| 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 |
| 36.12.284...125.1 |
$x^{36} - 6 x^{35} + 60 x^{33} - 57 x^{32} - 294 x^{31} + 291 x^{30} + 1422 x^{29} - 1557 x^{28} - 5353 x^{27} + 7917 x^{26} + 10818 x^{25} - 20355 x^{24} - 13839 x^{23} + 24501 x^{22} + 25311 x^{21} - 18582 x^{20} - 41181 x^{19} + 16259 x^{18} + 26163 x^{17} - 918 x^{16} - 11901 x^{15} + 2898 x^{14} + 6225 x^{13} - 12147 x^{12} - 5766 x^{11} + 6978 x^{10} + 7189 x^{9} - 354 x^{8} - 3519 x^{7} - 705 x^{6} + 174 x^{5} + 144 x^{4} + 189 x^{3} + 6 x^{2} - 12 x + 1$ |
$36$ |
[12,12] |
$3^{62}\cdot 5^{27}$ |
$2$ |
$22.178712478478406$ |
$22.178712478478406$ |
|
|
? |
$S_3\times C_{12}$ (as 36T27) |
trivial |
$2$ |
$23$ |
$30477301614.519817$ |
| 36.0.997...000.1 |
$x^{36} - 3 x^{35} + 6 x^{34} - 11 x^{33} + 21 x^{32} - 39 x^{31} + 113 x^{30} - 237 x^{29} + 381 x^{28} - 379 x^{27} + 102 x^{26} + 873 x^{25} - 2357 x^{24} + 5118 x^{23} - 8217 x^{22} + 11388 x^{21} - 11523 x^{20} + 7506 x^{19} + 5558 x^{18} - 23193 x^{17} + 47733 x^{16} - 72176 x^{15} + 93003 x^{14} - 106809 x^{13} + 114281 x^{12} - 118527 x^{11} + 110259 x^{10} - 81844 x^{9} + 43665 x^{8} - 14157 x^{7} + 1524 x^{6} + 732 x^{5} - 297 x^{4} + 7 x^{3} + 27 x^{2} - 9 x + 1$ |
$36$ |
[0,18] |
$2^{24}\cdot 3^{48}\cdot 5^{27}$ |
$3$ |
$22.965496550279074$ |
$28.934712524984697$ |
|
|
? |
$S_3\times C_{12}$ (as 36T27) |
trivial |
$10$ |
$17$ |
$17144737531.469992$ |
| 36.0.131...081.1 |
$x^{36} - x^{33} + x^{27} - x^{24} + x^{18} - x^{12} + x^{9} - x^{3} + 1$ |
$36$ |
[0,18] |
$3^{54}\cdot 7^{30}$ |
$2$ |
$26.2984558329$ |
$26.298455832887633$ |
✓ |
✓ |
✓ |
$C_6^2$ (as 36T4) |
$[7]$ |
$126$ |
$17$ |
$408184875586.38837$ |
| 36.12.726...000.1 |
$x^{36} - 6 x^{35} - 3 x^{34} + 59 x^{33} + 15 x^{32} - 279 x^{31} - 217 x^{30} + 516 x^{29} + 1215 x^{28} + 1213 x^{27} - 1803 x^{26} - 7314 x^{25} - 8642 x^{24} + 3423 x^{23} + 42462 x^{22} + 59494 x^{21} - 62922 x^{20} - 207459 x^{19} - 36534 x^{18} + 336093 x^{17} + 306237 x^{16} - 298274 x^{15} - 582171 x^{14} + 127764 x^{13} + 642679 x^{12} + 54240 x^{11} - 532242 x^{10} - 193653 x^{9} + 396555 x^{8} + 204474 x^{7} - 237572 x^{6} - 105576 x^{5} + 78012 x^{4} + 20263 x^{3} - 11730 x^{2} - 1278 x + 631$ |
$36$ |
[12,12] |
$2^{24}\cdot 3^{54}\cdot 5^{27}$ |
$3$ |
$27.580113501197143$ |
$34.748765558648074$ |
|
|
? |
$S_3\times C_{12}$ (as 36T27) |
trivial |
$2$ |
$23$ |
$1345229471621.8362$ |
| 36.0.116...569.1 |
$x^{36} - x^{35} + x^{33} - x^{32} + x^{30} - x^{29} + x^{27} - x^{26} + x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{16} + x^{15} - x^{13} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 19^{34}$ |
$2$ |
$27.9429569456$ |
$27.942956945645935$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[9]$ |
$114$ |
$17$ |
$719116485989.9799$ |
| 36.0.599...464.1 |
$x^{36} - x^{18} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}$ |
$2$ |
$31.1769145362$ |
$31.176914536239792$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$108$ |
$17$ |
$2861978396449.9033$ |
| 36.0.206...656.1 |
$x^{36} - x^{34} + x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 19^{34}$ |
$2$ |
$32.265747429$ |
$32.26574742904561$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$76$ |
$17$ |
$2595333985839.583$ |
| 36.0.236...584.1 |
