| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 36.12.284...125.1 |
x36 - 6x35 + 60x33 - 57x32 - 294x31 + 291x30 + 1422x29 - 1557x28 - 5353x27 + 7917x26 + 10818x25 - 20355x24 - 13839x23 + 24501x22 + 25311x21 - 18582x20 - 41181x19 + 16259x18 + 26163x17 - 918x16 - 11901x15 + 2898x14 + 6225x13 - 12147x12 - 5766x11 + 6978x10 + 7189x9 - 354x8 - 3519x7 - 705x6 + 174x5 + 144x4 + 189x3 + 6x2 - 12x + 1 |
$36$ |
[12,12] |
$3^{62}\cdot 5^{27}$ |
$2$ |
$22.178712478478406$ |
|
|
not computed |
$C_{12}\times S_3$ (as 36T27) |
trivial |
$2$ |
$23$ |
$30477301614.519817$ |
| 36.0.997...000.1 |
x36 - 3x35 + 6x34 - 11x33 + 21x32 - 39x31 + 113x30 - 237x29 + 381x28 - 379x27 + 102x26 + 873x25 - 2357x24 + 5118x23 - 8217x22 + 11388x21 - 11523x20 + 7506x19 + 5558x18 - 23193x17 + 47733x16 - 72176x15 + 93003x14 - 106809x13 + 114281x12 - 118527x11 + 110259x10 - 81844x9 + 43665x8 - 14157x7 + 1524x6 + 732x5 - 297x4 + 7x3 + 27x2 - 9x + 1 |
$36$ |
[0,18] |
$2^{24}\cdot 3^{48}\cdot 5^{27}$ |
$3$ |
$22.965496550279074$ |
|
|
not computed |
$C_{12}\times S_3$ (as 36T27) |
trivial |
$10$ |
$17$ |
$17144737531.469992$ |
| 36.0.131...081.1 |
x36 - x33 + x27 - x24 + x18 - x12 + x9 - x3 + 1 |
$36$ |
[0,18] |
$3^{54}\cdot 7^{30}$ |
$2$ |
$26.2984558329$ |
✓ |
✓ |
✓ |
$C_6^2$ (as 36T4) |
$[7]$ |
$126$ |
$17$ |
$408184875586.38837$ |
| 36.12.726...000.1 |
x36 - 6x35 - 3x34 + 59x33 + 15x32 - 279x31 - 217x30 + 516x29 + 1215x28 + 1213x27 - 1803x26 - 7314x25 - 8642x24 + 3423x23 + 42462x22 + 59494x21 - 62922x20 - 207459x19 - 36534x18 + 336093x17 + 306237x16 - 298274x15 - 582171x14 + 127764x13 + 642679x12 + 54240x11 - 532242x10 - 193653x9 + 396555x8 + 204474x7 - 237572x6 - 105576x5 + 78012x4 + 20263x3 - 11730x2 - 1278x + 631 |
$36$ |
[12,12] |
$2^{24}\cdot 3^{54}\cdot 5^{27}$ |
$3$ |
$27.580113501197143$ |
|
|
not computed |
$C_{12}\times S_3$ (as 36T27) |
trivial |
$2$ |
$23$ |
$1345229471621.8362$ |
| 36.0.116...569.1 |
x36 - x35 + x33 - x32 + x30 - x29 + x27 - x26 + x24 - x23 + x21 - x20 + x18 - x16 + x15 - x13 + x12 - x10 + x9 - x7 + x6 - x4 + x3 - x + 1 |
$36$ |
[0,18] |
$3^{18}\cdot 19^{34}$ |
$2$ |
$27.9429569456$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[9]$ |
$114$ |
$17$ |
$719116485989.9799$ |
| 36.0.599...464.1 |
x36 - x18 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{90}$ |
$2$ |
$31.1769145362$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$108$ |
$17$ |
$2861978396449.9033$ |
| 36.0.206...656.1 |
x36 - x34 + x32 - x30 + x28 - x26 + x24 - x22 + x20 - x18 + x16 - x14 + x12 - x10 + x8 - x6 + x4 - x2 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 19^{34}$ |
$2$ |
$32.265747429$ |
✓ |
✓ |
✓ |
$C_2\times C_{18}$ (as 36T2) |
$[19]$ |
$76$ |
$17$ |
$2595333985839.583$ |
