| 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 $p$ |
| 15.3.2581408254768721.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 11 x^{12} - 4 x^{11} - 19 x^{10} + 24 x^{9} + 6 x^{8} - 29 x^{7} + 13 x^{6} + 13 x^{5} - 14 x^{4} - x^{3} + 5 x^{2} - x - 1$ |
$15$ |
(3, 6) |
$7^{10}\cdot 3023^{2}$ |
$2$ |
$10.652636625745691$ |
$201.19527021937301$ |
|
|
✓ |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$33.36148075197536$ |
$3$ |
|
| 15.3.3187134619912369.1 |
$x^{15} - x^{14} - 3 x^{13} + 5 x^{12} + 3 x^{11} - 9 x^{10} - x^{9} + 8 x^{8} + 4 x^{7} - 7 x^{6} - 9 x^{5} + 5 x^{4} + 9 x^{3} - x^{2} - 4 x - 1$ |
$15$ |
(3, 6) |
$7^{10}\cdot 3359^{2}$ |
$2$ |
$10.803389325352759$ |
$212.08194383428116$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$37.83417450489708$ |
$3$ |
|
| 15.3.5318139197378329.1 |
$x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 12 x^{11} - 22 x^{10} + 20 x^{9} - 34 x^{8} + 27 x^{7} - 36 x^{6} + 22 x^{5} - 17 x^{4} + 5 x^{3} - x + 1$ |
$15$ |
(3, 6) |
$7^{10}\cdot 4339^{2}$ |
$2$ |
$11.178511553825736$ |
$241.04244193574246$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$52.4584251761628$ |
$3$ |
|
| 15.3.304...921.1 |
$x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{11} + 12 x^{10} + 37 x^{9} + 2 x^{8} + 37 x^{7} - 37 x^{6} - 39 x^{5} + 47 x^{4} - 22 x^{3} + 6 x^{2} - 1$ |
$15$ |
(3, 6) |
$7^{10}\cdot 47^{6}$ |
$2$ |
$17.0701696183$ |
$25.086936025192795$ |
|
|
? |
$D_5\times C_3$ (as 15T3) |
trivial |
trivial |
$2$ |
$8$ |
$1650.39003052$ |
$3$ |
|
| 15.15.886...529.1 |
$x^{15} - x^{14} - 22 x^{13} + 17 x^{12} + 166 x^{11} - 102 x^{10} - 533 x^{9} + 270 x^{8} + 729 x^{7} - 352 x^{6} - 393 x^{5} + 173 x^{4} + 80 x^{3} - 27 x^{2} - 6 x + 1$ |
$15$ |
(15, 0) |
$7^{10}\cdot 11^{12}$ |
$2$ |
$24.9179804908$ |
$24.91798049084744$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$14$ |
$286717.64844$ |
$11$ |
|
| 15.15.117...849.1 |
$x^{15} - x^{14} - 27 x^{13} + 22 x^{12} + 230 x^{11} - 157 x^{10} - 760 x^{9} + 399 x^{8} + 1014 x^{7} - 476 x^{6} - 540 x^{5} + 238 x^{4} + 94 x^{3} - 33 x^{2} - 6 x + 1$ |
$15$ |
(15, 0) |
$7^{10}\cdot 401^{6}$ |
$2$ |
$40.2398582683$ |
$73.27753973791762$ |
|
|
? |
$D_5\times C_3$ (as 15T3) |
trivial |
trivial |
$2$ |
$14$ |
$13124357.1833$ |
$15$ |
|
| 15.3.669...664.1 |
$x^{15} - 7 x^{14} + 6 x^{13} + 40 x^{12} - 102 x^{11} + 12 x^{10} - 120 x^{9} - 56 x^{8} + 863 x^{7} - 1541 x^{6} - 780 x^{5} - 4768 x^{4} - 2933 x^{3} - 1795 x^{2} - 316 x - 20$ |
$15$ |
(3, 6) |
$2^{18}\cdot 7^{10}\cdot 67^{6}$ |
$3$ |
$45.19231711829813$ |
$84.7190521533498$ |
|
|
|
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$[3]$ |
$2$ |
$8$ |
$14068105.95552779$ |
$3$ |
|
| 15.5.144...000.1 |