$x^{36} - x^{35} + x^{33} - 3 x^{32} - x^{30} - 34 x^{29} + 37 x^{28} + x^{27} - 12 x^{26} + 83 x^{25} - x^{24} + 40 x^{23} + 554 x^{22} - 720 x^{21} - 68 x^{20} + 48 x^{19} - 1240 x^{18} + 96 x^{17} - 272 x^{16} - 5760 x^{15} + 8864 x^{14} + 1280 x^{13} - 64 x^{12} + 10624 x^{11} - 3072 x^{10} + 512 x^{9} + 37888 x^{8} - 69632 x^{7} - 4096 x^{6} - 49152 x^{4} + 32768 x^{3} - 131072 x + 262144$ |
$36$ |
[0,18] |
$2^{18}\cdot 7^{32}\cdot 67^{12}$ |
$3$ |
$32.3895456956$ |
$137.8020245618911$ |
✓ |
|
? |
$C_2\times C_6\times S_4$ (as 36T330) |
$[6]$ |
$14$ |
$17$ |
$4137469685705.321$ |
| 36.0.771...893.1 |
$x^{36} - x^{35} + x^{34} - x^{33} + x^{32} - x^{31} + x^{30} - x^{29} + x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$36$ |
[0,18] |
$37^{35}$ |
$1$ |
$33.468832656$ |
$33.46883265603228$ |
✓ |
✓ |
✓ |
$C_{36}$ (as 36T1) |
$[37]$ |
$74$ |
$17$ |
$3171872728760.222$ |
| 36.0.332...625.1 |
$x^{36} - 76 x^{27} + 5777 x^{18} + 76 x^{9} + 1$ |
$36$ |
[0,18] |
$3^{90}\cdot 5^{18}$ |
$2$ |
$34.8568501159$ |
$34.85685011586675$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[37]$ |
$54$ |
$17$ |
$6550249244897.024$ |
| 36.0.559...125.1 |
$x^{36} - 2 x^{35} - 5 x^{34} + 15 x^{33} + 37 x^{32} - 147 x^{31} - 224 x^{30} + 1010 x^{29} + 1898 x^{28} - 7677 x^{27} + 15016 x^{26} - 2633 x^{25} - 23501 x^{24} + 7233 x^{23} + 70181 x^{22} - 185883 x^{21} + 150724 x^{20} + 74333 x^{19} - 196394 x^{18} + 25492 x^{17} + 539723 x^{16} - 835590 x^{15} + 653911 x^{14} - 237923 x^{13} - 88438 x^{12} + 471980 x^{11} - 579070 x^{10} + 377032 x^{9} - 114549 x^{8} - 5465 x^{7} + 78115 x^{6} - 92900 x^{5} + 61725 x^{4} - 24875 x^{3} + 9625 x^{2} - 3125 x + 625$ |
$36$ |
[0,18] |
$5^{27}\cdot 7^{12}\cdot 13^{24}$ |
$3$ |
$35.363541524324454$ |
$48.91087415715005$ |
|
|
? |
$S_3\times C_{12}$ (as 36T27) |
$[2, 2]$ |
$10$ |
$17$ |
$37522545233073.8$ |
| 36.0.105...261.1 |
$x^{36} - x + 1$ |
$36$ |
[0,18] |
$31\cdot 43\cdot 12231367\cdot 64\!\cdots\!51$ |
$4$ |
$35.989584292$ |
$1.0260840678246708e+28$ |
|
|
✓ |
$S_{36}$ (as 36T121279) |
trivial |
$2$ |
$17$ |
$42496810214502.4$ |
| 36.2.107...011.1 |
$x^{36} - x - 1$ |
$36$ |
[2,17] |
$-\,17\cdot 4159\cdot 15199\cdot 10\!\cdots\!63$ |
$4$ |
$36.010311291$ |
$1.0367731980673048e+28$ |
|
|
✓ |
$S_{36}$ (as 36T121279) |
trivial |
$2$ |
$18$ |
$24952568510934.543$ |
| 36.0.114...625.1 |
$x^{36} - x^{35} + 2 x^{34} - 3 x^{33} + 5 x^{32} - 8 x^{31} + 13 x^{30} - 21 x^{29} + 34 x^{28} - 55 x^{27} + 89 x^{26} - 144 x^{25} + 233 x^{24} - 377 x^{23} + 610 x^{22} - 987 x^{21} + 1597 x^{20} - 2584 x^{19} + 4181 x^{18} + 2584 x^{17} + 1597 x^{16} + 987 x^{15} + 610 x^{14} + 377 x^{13} + 233 x^{12} + 144 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$36$ |
[0,18] |
$5^{18}\cdot 19^{34}$ |
$2$ |
$36.0742022981$ |
$36.07420229809253$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[76]$ |
$38$ |
$17$ |
$3431432369157.3267$ |
| 36.0.765...984.1 |
$x^{36} - 38 x^{30} + 1315 x^{24} - 4900 x^{18} + 16603 x^{12} - 129 x^{6} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 7^{24}$ |
$3$ |
$38.0286204611$ |
$38.02862046112015$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[2, 14]$ |
$36$ |
$17$ |
$18271878541587.973$ |
| 36.0.107...569.1 |