| 36.0.236...584.1 |
x36 - x35 + x33 - 3x32 - x30 - 34x29 + 37x28 + x27 - 12x26 + 83x25 - x24 + 40x23 + 554x22 - 720x21 - 68x20 + 48x19 - 1240x18 + 96x17 - 272x16 - 5760x15 + 8864x14 + 1280x13 - 64x12 + 10624x11 - 3072x10 + 512x9 + 37888x8 - 69632x7 - 4096x6 - 49152x4 + 32768x3 - 131072x + 262144 |
$36$ |
[0,18] |
$2^{18}\cdot 7^{32}\cdot 67^{12}$ |
$3$ |
$32.3895456956$ |
✓ |
|
not computed |
$C_2\times C_6\times S_4$ (as 36T330) |
$[6]$ |
$14$ |
$17$ |
$4137469685705.321$ |
| 36.0.771...893.1 |
x36 - x35 + x34 - x33 + x32 - x31 + x30 - x29 + x28 - x27 + x26 - x25 + x24 - x23 + x22 - x21 + x20 - x19 + x18 - x17 + x16 - x15 + x14 - x13 + x12 - x11 + x10 - x9 + x8 - x7 + x6 - x5 + x4 - x3 + x2 - x + 1 |
$36$ |
[0,18] |
$37^{35}$ |
$1$ |
$33.468832656$ |
✓ |
✓ |
✓ |
$C_{36}$ (as 36T1) |
$[37]$ |
$74$ |
$17$ |
$3171872728760.222$ |
| 36.0.332...625.1 |
x36 - 76x27 + 5777x18 + 76x9 + 1 |
$36$ |
[0,18] |
$3^{90}\cdot 5^{18}$ |
$2$ |
$34.8568501159$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
$[37]$ |
$54$ |
$17$ |
$6550249244897.024$ |
| 36.0.559...125.1 |
x36 - 2x35 - 5x34 + 15x33 + 37x32 - 147x31 - 224x30 + 1010x29 + 1898x28 - 7677x27 + 15016x26 - 2633x25 - 23501x24 + 7233x23 + 70181x22 - 185883x21 + 150724x20 + 74333x19 - 196394x18 + 25492x17 + 539723x16 - 835590x15 + 653911x14 - 237923x13 - 88438x12 + 471980x11 - 579070x10 + 377032x9 - 114549x8 - 5465x7 + 78115x6 - 92900x5 + 61725x4 - 24875x3 + 9625x2 - 3125x + 625 |
$36$ |
[0,18] |
$5^{27}\cdot 7^{12}\cdot 13^{24}$ |
$3$ |
$35.363541524324454$ |
|
|
not computed |
$C_{12}\times S_3$ (as 36T27) |
$[2, 2]$ |
$10$ |
$17$ |
$37522545233073.8$ |
| 36.0.105...261.1 |
x36 - x + 1 |
$36$ |
[0,18] |
$31\cdot 43\cdot 12231367\cdot 64\!\cdots\!51$ |
$4$ |
$35.989584292$ |
|
|
✓ |
$S_{36}$ (as 36T121279) |
trivial |
$2$ |
$17$ |
$42496810214502.4$ |
| 36.2.107...011.1 |
x36 - x - 1 |
$36$ |
[2,17] |
$-\,17\cdot 4159\cdot 15199\cdot 10\!\cdots\!63$ |
$4$ |
$36.010311291$ |
|
|
✓ |
$S_{36}$ (as 36T121279) |
trivial |
$2$ |
$18$ |
$24952568510934.543$ |
| 36.0.114...625.1 |
x36 - x35 + 2x34 - 3x33 + 5x32 - 8x31 + 13x30 - 21x29 + 34x28 - 55x27 + 89x26 - 144x25 + 233x24 - 377x23 + 610x22 - 987x21 + 1597x20 - 2584x19 + 4181x18 + 2584x17 + 1597x16 + 987x15 + 610x14 + 377x13 + 233x12 + 144x11 + 89x10 + 55x9 + 34x8 + 21x7 + 13x6 + 8x5 + 5x4 + 3x3 + 2x2 + x + 1 |
$36$ |
[0,18] |
$5^{18}\cdot 19^{34}$ |
$2$ |
$36.0742022981$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
$[76]$ |
$38$ |
$17$ |
$3431432369157.3267$ |
| 36.0.765...984.1 |
x36 - 38x30 + 1315x24 - 4900x18 + 16603x12 - 129x6 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 7^{24}$ |
$3$ |
$38.0286204611$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[2, 14]$ |