$x^{15} + 5 x^{11} - 4 x^{10} - 50 x^{7} + 80 x^{6} - 32 x^{5} - 125 x^{3} + 300 x^{2} - 240 x + 64$ |
$15$ |
(5, 5) |
$-\,2^{24}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$55.4647028661$ |
|
|
|
? |
$S_5\wr C_3$ (as 15T101) |
trivial |
trivial |
$2$ |
$9$ |
$20873442.6932$ |
$5$ |
|
| 15.15.222...489.1 |
$x^{15} - 2 x^{14} - 47 x^{13} + 44 x^{12} + 796 x^{11} - 86 x^{10} - 5782 x^{9} - 2469 x^{8} + 18376 x^{7} + 14370 x^{6} - 21477 x^{5} - 22698 x^{4} + 4468 x^{3} + 10091 x^{2} + 2903 x + 211$ |
$15$ |
(15, 0) |
$7^{10}\cdot 31^{12}$ |
$2$ |
$57.0805367648$ |
$57.08053676475076$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
trivial |
$2$ |
$14$ |
$109278274.626$ |
$15$ |
|
| 15.15.637...169.1 |
$x^{15} - 2 x^{14} - 59 x^{13} + 150 x^{12} + 1100 x^{11} - 3368 x^{10} - 7356 x^{9} + 29167 x^{8} + 10106 x^{7} - 98196 x^{6} + 44261 x^{5} + 92292 x^{4} - 57764 x^{3} - 27115 x^{2} + 17047 x + 547$ |
$15$ |
(15, 0) |
$7^{10}\cdot 41^{12}$ |
$2$ |
$71.3880926669$ |
$71.38809266691113$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
trivial |
$2$ |
$14$ |
$873491470.835$ |
$15$ |
|
| 15.1.498...087.2 |
$x^{15} - 6 x^{14} - 87 x^{13} + 56 x^{12} + 5256 x^{11} + 16104 x^{10} - 117682 x^{9} - 951987 x^{8} - 742920 x^{7} + 16279090 x^{6} + 74985069 x^{5} + 49035396 x^{4} - 662107104 x^{3} - 2765333427 x^{2} - 4944661743 x - 3899468411$ |
$15$ |
(1, 7) |
$-\,3^{20}\cdot 7^{10}\cdot 47^{7}$ |
$3$ |
$95.47127005054602$ |
$108.54486810799125$ |
|
|
? |
$D_{15}$ (as 15T2) |
$[3, 3]$ |
$[3, 3]$ |
$2$ |
$7$ |
$86102572.9234292$ |
$1$ |
|
| 15.15.749...929.1 |
$x^{15} - 2 x^{14} - 83 x^{13} + 140 x^{12} + 2380 x^{11} - 3320 x^{10} - 29682 x^{9} + 34801 x^{8} + 167356 x^{7} - 161206 x^{6} - 393515 x^{5} + 250272 x^{4} + 359552 x^{3} - 96207 x^{2} - 115927 x - 9659$ |
$15$ |
(15, 0) |
$7^{10}\cdot 61^{12}$ |
$2$ |
$98.0985439587$ |
$98.09854395869841$ |
|
✓ |
|
$C_{15}$ (as 15T1) |
trivial |
trivial |
$2$ |
$14$ |
$32336716619.23167$ |
$15$ |
|
| 15.15.463...009.1 |
$x^{15} - 2 x^{14} - 95 x^{13} + 330 x^{12} + 2696 x^{11} - 13890 x^{10} - 14576 x^{9} + 183885 x^{8} - 244262 x^{7} - 421848 x^{6} + 1178315 x^{5} - 361390 x^{4} - 1098512 x^{3} + 1025879 x^{2} - 229827 x - 2911$ |
$15$ |
(15, 0) |
$7^{10}\cdot 71^{12}$ |
$2$ |
$110.765719355$ |
$110.76571935476852$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
trivial |
$2$ |
$14$ |
$26670515863.43193$ |
$15$ |
|
| 15.15.475...625.1 |
$x^{15} - 110 x^{13} - 145 x^{12} + 3950 x^{11} + 8819 x^{10} - 52050 x^{9} - 157290 x^{8} + 188340 x^{7} + 892410 x^{6} + 147955 x^{5} - 1649225 x^{4} - 1204580 x^{3} + 485235 x^{2} + 578100 x + 84419$ |
$15$ |
(15, 0) |
$5^{24}\cdot 7^{10}\cdot 41^{4}$ |
$3$ |
$129.367860383$ |
$1739.331119698566$ |
|
|
? |
$C_5\wr C_3$ (as 15T25) |