$x^{36} - 3 x^{35} - 9 x^{34} + 42 x^{33} + 6 x^{32} - 333 x^{31} + 591 x^{30} + 1194 x^{29} - 4608 x^{28} - 668 x^{27} + 17499 x^{26} - 15678 x^{25} - 36231 x^{24} + 53814 x^{23} + 124803 x^{22} - 24558 x^{21} - 687768 x^{20} - 167544 x^{19} + 2193193 x^{18} + 720423 x^{17} - 3444336 x^{16} - 2946924 x^{15} + 2834649 x^{14} + 9321507 x^{13} - 5570397 x^{12} - 13865742 x^{11} + 18532800 x^{10} + 4607712 x^{9} - 26329536 x^{8} + 9681120 x^{7} + 19051200 x^{6} - 18009216 x^{5} - 1866240 x^{4} + 11943936 x^{3} - 4478976 x^{2} - 4478976 x + 2985984$ |
$36$ |
[0,18] |
$3^{62}\cdot 23^{12}\cdot 71^{6}$ |
$3$ |
$38.3849663628$ |
$268.0414261188952$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
$[54]$ |
$18$ |
$17$ |
$21081556352989.12$ |
| 36.0.110...853.1 |
$x^{36} - x^{35} + 3 x^{34} - 4 x^{33} + 9 x^{32} - 14 x^{31} + 28 x^{30} - 47 x^{29} + 89 x^{28} - 155 x^{27} + 286 x^{26} - 507 x^{25} + 924 x^{24} + 442 x^{23} + 899 x^{22} + 909 x^{21} + 1331 x^{20} + 1386 x^{19} + 2185 x^{18} + 1918 x^{17} + 3838 x^{16} + 2183 x^{15} + 7411 x^{14} + 793 x^{13} + 16212 x^{12} - 7215 x^{11} + 3211 x^{10} - 1429 x^{9} + 636 x^{8} - 283 x^{7} + 126 x^{6} - 56 x^{5} + 25 x^{4} - 11 x^{3} + 5 x^{2} - 2 x + 1$ |
$36$ |
[0,18] |
$7^{24}\cdot 13^{33}$ |
$2$ |
$38.4161141302$ |
$38.416114130176354$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
$[2, 74]$ |
$26$ |
$17$ |
$4866030378143.887$ |
| 36.0.113...024.1 |
$x^{36} - 3 x^{35} - 9 x^{34} + 45 x^{33} - 6 x^{32} - 423 x^{31} + 987 x^{30} + 1500 x^{29} - 7605 x^{28} + 1541 x^{27} + 30849 x^{26} - 54360 x^{25} - 60048 x^{24} + 185232 x^{23} + 256266 x^{22} - 152940 x^{21} - 1073577 x^{20} - 336708 x^{19} + 2425303 x^{18} + 1698282 x^{17} - 2128815 x^{16} - 3681504 x^{15} - 275778 x^{14} + 5895882 x^{13} + 1320516 x^{12} - 4471362 x^{11} + 1316007 x^{10} + 878499 x^{9} - 806031 x^{8} + 4374 x^{7} + 235467 x^{6} - 78003 x^{5} - 16038 x^{4} + 16767 x^{3} - 2187 x^{2} - 2187 x + 729$ |
$36$ |
[0,18] |
$2^{24}\cdot 3^{62}\cdot 7^{12}\cdot 71^{6}$ |
$4$ |
$40.9862227624$ |
$234.73274943944722$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
$[3, 24]$ |
$18$ |
$17$ |
$39375341234339.234$ |
| 36.0.142...601.1 |
$x^{36} - 5 x^{27} - 487 x^{18} - 2560 x^{9} + 262144$ |
$36$ |
[0,18] |
$3^{90}\cdot 7^{18}$ |
$2$ |
$41.2431812546$ |
$41.24318125460256$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.384...729.1 |
$x^{36} + 69 x^{34} + 2067 x^{32} + 35559 x^{30} + 392508 x^{28} + 2947140 x^{26} + 15578598 x^{24} + 59180736 x^{22} + 163426134 x^{20} + 329538049 x^{18} + 484507821 x^{16} + 515577135 x^{14} + 391420464 x^{12} + 207035712 x^{10} + 73469547 x^{8} + 16457853 x^{6} + 2099463 x^{4} + 127086 x^{2} + 2809$ |
$36$ |
[0,18] |
$3^{62}\cdot 31^{12}\cdot 71^{6}$ |
$3$ |
$42.4006437463$ |
$311.1851391885534$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
$[84]$ |
$18$ |
$17$ |
$53188572905191.91$ |
| 36.0.424...625.1 |
$x^{36} - 16 x^{33} + 470 x^{30} + 3624 x^{27} + 44003 x^{24} + 27532 x^{21} + 50596 x^{18} - 38116 x^{15} + 32635 x^{12} - 8692 x^{9} + 2129 x^{6} + 44 x^{3} + 1$ |
$36$ |
[0,18] |
$3^{54}\cdot 5^{18}\cdot 7^{24}$ |
$3$ |
$42.5172902208$ |
$42.517290220802025$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[2, 74]$ |
$18$ |
$17$ |
$13624539961495.691$ |
| 36.0.489...729.1 |