$36$ |
$17$ |
$18271878541587.973$ |
| 36.0.107...569.1 |
x36 - 3x35 - 9x34 + 42x33 + 6x32 - 333x31 + 591x30 + 1194x29 - 4608x28 - 668x27 + 17499x26 - 15678x25 - 36231x24 + 53814x23 + 124803x22 - 24558x21 - 687768x20 - 167544x19 + 2193193x18 + 720423x17 - 3444336x16 - 2946924x15 + 2834649x14 + 9321507x13 - 5570397x12 - 13865742x11 + 18532800x10 + 4607712x9 - 26329536x8 + 9681120x7 + 19051200x6 - 18009216x5 - 1866240x4 + 11943936x3 - 4478976x2 - 4478976x + 2985984 |
$36$ |
[0,18] |
$3^{62}\cdot 23^{12}\cdot 71^{6}$ |
$3$ |
$38.3849663628$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
$[54]$ |
$18$ |
$17$ |
$21081556352989.12$ |
| 36.0.110...853.1 |
x36 - x35 + 3x34 - 4x33 + 9x32 - 14x31 + 28x30 - 47x29 + 89x28 - 155x27 + 286x26 - 507x25 + 924x24 + 442x23 + 899x22 + 909x21 + 1331x20 + 1386x19 + 2185x18 + 1918x17 + 3838x16 + 2183x15 + 7411x14 + 793x13 + 16212x12 - 7215x11 + 3211x10 - 1429x9 + 636x8 - 283x7 + 126x6 - 56x5 + 25x4 - 11x3 + 5x2 - 2x + 1 |
$36$ |
[0,18] |
$7^{24}\cdot 13^{33}$ |
$2$ |
$38.4161141302$ |
✓ |
✓ |
|
$C_3\times C_{12}$ (as 36T3) |
$[2, 74]$ |
$26$ |
$17$ |
$4866030378143.887$ |
| 36.0.113...024.1 |
x36 - 3x35 - 9x34 + 45x33 - 6x32 - 423x31 + 987x30 + 1500x29 - 7605x28 + 1541x27 + 30849x26 - 54360x25 - 60048x24 + 185232x23 + 256266x22 - 152940x21 - 1073577x20 - 336708x19 + 2425303x18 + 1698282x17 - 2128815x16 - 3681504x15 - 275778x14 + 5895882x13 + 1320516x12 - 4471362x11 + 1316007x10 + 878499x9 - 806031x8 + 4374x7 + 235467x6 - 78003x5 - 16038x4 + 16767x3 - 2187x2 - 2187x + 729 |
$36$ |
[0,18] |
$2^{24}\cdot 3^{62}\cdot 7^{12}\cdot 71^{6}$ |
$4$ |
$40.9862227624$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
$[3, 24]$ |
$18$ |
$17$ |
$39375341234339.234$ |
| 36.0.142...601.1 |
x36 - 5x27 - 487x18 - 2560x9 + 262144 |
$36$ |
[0,18] |
$3^{90}\cdot 7^{18}$ |
$2$ |
$41.2431812546$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
$$ |
| 36.0.384...729.1 |
x36 + 69x34 + 2067x32 + 35559x30 + 392508x28 + 2947140x26 + 15578598x24 + 59180736x22 + 163426134x20 + 329538049x18 + 484507821x16 + 515577135x14 + 391420464x12 + 207035712x10 + 73469547x8 + 16457853x6 + 2099463x4 + 127086x2 + 2809 |
$36$ |
[0,18] |
$3^{62}\cdot 31^{12}\cdot 71^{6}$ |
$3$ |
$42.4006437463$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
$[84]$ |
$18$ |
$17$ |
$53188572905191.91$ |
| 36.0.424...625.1 |
x36 - 16x33 + 470x30 + 3624x27 + 44003x24 + 27532x21 + 50596x18 - 38116x15 + 32635x12 - 8692x9 + 2129x6 + 44x3 + 1 |
$36$ |
[0,18] |
$3^{54}\cdot 5^{18}\cdot 7^{24}$ |
$3$ |
$42.5172902208$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[2, 74]$ |
$18$ |
$17$ |
$13624539961495.691$ |
| 36.0.489...729.1 |