trivial |
trivial |
$2$ |
$14$ |
$94377547844.7$ |
$15$ |
|
| 15.15.475...625.2 |
$x^{15} - 110 x^{13} - 5 x^{12} + 3825 x^{11} - 894 x^{10} - 54550 x^{9} + 28465 x^{8} + 350165 x^{7} - 261960 x^{6} - 994230 x^{5} + 947100 x^{4} + 1004295 x^{3} - 1183260 x^{2} - 36900 x + 189461$ |
$15$ |
(15, 0) |
$5^{24}\cdot 7^{10}\cdot 41^{4}$ |
$3$ |
$129.367860383$ |
$1739.331119698566$ |
|
|
? |
$C_5\wr C_3$ (as 15T25) |
trivial |
trivial |
$2$ |
$14$ |
$78914062103.7$ |
$15$ |
|
| 15.1.145...000.1 |
$x^{15} - 3 x^{14} + 56 x^{13} - 40 x^{12} + 1313 x^{11} + 1645 x^{10} + 23526 x^{9} + 60814 x^{8} + 448956 x^{7} + 1131964 x^{6} + 5118440 x^{5} + 10233032 x^{4} + 27247040 x^{3} + 38644224 x^{2} + 50848768 x + 46155264$ |
$15$ |
(1, 7) |
$-\,2^{21}\cdot 5^{7}\cdot 7^{10}\cdot 11^{12}$ |
$4$ |
$139.36086632361796$ |
$157.59514608543674$ |
|
|
|
$D_{15}$ (as 15T2) |
$[15]$ |
$[15]$ |
$2$ |
$7$ |
$1496162404931.6238$ |
$1$ |
|
| 15.15.318...049.1 |
$x^{15} - 2 x^{14} - 131 x^{13} + 582 x^{12} + 4862 x^{11} - 37014 x^{10} + 4666 x^{9} + 624063 x^{8} - 2105658 x^{7} + 1891060 x^{6} + 3272277 x^{5} - 8403710 x^{4} + 5121648 x^{3} + 1384213 x^{2} - 2005313 x + 229963$ |
$15$ |
(15, 0) |
$7^{10}\cdot 101^{12}$ |
$2$ |
$146.843860114$ |
$146.84386011427227$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$14$ |
$163490942894.50964$ |
$11$ |
|
| 15.15.664...064.1 |
$x^{15} - 5 x^{14} - 97 x^{13} + 473 x^{12} + 2481 x^{11} - 13381 x^{10} - 15393 x^{9} + 124473 x^{8} - 25813 x^{7} - 367383 x^{6} + 182005 x^{5} + 402515 x^{4} - 197917 x^{3} - 110047 x^{2} + 54733 x - 3877$ |
$15$ |
(15, 0) |
$2^{12}\cdot 7^{10}\cdot 13^{4}\cdot 83^{2}\cdot 293^{2}\cdot 18439^{2}$ |
$6$ |
$179.817516029$ |
$790236.1655745264$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$2157836539700$ |
$13$ |
|
| 15.15.721...289.1 |
$x^{15} - 2 x^{14} - 167 x^{13} + 120 x^{12} + 9848 x^{11} + 4506 x^{10} - 239054 x^{9} - 327645 x^{8} + 2072932 x^{7} + 3866574 x^{6} - 4736545 x^{5} - 10718242 x^{4} - 764276 x^{3} + 3000575 x^{2} - 692889 x + 42491$ |
$15$ |
(15, 0) |
$7^{10}\cdot 131^{12}$ |
$2$ |
$180.807203813$ |
$180.80720381330573$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
trivial |
$2$ |
$14$ |
$876762315058.978$ |
$15$ |
|
| 15.11.721...896.1 |
$x^{15} - 4 x^{14} - 201 x^{13} + 121 x^{12} + 12616 x^{11} + 34020 x^{10} - 207932 x^{9} - 1372760 x^{8} - 2713681 x^{7} + 1113480 x^{6} + 16513183 x^{5} + 35754551 x^{4} + 36074673 x^{3} + 12241538 x^{2} - 11026275 x - 10525969$ |
$15$ |
(11, 2) |
$2^{12}\cdot 7^{10}\cdot 13^{3}\cdot 29^{2}\cdot 97^{3}\cdot 192263^{2}$ |
$6$ |
$210.800450914$ |
$6150130.864484555$ |
|
|
? |
$F_5\wr C_3$ (as 15T75) |
trivial |
trivial |
$2$ |
$12$ |
$1804860014880$ |
$11$ |
|
| 15.7.432...000.1 |