$x^{36} - x^{35} - x^{34} + 3 x^{33} - x^{32} - 5 x^{31} + 7 x^{30} + 3 x^{29} - 17 x^{28} + 11 x^{27} + 23 x^{26} - 45 x^{25} - x^{24} + 91 x^{23} - 89 x^{22} - 93 x^{21} + 271 x^{20} - 85 x^{19} - 457 x^{18} - 170 x^{17} + 1084 x^{16} - 744 x^{15} - 1424 x^{14} + 2912 x^{13} - 64 x^{12} - 5760 x^{11} + 5888 x^{10} + 5632 x^{9} - 17408 x^{8} + 6144 x^{7} + 28672 x^{6} - 40960 x^{5} - 16384 x^{4} + 98304 x^{3} - 65536 x^{2} - 131072 x + 262144$ |
$36$ |
[0,18] |
$7^{18}\cdot 19^{34}$ |
$2$ |
$42.6835717814$ |
$42.68357178143818$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[2, 74]$ |
$38$ |
$17$ |
$28076820524481.113$ |
| 36.0.590...201.1 |
$x^{36} - x^{35} + 6 x^{34} - 7 x^{33} + 27 x^{32} - 35 x^{31} + 110 x^{30} - 90 x^{29} + 365 x^{28} - 253 x^{27} + 1190 x^{26} - 820 x^{25} + 3948 x^{24} - 2955 x^{23} + 8389 x^{22} - 6275 x^{21} + 16362 x^{20} - 9115 x^{19} + 28304 x^{18} + 1097 x^{17} + 33005 x^{16} + 594 x^{15} + 42702 x^{14} - 8321 x^{13} + 51190 x^{12} - 23469 x^{11} + 21146 x^{10} - 11317 x^{9} + 10292 x^{8} - 3370 x^{7} + 4283 x^{6} + 1030 x^{5} + 250 x^{4} + 59 x^{3} + 15 x^{2} + 3 x + 1$ |
$36$ |
[0,18] |
$7^{30}\cdot 13^{30}$ |
$2$ |
$42.9076267033$ |
$42.90762670326212$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[2, 182]$ |
$14$ |
$17$ |
$4866030378143.887$ |
| 36.0.123...304.1 |
$x^{36} - 6 x^{34} + 27 x^{32} - 109 x^{30} + 417 x^{28} - 1548 x^{26} + 5644 x^{24} - 13098 x^{22} + 29340 x^{20} - 63802 x^{18} + 131850 x^{16} - 246222 x^{14} + 354484 x^{12} - 42756 x^{10} + 5157 x^{8} - 622 x^{6} + 75 x^{4} - 9 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{48}\cdot 7^{30}$ |
$3$ |
$43.7965635407$ |
$43.796563540728876$ |
✓ |
✓ |
|
$C_6^2$ (as 36T4) |
$[14, 14]$ |
$28$ |
$17$ |
$57365817603378.39$ |
| 36.0.152...281.1 |
$x^{36} - 4 x^{33} + 57 x^{30} - 36 x^{27} + 1910 x^{24} - 2801 x^{21} + 16733 x^{18} + 11446 x^{15} + 36100 x^{12} - 11599 x^{9} + 4932 x^{6} + 69 x^{3} + 1$ |
$36$ |
[0,18] |
$3^{54}\cdot 13^{30}$ |
$2$ |
$44.0522412551$ |
$44.05224125514256$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[182]$ |
$18$ |
$17$ |
$20980577392492.816$ |
| 36.0.157...816.1 |
$x^{36} - 512 x^{18} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
$44.090815370097204$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.157...816.2 |
$x^{36} + 512 x^{18} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
$44.090815370097204$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.0.230...769.1 |
$x^{36} - 3 x^{35} + 3 x^{34} - 3 x^{32} + 6 x^{31} - 8 x^{30} + 6 x^{29} - 12 x^{28} + 36 x^{27} - 42 x^{26} - 6 x^{25} + 82 x^{24} - 168 x^{23} + 177 x^{22} + 27 x^{21} - 207 x^{20} - 54 x^{19} + 397 x^{18} - 108 x^{17} - 828 x^{16} + 216 x^{15} + 2832 x^{14} - 5376 x^{13} + 5248 x^{12} - 768 x^{11} - 10752 x^{10} + 18432 x^{9} - 12288 x^{8} + 12288 x^{7} - 32768 x^{6} + 49152 x^{5} - 49152 x^{4} + 196608 x^{2} - 393216 x + 262144$ |
$36$ |
[0,18] |
$3^{48}\cdot 7^{30}\cdot 71^{6}$ |
$3$ |
$44.5608121724$ |
$184.5182019723083$ |
✓ |
|
|
$C_2^2:C_6^2$ (as 36T103) |
$[14, 14]$ |
$14$ |
$17$ |
$104721329817071.11$ |
| 36.0.368...256.1 |
$x^{36} - x^{35} - 2 x^{33} + 3 x^{32} - 3 x^{31} + 2 x^{30} - 37 x^{29} + 46 x^{28} - 5 x^{27} + 54 x^{26} - 97 x^{25} + 98 x^{24} - 41 x^{23} + 689 x^{22} - 924 x^{21} + 118 x^{20} - 795 x^{19} + 1451 x^{18} - 1590 x^{17} + 472 x^{16} - 7392 x^{15} + 11024 x^{14} - 1312 x^{13} + 6272 x^{12} - 12416 x^{11} + 13824 x^{10} - 2560 x^{9} + 47104 x^{8} - 75776 x^{7} + 8192 x^{6} - 24576 x^{5} + 49152 x^{4} - 65536 x^{3} - 131072 x + 262144$ |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 23^{6}\cdot 37^{12}$ |