x36 - x35 - x34 + 3x33 - x32 - 5x31 + 7x30 + 3x29 - 17x28 + 11x27 + 23x26 - 45x25 - x24 + 91x23 - 89x22 - 93x21 + 271x20 - 85x19 - 457x18 - 170x17 + 1084x16 - 744x15 - 1424x14 + 2912x13 - 64x12 - 5760x11 + 5888x10 + 5632x9 - 17408x8 + 6144x7 + 28672x6 - 40960x5 - 16384x4 + 98304x3 - 65536x2 - 131072x + 262144 |
$36$ |
[0,18] |
$7^{18}\cdot 19^{34}$ |
$2$ |
$42.6835717814$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
$[2, 74]$ |
$38$ |
$17$ |
$28076820524481.113$ |
| 36.0.590...201.1 |
x36 - x35 + 6x34 - 7x33 + 27x32 - 35x31 + 110x30 - 90x29 + 365x28 - 253x27 + 1190x26 - 820x25 + 3948x24 - 2955x23 + 8389x22 - 6275x21 + 16362x20 - 9115x19 + 28304x18 + 1097x17 + 33005x16 + 594x15 + 42702x14 - 8321x13 + 51190x12 - 23469x11 + 21146x10 - 11317x9 + 10292x8 - 3370x7 + 4283x6 + 1030x5 + 250x4 + 59x3 + 15x2 + 3x + 1 |
$36$ |
[0,18] |
$7^{30}\cdot 13^{30}$ |
$2$ |
$42.9076267033$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[2, 182]$ |
$14$ |
$17$ |
$4866030378143.887$ |
| 36.0.123...304.1 |
x36 - 6x34 + 27x32 - 109x30 + 417x28 - 1548x26 + 5644x24 - 13098x22 + 29340x20 - 63802x18 + 131850x16 - 246222x14 + 354484x12 - 42756x10 + 5157x8 - 622x6 + 75x4 - 9x2 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{48}\cdot 7^{30}$ |
$3$ |
$43.7965635407$ |
✓ |
✓ |
|
$C_6^2$ (as 36T4) |
$[14, 14]$ |
$28$ |
$17$ |
$57365817603378.39$ |
| 36.0.152...281.1 |
x36 - 4x33 + 57x30 - 36x27 + 1910x24 - 2801x21 + 16733x18 + 11446x15 + 36100x12 - 11599x9 + 4932x6 + 69x3 + 1 |
$36$ |
[0,18] |
$3^{54}\cdot 13^{30}$ |
$2$ |
$44.0522412551$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[182]$ |
$18$ |
$17$ |
$20980577392492.816$ |
| 36.0.157...816.1 |
x36 - 512x18 + 262144 |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
$$ |
| 36.0.157...816.2 |
x36 + 512x18 + 262144 |
$36$ |
[0,18] |
$2^{54}\cdot 3^{90}$ |
$2$ |
$44.0908153701$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
$$ |
| 36.0.230...769.1 |
x36 - 3x35 + 3x34 - 3x32 + 6x31 - 8x30 + 6x29 - 12x28 + 36x27 - 42x26 - 6x25 + 82x24 - 168x23 + 177x22 + 27x21 - 207x20 - 54x19 + 397x18 - 108x17 - 828x16 + 216x15 + 2832x14 - 5376x13 + 5248x12 - 768x11 - 10752x10 + 18432x9 - 12288x8 + 12288x7 - 32768x6 + 49152x5 - 49152x4 + 196608x2 - 393216x + 262144 |
$36$ |
[0,18] |
$3^{48}\cdot 7^{30}\cdot 71^{6}$ |
$3$ |
$44.5608121724$ |
✓ |
|
|
$C_2\times C_6\times A_4$ (as 36T103) |
$[14, 14]$ |
$14$ |
$17$ |
$104721329817071.11$ |
| 36.0.368...256.1 |
x36 - x35 - 2x33 + 3x32 - 3x31 + 2x30 - 37x29 + 46x28 - 5x27 + 54x26 - 97x25 + 98x24 - 41x23 + 689x22 - 924x21 + 118x20 - 795x19 + 1451x18 - 1590x17 + 472x16 - 7392x15 + 11024x14 - 1312x13 + 6272x12 - 12416x11 + 13824x10 - 2560x9 + 47104x8 - 75776x7 + 8192x6 - 24576x5 + 49152x4 - 65536x3 - 131072x + 262144 |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 23^{6}\cdot 37^{12}$ |