$x^{15} - 5 x^{11} - 4 x^{10} - 1100 x^{7} - 1760 x^{6} - 704 x^{5} + 8000 x^{3} + 19200 x^{2} + 15360 x + 4096$ |
$15$ |
(7, 4) |
$2^{14}\cdot 5^{16}\cdot 7^{10}\cdot 19^{10}$ |
$4$ |
$276.968531193$ |
$1345.9069739259899$ |
|
|
|
$A_5^3.A_4$ (as 15T98) |
$[3]$ |
$[3]$ |
$2$ |
$10$ |
$190235235181000$ |
$7$ |
|
| 15.7.199...000.1 |
$x^{15} - 110 x^{13} - 180 x^{12} + 3485 x^{11} + 7528 x^{10} - 41050 x^{9} - 185620 x^{8} + 693510 x^{7} + 2174580 x^{6} - 16746956 x^{5} + 18406300 x^{4} + 87814465 x^{3} - 146316600 x^{2} - 82482960 x + 86138816$ |
$15$ |
(7, 4) |
$2^{24}\cdot 5^{24}\cdot 7^{10}\cdot 29^{4}$ |
$4$ |
$357.578577848$ |
|
|
|
? |
$A_5^3.A_4$ (as 15T98) |
trivial |
trivial |
$2$ |
$10$ |
$41444248102300$ |
$7$ |
|
| 15.7.695...000.1 |
$x^{15} - 180 x^{13} - 144 x^{12} + 6684 x^{11} + 22688 x^{10} - 62424 x^{9} - 624384 x^{8} + 10372064 x^{7} + 60653056 x^{6} + 29354240 x^{5} - 267264000 x^{4} - 302528000 x^{3} + 277657600 x^{2} + 415744000 x + 118784000$ |
$15$ |
(7, 4) |
$2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 29^{4}\cdot 921789289^{2}$ |
$5$ |
$615.856756381$ |
$17475733.482182756$ |
|
|
|
$A_5\wr C_3$ (as 15T92) |
$[3]$ |
$[3]$ |
$2$ |
$10$ |
$658851832895000$ |
$7$ |
|
| 15.11.145...000.1 |
$x^{15} - 360 x^{13} - 648 x^{12} + 39784 x^{11} + 127584 x^{10} - 1599876 x^{9} - 6284088 x^{8} + 21382724 x^{7} + 72393848 x^{6} + 18576960 x^{5} - 80928000 x^{4} - 45803000 x^{3} + 21018800 x^{2} + 15736000 x + 2248000$ |
$15$ |
(11, 2) |
$2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 281^{4}\cdot 44850007^{2}$ |
$5$ |
$754.129698025$ |
$19515640.66436397$ |
|
|
? |
$A_5\wr C_3$ (as 15T92) |
$[3]$ |
$[3]$ |
$2$ |
$12$ |
$8314234047450000$ |
$11$ |
|
| 15.11.155...000.1 |
$x^{15} + 36 x^{13} - 144 x^{12} - 32503 x^{11} + 261104 x^{10} - 2848725 x^{9} + 25958664 x^{8} - 124445806 x^{7} + 333271318 x^{6} - 536215885 x^{5} + 540397440 x^{4} - 344500525 x^{3} + 135184650 x^{2} - 29851500 x + 2843000$ |
$15$ |
(11, 2) |
$2^{12}\cdot 5^{6}\cdot 7^{10}\cdot 13^{2}\cdot 71^{2}\cdot 337^{2}\cdot 2843^{4}\cdot 116719^{2}$ |
$8$ |
$2587.10631179$ |
$3313774907.813876$ |
|
|
? |
$A_5^3.A_4$ (as 15T98) |
trivial |
trivial |
$2$ |
$12$ |
$263754998565000000000$ |
$11$ |
|
| 15.11.380...000.1 |
$x^{15} - 54 x^{13} - 864 x^{12} - 909588 x^{11} - 29003136 x^{10} - 655037640 x^{9} - 16826161536 x^{8} - 301773467776 x^{7} - 3198404365312 x^{6} - 20553073039360 x^{5} - 82841158287360 x^{4} - 211243210342400 x^{3} - 331573827993600 x^{2} - 292872781824000 x - 111570583552000$ |
$15$ |
(11, 2) |
$2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 337\cdot 53201^{4}\cdot 1103777641^{2}$ |
$6$ |
$6897.5391538$ |
$85196209371.05563$ |
|
|
|
$S_5\wr C_3$ (as 15T101) |
trivial |