$4$ |
$45.1464470572$ |
$234.36880761650926$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[63]$ |
$14$ |
$17$ |
$102773304267872.48$ |
| 36.0.459...733.1 |
$x^{36} + 3 x^{34} - x^{33} + 9 x^{32} - 6 x^{31} + 28 x^{30} - 27 x^{29} + 90 x^{28} - 109 x^{27} + 297 x^{26} - 417 x^{25} + 1000 x^{24} + 1845 x^{23} + 3417 x^{22} + 4535 x^{21} + 8406 x^{20} + 10188 x^{19} + 20683 x^{18} + 22158 x^{17} + 51861 x^{16} + 45791 x^{15} + 133425 x^{14} + 85512 x^{13} + 354484 x^{12} + 123111 x^{11} + 42756 x^{10} + 14849 x^{9} + 5157 x^{8} + 1791 x^{7} + 622 x^{6} + 216 x^{5} + 75 x^{4} + 26 x^{3} + 9 x^{2} + 3 x + 1$ |
$36$ |
[0,18] |
$3^{48}\cdot 13^{33}$ |
$2$ |
$45.423062587$ |
$45.423062587011394$ |
✓ |
✓ |
? |
$C_3\times C_{12}$ (as 36T3) |
$[3, 3, 9, 9]$ |
$26$ |
$17$ |
$20980577392492.816$ |
| 36.0.519...889.1 |
$x^{36} - 6 x^{35} + 54 x^{34} - 249 x^{33} + 1281 x^{32} - 4767 x^{31} + 17772 x^{30} - 55056 x^{29} + 164652 x^{28} - 444090 x^{27} + 1149975 x^{26} - 2811774 x^{25} + 6542481 x^{24} - 14483877 x^{23} + 30345297 x^{22} - 60803709 x^{21} + 116322072 x^{20} - 213103239 x^{19} + 373433528 x^{18} - 621567384 x^{17} + 980981811 x^{16} - 1465192428 x^{15} + 2079415686 x^{14} - 2795268228 x^{13} + 3496953564 x^{12} - 4091067075 x^{11} + 4483655439 x^{10} - 4385043570 x^{9} + 3744819675 x^{8} - 2928547434 x^{7} + 2036109996 x^{6} - 1081958046 x^{5} + 405353103 x^{4} - 123233361 x^{3} + 32860329 x^{2} - 5284761 x + 749197$ |
$36$ |
[0,18] |
$3^{62}\cdot 23^{12}\cdot 199^{6}$ |
$3$ |
$45.5785270042$ |
$448.74464988853384$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
not computed |
$18$ |
$17$ |
|
| 36.0.541...464.1 |
$x^{36} - 2 x^{34} + 4 x^{32} - 8 x^{30} + 16 x^{28} - 32 x^{26} + 64 x^{24} - 128 x^{22} + 256 x^{20} - 512 x^{18} + 1024 x^{16} - 2048 x^{14} + 4096 x^{12} - 8192 x^{10} + 16384 x^{8} - 32768 x^{6} + 65536 x^{4} - 131072 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
$45.630657614261125$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.541...464.2 |
$x^{36} + 2 x^{34} + 4 x^{32} + 8 x^{30} + 16 x^{28} + 32 x^{26} + 64 x^{24} + 128 x^{22} + 256 x^{20} + 512 x^{18} + 1024 x^{16} + 2048 x^{14} + 4096 x^{12} + 8192 x^{10} + 16384 x^{8} + 32768 x^{6} + 65536 x^{4} + 131072 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
$45.630657614261125$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
|
| 36.0.619...125.1 |
$x^{36} - x^{35} + 9 x^{34} - 10 x^{33} + 54 x^{32} - 49 x^{31} + 257 x^{30} - 206 x^{29} + 1100 x^{28} - 836 x^{27} + 3655 x^{26} - 2571 x^{25} + 10339 x^{24} - 5625 x^{23} + 24829 x^{22} - 12149 x^{21} + 52298 x^{20} - 24437 x^{19} + 84375 x^{18} - 31001 x^{17} + 114806 x^{16} - 20386 x^{15} + 122457 x^{14} - 26351 x^{13} + 111183 x^{12} - 31899 x^{11} + 59771 x^{10} - 9196 x^{9} + 26744 x^{8} + 4893 x^{7} + 5542 x^{6} + 509 x^{5} + 1260 x^{4} - 205 x^{3} + 35 x^{2} - 5 x + 1$ |
$36$ |
[0,18] |
$5^{27}\cdot 19^{32}$ |
$2$ |
$45.803363483$ |
$45.80336348303902$ |
✓ |
✓ |
? |
$C_{36}$ (as 36T1) |
$[1417]$ |
$10$ |
$17$ |
$3431432369157.3267$ |