$4$ |
$45.1464470572$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[63]$ |
$14$ |
$17$ |
$102773304267872.48$ |
| 36.0.459...733.1 |
x36 + 3x34 - x33 + 9x32 - 6x31 + 28x30 - 27x29 + 90x28 - 109x27 + 297x26 - 417x25 + 1000x24 + 1845x23 + 3417x22 + 4535x21 + 8406x20 + 10188x19 + 20683x18 + 22158x17 + 51861x16 + 45791x15 + 133425x14 + 85512x13 + 354484x12 + 123111x11 + 42756x10 + 14849x9 + 5157x8 + 1791x7 + 622x6 + 216x5 + 75x4 + 26x3 + 9x2 + 3x + 1 |
$36$ |
[0,18] |
$3^{48}\cdot 13^{33}$ |
$2$ |
$45.423062587$ |
✓ |
✓ |
not computed |
$C_3\times C_{12}$ (as 36T3) |
$[3, 3, 9, 9]$ |
$26$ |
$17$ |
$20980577392492.816$ |
| 36.0.519...889.1 |
x36 - 6x35 + 54x34 - 249x33 + 1281x32 - 4767x31 + 17772x30 - 55056x29 + 164652x28 - 444090x27 + 1149975x26 - 2811774x25 + 6542481x24 - 14483877x23 + 30345297x22 - 60803709x21 + 116322072x20 - 213103239x19 + 373433528x18 - 621567384x17 + 980981811x16 - 1465192428x15 + 2079415686x14 - 2795268228x13 + 3496953564x12 - 4091067075x11 + 4483655439x10 - 4385043570x9 + 3744819675x8 - 2928547434x7 + 2036109996x6 - 1081958046x5 + 405353103x4 - 123233361x3 + 32860329x2 - 5284761x + 749197 |
$36$ |
[0,18] |
$3^{62}\cdot 23^{12}\cdot 199^{6}$ |
$3$ |
$45.5785270042$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
not computed |
$18$ |
$17$ |
$$ |
| 36.0.541...464.1 |
x36 - 2x34 + 4x32 - 8x30 + 16x28 - 32x26 + 64x24 - 128x22 + 256x20 - 512x18 + 1024x16 - 2048x14 + 4096x12 - 8192x10 + 16384x8 - 32768x6 + 65536x4 - 131072x2 + 262144 |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
$$ |
| 36.0.541...464.2 |
x36 + 2x34 + 4x32 + 8x30 + 16x28 + 32x26 + 64x24 + 128x22 + 256x20 + 512x18 + 1024x16 + 2048x14 + 4096x12 + 8192x10 + 16384x8 + 32768x6 + 65536x4 + 131072x2 + 262144 |
$36$ |
[0,18] |
$2^{54}\cdot 19^{34}$ |
$2$ |
$45.6306576143$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$38$ |
$17$ |
$$ |
| 36.0.619...125.1 |
x36 - x35 + 9x34 - 10x33 + 54x32 - 49x31 + 257x30 - 206x29 + 1100x28 - 836x27 + 3655x26 - 2571x25 + 10339x24 - 5625x23 + 24829x22 - 12149x21 + 52298x20 - 24437x19 + 84375x18 - 31001x17 + 114806x16 - 20386x15 + 122457x14 - 26351x13 + 111183x12 - 31899x11 + 59771x10 - 9196x9 + 26744x8 + 4893x7 + 5542x6 + 509x5 + 1260x4 - 205x3 + 35x2 - 5x + 1 |
$36$ |
[0,18] |
$5^{27}\cdot 19^{32}$ |
$2$ |
$45.803363483$ |
✓ |
✓ |
not computed |
$C_{36}$ (as 36T1) |
$[1417]$ |
$10$ |
$17$ |
$3431432369157.3267$ |
| 36.0.220...024.1 |
x36 - 2x34 - 2x33 + 8x31 + 4x30 - 8x29 - 8x28 - 8x27 + 16x26 - 16x24 + 64x23 - 64x22 - 32x21 - 64x20 - 64x19 + 576x18 - 128x17 - 256x16 - 256x15 - 1024x14 + 2048x13 - 1024x12 + 4096x10 - 4096x9 - 8192x8 - 16384x7 + 16384x6 + 65536x5 - 65536x3 - 131072x2 + 262144 |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 31^{6}\cdot 37^{12}$ |