trivial |
$2$ |
$12$ |
$473856133750000000000000$ |
$11$ |
|
| 15.15.919...000.1 |
$x^{15} - 2691 x^{13} - 21528 x^{12} + 2027042 x^{11} + 33078512 x^{10} - 224467605 x^{9} - 9558128952 x^{8} - 99741836916 x^{7} - 540865750896 x^{6} - 1743471235440 x^{5} - 3514728222720 x^{4} - 4481241502400 x^{3} - 3516947116800 x^{2} - 1553225856000 x - 295852544000$ |
$15$ |
(15, 0) |
$2^{15}\cdot 5^{6}\cdot 7^{10}\cdot 13^{4}\cdot 827^{2}\cdot 44449^{4}\cdot 28872271^{2}$ |
$7$ |
$11593.9025041$ |
$244702660350.29828$ |
|
|
|
$A_5^3:C_6$ (as 15T95) |
trivial |
trivial |
$2$ |
$14$ |
$63171683869200000000000000$ |
$15$ |
|
| 16.0.126...576.1 |
$x^{16} - 2 x^{15} + 42 x^{14} - 174 x^{13} + 830 x^{12} - 3498 x^{11} + 9410 x^{10} - 26270 x^{9} + 28950 x^{8} - 19962 x^{7} + 22478 x^{6} + 263962 x^{5} + 902098 x^{4} - 2488322 x^{3} + 10518070 x^{2} - 17074302 x + 8328959$ |
$16$ |
(0, 8) |
$2^{30}\cdot 7^{10}\cdot 401^{6}$ |
$3$ |
$117.16466540290409$ |
$268.7832008630457$ |
|
|
? |
$F_{16}:C_2$ (as 16T777) |
trivial |
trivial |
$2$ |
$7$ |
$36850361303.18397$ |
$0$ |
|
| 16.16.111...496.1 |
$x^{16} - 2 x^{15} - 428 x^{14} + 1320 x^{13} + 62092 x^{12} - 220480 x^{11} - 3633464 x^{10} + 12204344 x^{9} + 81935950 x^{8} - 175605868 x^{7} - 729549480 x^{6} + 168712188 x^{5} + 1147884592 x^{4} - 3407876 x^{3} - 91633952 x^{2} + 2724436 x + 1022790$ |
$16$ |
(16, 0) |
$2^{30}\cdot 7^{10}\cdot 11^{12}\cdot 43^{8}$ |
$4$ |
$490.225906804$ |
$599.346965909669$ |
|
|
? |
$F_{16}$ (as 16T447) |
trivial |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$15$ |
$99361010062300000$ |
$10$ |
|
| 18.6.328...536.1 |
$x^{18} - 2 x^{17} + 7 x^{16} - 14 x^{15} - 4 x^{14} - 24 x^{13} - 169 x^{12} + 16 x^{11} - 509 x^{10} + 220 x^{9} - 545 x^{8} + 402 x^{7} - 49 x^{6} + 16 x^{5} + 74 x^{4} - 32 x^{3} + 16 x^{2} - 4 x - 1$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{12}\cdot 67^{6}$ |
$3$ |
$29.724892311$ |
$84.7190521533498$ |
|
|
|
$\GL(2,4)$ (as 18T90) |
trivial |
trivial |
$2$ |
$11$ |
$3174843.46449$ |
$6$ |
|
| 18.6.328...536.2 |
$x^{18} - 10 x^{16} + 37 x^{14} - 32 x^{13} - 100 x^{12} + 92 x^{11} + 192 x^{10} - 62 x^{9} - 416 x^{8} - 46 x^{7} + 272 x^{6} + 18 x^{5} - 65 x^{4} + 10 x^{3} + 10 x^{2} - 4 x - 1$ |
$18$ |
(6, 6) |
$2^{18}\cdot 7^{12}\cdot 67^{6}$ |
$3$ |
$29.724892311$ |
$170.73670216973045$ |
|
|
|
$C_3\times A_6$ (as 18T261) |
trivial |
trivial |
$2$ |
$11$ |
$3358324.05727$ |
$6$ |
|
| 18.4.453...000.1 |
$x^{18} - 6 x^{17} + 12 x^{16} - 8 x^{15} + 10 x^{14} - 52 x^{13} + 92 x^{12} - 64 x^{11} - 184 x^{10} + 880 x^{9} - 1408 x^{8} + 1088 x^{7} - 1416 x^{6} + 3664 x^{5} - 5520 x^{4} + 4608 x^{3} - 2208 x^{2} + 576 x - 64$ |
$18$ |
(4, 7) |
$-\,2^{30}\cdot 5^{15}\cdot 7^{12}$ |
$3$ |
$44.4212071535$ |
