^{15} + 321 x^{14} + 147 x^{13} + 641 x^{12} - 11589 x^{11} + 15447 x^{10} + 30186 x^{9} - 55196 x^{8} - 52869 x^{7} + 188785 x^{6} + 172251 x^{5} + 49959 x^{4} + 210708 x^{3} + 285795 x^{2} + 30537 x + 1161$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 13^{10}\cdot 31^{6}$ |
$5$ |
$61.4066315858$ |
$514.3509537200081$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
$[3]$ |
$6$ |
$8$ |
$1503257555.4600825$ |
| 18.0.172...168.1 |
$x^{18} - 3 x^{17} - 5 x^{16} + 51 x^{15} - 122 x^{14} - 612 x^{13} + 1167 x^{12} - 306 x^{11} + 4617 x^{10} + 27540 x^{9} + 20628 x^{8} + 39366 x^{7} + 164835 x^{6} + 227691 x^{5} + 857304 x^{4} + 2226366 x^{3} + 3332988 x^{2} + 2243862 x + 531441$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 271^{10}$ |
$3$ |
$61.7869698591$ |
$292.90157041882645$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$6$ |
$8$ |
$3453478086.089924$ |