| 36.0.220...024.1 |
$x^{36} - 2 x^{34} - 2 x^{33} + 8 x^{31} + 4 x^{30} - 8 x^{29} - 8 x^{28} - 8 x^{27} + 16 x^{26} - 16 x^{24} + 64 x^{23} - 64 x^{22} - 32 x^{21} - 64 x^{20} - 64 x^{19} + 576 x^{18} - 128 x^{17} - 256 x^{16} - 256 x^{15} - 1024 x^{14} + 2048 x^{13} - 1024 x^{12} + 4096 x^{10} - 4096 x^{9} - 8192 x^{8} - 16384 x^{7} + 16384 x^{6} + 65536 x^{5} - 65536 x^{3} - 131072 x^{2} + 262144$ |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 31^{6}\cdot 37^{12}$ |
$4$ |
$47.4492356417$ |
$272.0926055185523$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[3, 63]$ |
$14$ |
$17$ |
$161164499152547.9$ |
| 36.0.221...944.1 |
$x^{36} - 17 x^{34} + 169 x^{32} - 1130 x^{30} + 5664 x^{28} - 21853 x^{26} + 66874 x^{24} - 162613 x^{22} + 316711 x^{20} - 487810 x^{18} + 592078 x^{16} - 549123 x^{14} + 384931 x^{12} - 190091 x^{10} + 66033 x^{8} - 13002 x^{6} + 1695 x^{4} - 45 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{32}$ |
$3$ |
$47.4526521699$ |
$47.4526521699425$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[171]$ |
$12$ |
$17$ |
$119587984215961.08$ |
| 36.0.400...241.1 |
$x^{36} - 14 x^{35} + 129 x^{34} - 874 x^{33} + 4865 x^{32} - 22922 x^{31} + 94283 x^{30} - 342666 x^{29} + 1112273 x^{28} - 3234952 x^{27} + 8438667 x^{26} - 19663764 x^{25} + 40577370 x^{24} - 72857172 x^{23} + 109953255 x^{22} - 128328007 x^{21} + 83898469 x^{20} + 71389621 x^{19} - 339203441 x^{18} + 610359985 x^{17} - 658477439 x^{16} + 279191379 x^{15} + 463357277 x^{14} - 1113046997 x^{13} + 1096834803 x^{12} - 317516043 x^{11} - 517559160 x^{10} + 549915913 x^{9} + 131226304 x^{8} - 546397416 x^{7} + 300520880 x^{6} + 8345200 x^{5} - 14423488 x^{4} - 397760 x^{3} + 206720 x^{2} + 13568 x + 512$ |
$36$ |
[0,18] |
$7^{30}\cdot 67^{12}\cdot 167^{6}$ |
$3$ |
$48.2383798222$ |
$535.3576385241264$ |
✓ |
|
|
$C_2\times A_4\times D_6$ (as 36T334) |
$[228]$ |
$14$ |
$17$ |
$154416550498474.53$ |
| 36.0.473...721.1 |
$x^{36} - x^{35} - 4 x^{34} + 15 x^{33} - 16 x^{32} - 64 x^{31} + 289 x^{30} + 606 x^{29} - 2131 x^{28} + 1716 x^{27} + 8000 x^{26} - 37236 x^{25} + 41632 x^{24} + 157678 x^{23} + 138311 x^{22} - 88085 x^{21} - 438826 x^{20} - 452289 x^{19} + 632324 x^{18} + 713006 x^{17} - 496621 x^{16} - 2036590 x^{15} - 2057459 x^{14} + 1547178 x^{13} + 6189592 x^{12} + 1579124 x^{11} - 31870 x^{10} - 127114 x^{9} - 32211 x^{8} + 891 x^{7} + 2434 x^{6} - 49 x^{5} - 196 x^{4} - 50 x^{3} + x^{2} + 4 x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 7^{30}\cdot 13^{24}$ |
$3$ |
$48.4660800825$ |
$48.46608008250512$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[6, 78]$ |
$42$ |
$17$ |
$118794051645799.06$ |
| 36.0.550...744.1 |
$x^{36} - 12 x^{35} + 117 x^{34} - 801 x^{33} + 4695 x^{32} - 22944 x^{31} + 99156 x^{30} - 377772 x^{29} + 1300485 x^{28} - 4063386 x^{27} + 11677437 x^{26} - 31091397 x^{25} + 77290173 x^{24} - 180440796 x^{23} + 396698646 x^{22} - 823211451 x^{21} + 1614415197 x^{20} - 3001125603 x^{19} + 5316812738 x^{18} - 9023396952 x^{17} + 14711412132 x^{16} - 22930637760 x^{15} + 33755151003 x^{14} - 46228515924 x^{13} + 58054312566 x^{12} - 66243228153 x^{11} + 68283850818 x^{10} - 62712669783 x^{9} + 49993043427 x^{8} - 33497730303 x^{7} + 18223735458 x^{6} - 7755245535 x^{5} + 2488299969 x^{4} - 581944761 x^{3} + 94855845 x^{2} - 9757218 x + 507547$ |