|
|
|
? |
$S_5\wr C_3$ (as 18T953) |
trivial |
trivial |
$2$ |
$10$ |
$78965501.5477$ |
$4$ |
|
| 18.4.670...000.1 |
$x^{18} - 6 x^{13} + 5 x^{12} - 72 x^{8} + 120 x^{7} - 50 x^{6} + 216 x^{3} - 540 x^{2} + 450 x - 125$ |
$18$ |
(4, 7) |
$-\,2^{12}\cdot 3^{18}\cdot 5^{15}\cdot 7^{12}$ |
$4$ |
$66.6318107303$ |
|
|
|
? |
$S_6\wr C_3$ (as 18T974) |
trivial |
trivial |
$2$ |
$10$ |
$2406239609.49$ |
$4$ |
|
| 18.6.557...000.1 |
$x^{18} - 30 x^{13} - 25 x^{12} + 216 x^{8} + 360 x^{7} + 150 x^{6} - 216 x^{3} - 540 x^{2} - 450 x - 125$ |
$18$ |
(6, 6) |
$2^{18}\cdot 3^{18}\cdot 5^{15}\cdot 7^{12}\cdot 13$ |
$5$ |
$96.8078754395$ |
|
|
|
? |
$S_6\wr C_3$ (as 18T974) |
trivial |
trivial |
$2$ |
$11$ |
$108027015218$ |
$6$ |
|
| 18.8.274...000.1 |
$x^{18} - 30 x^{16} - 80 x^{15} - 495 x^{14} - 1344 x^{13} + 2395 x^{12} + 29160 x^{11} + 103035 x^{10} + 192800 x^{9} + 182880 x^{8} + 480 x^{7} - 134890 x^{6} - 158040 x^{5} - 91335 x^{4} - 30424 x^{3} - 4635 x^{2} + 600 x + 125$ |
$18$ |
(8, 5) |
$-\,2^{24}\cdot 3^{18}\cdot 5^{15}\cdot 7^{12}$ |
$4$ |
$105.771406448$ |
|
|
|
? |
$S_6\wr C_3$ (as 18T974) |
$[2]$ |
$[2, 2]$ |
$2$ |
$12$ |
$195498311108$ |
$7$ |
|
| 18.6.977...272.1 |
$x^{18} - x^{17} + 73 x^{16} - 180 x^{15} + 2191 x^{14} - 6877 x^{13} + 38931 x^{12} - 54130 x^{11} + 238744 x^{10} - 682492 x^{9} - 5433700 x^{8} + 25520584 x^{7} - 81853156 x^{6} + 139456292 x^{5} + 188893300 x^{4} - 1358491656 x^{3} + 2364884032 x^{2} - 1561914400 x + 238043072$ |
$18$ |
(6, 6) |
$2^{33}\cdot 3^{20}\cdot 7^{12}\cdot 11^{9}$ |
$4$ |
$146.594639144$ |
$1326.1458202583192$ |
|
|
|
$C_3\wr S_5$ (as 18T787) |
$[3]$ |
$[3]$ |
$2$ |
$11$ |
$19019199156200$ |
$6$ |
|
| 18.6.603...000.1 |
$x^{18} - 90 x^{16} - 60 x^{15} + 3375 x^{14} + 2964 x^{13} - 71120 x^{12} - 42840 x^{11} + 1038015 x^{10} + 136200 x^{9} - 11507634 x^{8} + 980340 x^{7} + 85580545 x^{6} - 33901020 x^{5} - 466085700 x^{4} + 201908256 x^{3} + 1552178160 x^{2} - 578980800 x - 2679832000$ |
$18$ |
(6, 6) |
$2^{24}\cdot 3^{18}\cdot 5^{15}\cdot 7^{12}\cdot 13^{3}$ |
$5$ |
$162.190534345$ |
|
|
|
? |
$S_6\wr C_3$ (as 18T974) |
trivial |
$[2]$ |
$2$ |
$11$ |
$11250859616100$ |
$5$ |
|
| 18.2.306...000.1 |
$x^{18} - 6 x^{17} - 3 x^{16} + 112 x^{15} - 280 x^{14} - 304 x^{13} + 2704 x^{12} - 4288 x^{11} - 20798 x^{10} + 155620 x^{9} - 370334 x^{8} - 124496 x^{7} + 2467392 x^{6} - 4137888 x^{5} - 3055080 x^{4} + 21254816 x^{3} - 34422251 x^{2} + 26634482 x - 8641543$ |
$18$ |
(2, 8) |
$2^{16}\cdot 5^{16}\cdot 7^{12}\cdot 19^{12}$ |
$4$ |
$201.739055335$ |
$1345.9069739259899$ |
|
|
|
$A_5^3.A_4$ (as 18T947) |
$[3]$ |
$[3]$ |
$2$ |
$9$ |
$219200452118000$ |
$2$ |
|
| 18.2.626...000.1 |