$36$ |
[0,18] |
$2^{24}\cdot 3^{62}\cdot 7^{12}\cdot 199^{6}$ |
$4$ |
$48.6672736228$ |
$392.98054405162793$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
not computed |
$18$ |
$17$ |
|
| 36.0.685...625.1 |
$x^{36} + 9 x^{34} - 4 x^{33} + 72 x^{32} - 69 x^{31} + 584 x^{30} + 981 x^{29} + 4881 x^{28} + 7326 x^{27} + 34614 x^{26} + 39264 x^{25} + 241820 x^{24} + 164610 x^{23} + 347325 x^{22} + 272002 x^{21} + 443511 x^{20} + 341952 x^{19} + 513316 x^{18} + 62091 x^{17} + 423768 x^{16} + 53105 x^{15} + 415071 x^{14} + 105954 x^{13} + 408896 x^{12} + 148752 x^{11} + 103692 x^{10} + 47916 x^{9} + 30861 x^{8} + 10350 x^{7} + 8009 x^{6} - 1710 x^{5} + 372 x^{4} - 77 x^{3} + 18 x^{2} - 3 x + 1$ |
$36$ |
[0,18] |
$3^{48}\cdot 5^{18}\cdot 7^{30}$ |
$3$ |
$48.966046629$ |
$48.96604662897932$ |
✓ |
✓ |
? |
$C_6^2$ (as 36T4) |
$[18, 126]$ |
$14$ |
$17$ |
$13624539961495.691$ |
| 36.0.722...125.1 |
$x^{36} + 9 x^{34} + 54 x^{32} + 273 x^{30} + 1260 x^{28} - x^{27} + 4374 x^{26} - 18 x^{25} + 13050 x^{24} - 189 x^{23} + 34695 x^{22} - 153 x^{21} + 79785 x^{20} + 1935 x^{19} + 133435 x^{18} + 11664 x^{17} + 197460 x^{16} + 36792 x^{15} + 255879 x^{14} + 40932 x^{13} + 256629 x^{12} + 26649 x^{11} + 121878 x^{10} + 26 x^{9} + 55485 x^{8} - 19917 x^{7} + 22041 x^{6} - 4752 x^{5} + 6021 x^{4} - 699 x^{3} + 81 x^{2} - 9 x + 1$ |
$36$ |
[0,18] |
$3^{88}\cdot 5^{27}$ |
$2$ |
$49.0370012138$ |
$49.037001213832596$ |
✓ |
✓ |
? |
$C_{36}$ (as 36T1) |
$[2053]$ |
$10$ |
$17$ |
$6550249244897.024$ |
| 36.0.786...544.1 |
$x^{36} - x^{35} + x^{34} - x^{33} + x^{32} - 5 x^{31} + x^{30} - 24 x^{29} + 20 x^{28} - 16 x^{27} + 28 x^{26} + 8 x^{25} + 80 x^{24} + 32 x^{23} + 208 x^{22} - 192 x^{21} - 64 x^{20} - 320 x^{19} - 448 x^{18} - 640 x^{17} - 256 x^{16} - 1536 x^{15} + 3328 x^{14} + 1024 x^{13} + 5120 x^{12} + 1024 x^{11} + 7168 x^{10} - 8192 x^{9} + 20480 x^{8} - 49152 x^{7} + 4096 x^{6} - 40960 x^{5} + 16384 x^{4} - 32768 x^{3} + 65536 x^{2} - 131072 x + 262144$ |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 229^{12}$ |
$3$ |
$49.1526410239$ |
$216.62625977783622$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[3, 3, 18]$ |
$14$ |
$17$ |
$290558369176692.94$ |
| 36.0.186...849.1 |
$x^{36} - 9 x^{35} + 84 x^{34} - 474 x^{33} + 2544 x^{32} - 10560 x^{31} + 40809 x^{30} - 131799 x^{29} + 391791 x^{28} - 999422 x^{27} + 2325150 x^{26} - 4660386 x^{25} + 8396052 x^{24} - 12580209 x^{23} + 15643398 x^{22} - 11729097 x^{21} - 3258969 x^{20} + 36356592 x^{19} - 76149739 x^{18} + 110085921 x^{17} - 89826543 x^{16} - 1425666 x^{15} + 198417867 x^{14} - 384743850 x^{13} + 432712269 x^{12} - 69755586 x^{11} - 550371321 x^{10} + 1063020818 x^{9} - 679694445 x^{8} - 366468081 x^{7} + 1347871539 x^{6} - 962673774 x^{5} - 198005841 x^{4} + 1059232617 x^{3} - 493446843 x^{2} - 181048875 x + 361488133$ |
$36$ |
[0,18] |
$3^{62}\cdot 31^{12}\cdot 199^{6}$ |
$3$ |
$50.3467651299$ |
$520.9741955101401$ |
✓ |
|
? |
$C_2\times A_4\times D_6$ (as 36T334) |
not computed |
$18$ |
$17$ |
|
| 36.0.343...529.1 |
$x^{36} - 4 x^{35} + 29 x^{34} - 102 x^{33} + 387 x^{32} - 1124 x^{31} + 3306 x^{30} - 8114 x^{29} + 22893 x^{28} - 48914 x^{27} + 130172 x^{26} - 236820 x^{25} + 491340 x^{24} - 771909 x^{23} + 1556952 x^{22} - 2575973 x^{21} + 9578578 x^{20} - 17316065 x^{19} + 51912793 x^{18} - 76656575 x^{17} + 141757837 x^{16} - 135159634 x^{15} + 136402715 x^{14} - 44564002 x^{13} - 58867556 x^{12} + 59049233 x^{11} - 7027542 x^{10} - 75995389 x^{9} + 25472394 x^{8} + 135493988 x^{7} + 125206304 x^{6} + 59315184 x^{5} + 16879200 x^{4} + 3007232 x^{3} + 327552 x^{2} + 19712 x + 512$ |
$36$ |
[0,18] |
$7^{30}\cdot 67^{12}\cdot 239^{6}$ |
$3$ |
$51.2082126583$ |
$640.4492457191162$ |
✓ |
|
|
$C_2\times A_4\times D_6$ (as 36T334) |
$[252]$ |
$14$ |
$17$ |
$338042130880954.0$ |
| 36.0.485...969.1 |
$x^{36} - 136 x^{27} - 1187 x^{18} - 2676888 x^{9} + 387420489$ |
$36$ |
[0,18] |
$3^{90}\cdot 11^{18}$ |
$2$ |
$51.7010638188$ |
$51.70106381884226$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
|
| 36.36.650...125.1 |
$x^{36} - 36 x^{34} + 594 x^{32} - 5952 x^{30} + 40455 x^{28} - x^{27} - 197316 x^{26} + 27 x^{25} + 712530 x^{24} - 324 x^{23} - 1937520 x^{22} + 2277 x^{21} + 3996135 x^{20} - 10395 x^{19} - 6249100 x^{18} + 32319 x^{17} + 7354710 x^{16} - 69768 x^{15} - 6418656 x^{14} + 104652 x^{13} + 4056234 x^{12} - 107406 x^{11} - 1790712 x^{10} + 72931 x^{9} + 523260 x^{8} - 30897 x^{7} - 93024 x^{6} + 7398 x^{5} + 8721 x^{4} - 849 x^{3} - 324 x^{2} + 36 x + 1$ |
$36$ |
[36,0] |
$3^{90}\cdot 5^{27}$ |
$2$ |
$52.123148338$ |
$52.123148337972104$ |
|
✓ |
✓ |
$C_{36}$ (as 36T1) |
trivial |
$2$ |
$35$ |
$31157843880432600000$ |
| 36.0.774...632.1 |
$x^{36} + 3$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{107}$ |
$2$ |
$52.3769724955$ |
$82.00366889518594$ |
|
|
|
$D_{18}:C_6$ (as 36T185) |
trivial |
$6$ |
$17$ |
$146190247413682400$ |
| 36.0.807...721.1 |
$x^{36} - x^{35} + 18 x^{34} - 15 x^{33} + 185 x^{32} - 137 x^{31} + 1281 x^{30} - 831 x^{29} + 6616 x^{28} - 3799 x^{27} + 26339 x^{26} - 13196 x^{25} + 83006 x^{24} - 36260 x^{23} + 208286 x^{22} - 77735 x^{21} + 418163 x^{20} - 132518 x^{19} + 666068 x^{18} - 173318 x^{17} + 834766 x^{16} - 177139 x^{15} + 804267 x^{14} - 129870 x^{13} + 582511 x^{12} - 73129 x^{11} + 302060 x^{10} - 23507 x^{9} + 107217 x^{8} - 7128 x^{7} + 23244 x^{6} - 78 x^{5} + 2775 x^{4} - 165 x^{3} + 126 x^{2} + 9 x + 1$ |
$36$ |
[0,18] |
$3^{18}\cdot 37^{34}$ |
$2$ |
$52.4372651879$ |
$52.43726518793858$ |
✓ |
✓ |
? |
$C_2\times C_{18}$ (as 36T2) |
$[19, 684]$ |
$6$ |
$17$ |
$3171872728760.222$ |
| 36.0.900...616.1 |
$x^{36} + 36 x^{34} + 594 x^{32} + 5953 x^{30} + 40485 x^{28} + 197721 x^{26} + 715780 x^{24} + 1954770 x^{22} + 4059891 x^{20} + 6417344 x^{18} + 7674462 x^{16} + 6854571 x^{14} + 4475587 x^{12} + 2066547 x^{10} + 640764 x^{8} + 122466 x^{6} + 12276 x^{4} + 432 x^{2} + 1$ |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 7^{30}$ |
$3$ |
$52.5969116658$ |
$52.596911665775266$ |
✓ |
✓ |
✓ |
$C_6^2$ (as 36T4) |
$[2, 28, 364]$ |
$4$ |
$17$ |
$816369751172.7767$ |
| 36.36.900...616.1 |
$x^{36} - 36 x^{34} + 594 x^{32} - 5951 x^{30} + 40425 x^{28} - 196911 x^{26} + 709280 x^{24} - 1920270 x^{22} + 3932379 x^{20} - 6080856 x^{18} + 7034958 x^{16} - 5982741 x^{14} + 3636879 x^{12} - 1514853 x^{10} + 405648 x^{8} - 63358 x^{6} + 4956 x^{4} - 144 x^{2} + 1$ |
$36$ |
[36,0] |
$2^{36}\cdot 3^{54}\cdot 7^{30}$ |
$3$ |
$52.5969116658$ |
$52.596911665775266$ |
|
✓ |
✓ |
$C_6^2$ (as 36T4) |
trivial |
$2$ |
$35$ |
$33651165194729250000$ |