$x^{18} - 4 x^{17} - 4 x^{16} + 8 x^{15} + 5 x^{14} - 92 x^{13} + 8 x^{12} - 52 x^{11} - 781 x^{10} + 2340 x^{9} - 1516 x^{8} - 1896 x^{7} - 2501 x^{6} + 9172 x^{5} - 3480 x^{4} - 4524 x^{3} + 1276 x^{2} + 696 x - 232$ |
$18$ |
(2, 8) |
$2^{30}\cdot 5^{24}\cdot 7^{12}\cdot 29^{4}$ |
$4$ |
$209.919455611$ |
|
|
|
? |
$A_5^3.A_4$ (as 18T947) |
trivial |
trivial |
$2$ |
$9$ |
$45436453597100$ |
$2$ |
|
| 18.2.379...000.1 |
$x^{18} - 1494 x^{13} + 670 x^{12} + 270504 x^{8} - 2223630 x^{7} - 4205475 x^{6} + 152772696 x^{3} + 127310580 x^{2} - 1697474400 x - 2563893625$ |
$18$ |
(2, 8) |
$2^{18}\cdot 3^{18}\cdot 5^{18}\cdot 7^{12}\cdot 29^{4}$ |
$5$ |
$232.004965994$ |
|
|
|
? |
$A_6^3.A_4$ (as 18T973) |
trivial |
trivial |
$2$ |
$9$ |
$120497310049000$ |
$2$ |
|
| 18.10.242...000.1 |
$x^{18} - 75 x^{16} - 110 x^{15} + 2025 x^{14} + 8136 x^{13} - 78980 x^{12} - 264540 x^{11} + 2786745 x^{10} + 2568510 x^{9} - 32671602 x^{8} + 117158010 x^{7} + 452047795 x^{6} - 1494504180 x^{5} - 4575067740 x^{4} + 2052516664 x^{3} + 10256829090 x^{2} + 172093350 x - 6274199875$ |
$18$ |
(10, 4) |
$2^{24}\cdot 3^{18}\cdot 5^{18}\cdot 7^{12}\cdot 29^{4}$ |
$5$ |
$292.307940336$ |
|
|
|
? |
$A_6^3.A_4$ (as 18T973) |
trivial |
trivial |
$2$ |
$13$ |
$6832403275640000$ |
$10$ |
|
| 18.14.711...000.1 |
$x^{18} - 193 x^{16} - 576 x^{15} + 11295 x^{14} + 61734 x^{13} - 118219 x^{12} - 1220098 x^{11} - 361760 x^{10} + 9026552 x^{9} + 9093306 x^{8} - 22831382 x^{7} - 29637562 x^{6} - 28068852 x^{5} - 3019209 x^{4} + 222423922 x^{3} + 23646223 x^{2} - 311813394 x + 133763321$ |
$18$ |
(14, 2) |
$2^{18}\cdot 5^{6}\cdot 7^{12}\cdot 281^{4}\cdot 44850007^{2}$ |
$5$ |
$310.292647866$ |
|
|
|
? |
$A_5\wr C_3$ (as 18T911) |
trivial |
trivial |
$2$ |
$15$ |
$24784770333500000$ |
$14$ |
|
| 20.0.211...616.1 |
$x^{20} - 2 x^{19} + 2 x^{18} - 4 x^{17} + 10 x^{16} - 8 x^{15} - 2 x^{12} - 32 x^{11} + 20 x^{10} + 44 x^{9} - 28 x^{8} + 24 x^{6} - 8 x^{5} + x^{4} + 10 x^{3} + 2 x^{2} + 2$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 17^{8}$ |
$3$ |
$23.2420045598$ |
$68.42943713932411$ |
|
|
? |
$A_4\times A_5$ (as 20T147) |
trivial |
trivial |
$2$ |
$9$ |
$918494.212845$ |
$0$ |
|
| 20.0.722...936.1 |
$x^{20} - 4 x^{19} + 8 x^{18} - 12 x^{17} + 16 x^{16} - 36 x^{15} + 52 x^{14} + 16 x^{13} - 64 x^{12} - 56 x^{11} + 200 x^{10} + 192 x^{9} + 136 x^{8} + 208 x^{7} + 64 x^{6} - 96 x^{5} + 64 x^{4} + 192 x^{3} + 64 x^{2} + 32$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 47^{8}$ |
$3$ |
$34.9086582577$ |
$70.95657033042767$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
trivial |
$2$ |
$9$ |
$13684855.6842$ |
$0$ |
|
| 20.4.125...816.1 |
$x^{20} - 8 x^{18} - 22 x^{17} - 44 x^{16} + 48 x^{15} + 390 x^{14} + 878 x^{13} + 1192 x^{12} - 238 x^{11} - 5046 x^{10} - 12784 x^{9} - 21285 x^{8} - 24460 x^{7} - 18100 x^{6} - 7404 x^{5} + 738 x^{4} + 2406 x^{3} - 38 x^{2} + 136 x - 67$ |
$20$ |
(4, 8) |
$2^{30}\cdot 7^{10}\cdot 13^{4}\cdot 347^{4}$ |
$4$ |
$40.2669354885$ |
|
|
|
? |
$C_2^8.(C_3\times S_5)$ (as 20T753) |
trivial |
trivial |
$2$ |
$11$ |
$158343620.216$ |
$4$ |
|
| 20.0.688...000.1 |
$x^{20} - 2 x^{19} - 6 x^{18} - 8 x^{17} + 83 x^{16} + 12 x^{15} - 256 x^{14} - 302 x^{13} + 984 x^{12} + 418 x^{11} - 1314 x^{10} - 870 x^{9} + 1083 x^{8} + 990 x^{7} + 70 x^{6} - 1504 x^{5} + 323 x^{4} + 546 x^{3} - 100 x^{2} - 148 x + 53$ |
$20$ |
(0, 10) |
$2^{30}\cdot 5^{8}\cdot 7^{10}\cdot 491^{4}$ |
$4$ |
$49.1924342319$ |
|
|
|
? |
$C_5\wr A_4$ (as 20T364) |
trivial |
trivial |
$2$ |
$9$ |
$472042407.989$ |
$0$ |
|
| 20.0.133...664.1 |
$x^{20} + 4 x^{18} - 26 x^{17} - 30 x^{16} - 310 x^{15} + 160 x^{14} + 1048 x^{13} + 13061 x^{12} + 49516 x^{11} + 187644 x^{10} + 517242 x^{9} + 1331213 x^{8} + 2899566 x^{7} + 5714924 x^{6} + 9737608 x^{5} + 14566669 x^{4} + 17635358 x^{3} + 16603636 x^{2} + 11012328 x + 4184395$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 43^{2}\cdot 47^{8}$ |
$4$ |
$50.8487173314$ |
|
|
|
? |
$C_2^8.(D_5\times A_4)$ (as 20T572) |
trivial |
trivial |
$2$ |
$9$ |
$948134957.677$ |
$0$ |
|
| 20.0.139...336.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 4 x^{17} + 90 x^{16} - 100 x^{15} + 340 x^{14} - 216 x^{13} + 1704 x^{12} + 208 x^{11} + 4144 x^{10} + 848 x^{9} + 7512 x^{8} - 1024 x^{7} + 6032 x^{6} - 3104 x^{5} + 3600 x^{4} - 1344 x^{3} + 480 x^{2} + 32$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 11^{16}$ |
$3$ |
$50.9575056884$ |
$70.47869191420928$ |
|
|
? |
$C_5\times A_4$ (as 20T14) |
trivial |
trivial |
$2$ |
$9$ |
$421620502.283$ |
$0$ |
|
| 20.0.104...096.1 |
$x^{20} - 2 x^{19} - 14 x^{18} + 18 x^{17} + 113 x^{16} - 108 x^{15} - 358 x^{14} + 212 x^{13} + 1159 x^{12} - 510 x^{11} - 304 x^{10} - 2080 x^{9} + 4221 x^{8} - 2020 x^{7} + 8964 x^{6} - 2206 x^{5} + 7628 x^{4} - 3296 x^{3} + 13598 x^{2} + 1776 x + 7325$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 61^{4}\cdot 397^{4}$ |
$4$ |
$56.3531350549$ |
$1610.6599421911321$ |
|
|
? |
$A_4\times S_5$ (as 20T206) |
trivial |
trivial |
$2$ |
$9$ |
$1525746632.91$ |
$0$ |
|
| 20.0.358...776.1 |
$x^{20} - 2 x^{19} + 20 x^{18} + 10 x^{17} + 136 x^{16} - 436 x^{15} + 1884 x^{14} - 6282 x^{13} - 5659 x^{12} - 34058 x^{11} + 96000 x^{10} - 219470 x^{9} + 303362 x^{8} - 191058 x^{7} + 2797418 x^{6} - 3857642 x^{5} + 9325074 x^{4} - 6211752 x^{3} + 26191940 x^{2} - 12185368 x + 22370543$ |
$20$ |
(0, 10) |
$2^{30}\cdot 7^{10}\cdot 13^{8}\cdot 347^{4}$ |
$4$ |
$67.2569624745$ |
|
|
|
? |
$C_2^8.(C_3\times S_5)$ (as 20T753) |
trivial |
trivial |
$2$ |
$9$ |
$10669550522.2$ |
$0$ |
|