$4$ |
$47.4492356417$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[3, 63]$ |
$14$ |
$17$ |
$161164499152547.9$ |
| 36.0.221...944.1 |
x36 - 17x34 + 169x32 - 1130x30 + 5664x28 - 21853x26 + 66874x24 - 162613x22 + 316711x20 - 487810x18 + 592078x16 - 549123x14 + 384931x12 - 190091x10 + 66033x8 - 13002x6 + 1695x4 - 45x2 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{18}\cdot 19^{32}$ |
$3$ |
$47.4526521699$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
$[171]$ |
$12$ |
$17$ |
$119587984215961.08$ |
| 36.0.400...241.1 |
x36 - 14x35 + 129x34 - 874x33 + 4865x32 - 22922x31 + 94283x30 - 342666x29 + 1112273x28 - 3234952x27 + 8438667x26 - 19663764x25 + 40577370x24 - 72857172x23 + 109953255x22 - 128328007x21 + 83898469x20 + 71389621x19 - 339203441x18 + 610359985x17 - 658477439x16 + 279191379x15 + 463357277x14 - 1113046997x13 + 1096834803x12 - 317516043x11 - 517559160x10 + 549915913x9 + 131226304x8 - 546397416x7 + 300520880x6 + 8345200x5 - 14423488x4 - 397760x3 + 206720x2 + 13568x + 512 |
$36$ |
[0,18] |
$7^{30}\cdot 67^{12}\cdot 167^{6}$ |
$3$ |
$48.2383798222$ |
✓ |
|
|
$C_2^2\times S_3\times A_4$ (as 36T334) |
$[228]$ |
$14$ |
$17$ |
$154416550498474.53$ |
| 36.0.473...721.1 |
x36 - x35 - 4x34 + 15x33 - 16x32 - 64x31 + 289x30 + 606x29 - 2131x28 + 1716x27 + 8000x26 - 37236x25 + 41632x24 + 157678x23 + 138311x22 - 88085x21 - 438826x20 - 452289x19 + 632324x18 + 713006x17 - 496621x16 - 2036590x15 - 2057459x14 + 1547178x13 + 6189592x12 + 1579124x11 - 31870x10 - 127114x9 - 32211x8 + 891x7 + 2434x6 - 49x5 - 196x4 - 50x3 + x2 + 4x + 1 |
$36$ |
[0,18] |
$3^{18}\cdot 7^{30}\cdot 13^{24}$ |
$3$ |
$48.4660800825$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[6, 78]$ |
$42$ |
$17$ |
$118794051645799.06$ |
| 36.0.550...744.1 |
x36 - 12x35 + 117x34 - 801x33 + 4695x32 - 22944x31 + 99156x30 - 377772x29 + 1300485x28 - 4063386x27 + 11677437x26 - 31091397x25 + 77290173x24 - 180440796x23 + 396698646x22 - 823211451x21 + 1614415197x20 - 3001125603x19 + 5316812738x18 - 9023396952x17 + 14711412132x16 - 22930637760x15 + 33755151003x14 - 46228515924x13 + 58054312566x12 - 66243228153x11 + 68283850818x10 - 62712669783x9 + 49993043427x8 - 33497730303x7 + 18223735458x6 - 7755245535x5 + 2488299969x4 - 581944761x3 + 94855845x2 - 9757218x + 507547 |
$36$ |
[0,18] |
$2^{24}\cdot 3^{62}\cdot 7^{12}\cdot 199^{6}$ |
$4$ |
$48.6672736228$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
not computed |
$18$ |
$17$ |
$$ |
| 36.0.685...625.1 |
x36 + 9x34 - 4x33 + 72x32 - 69x31 + 584x30 + 981x29 + 4881x28 + 7326x27 + 34614x26 + 39264x25 + 241820x24 + 164610x23 + 347325x22 + 272002x21 + 443511x20 + 341952x19 + 513316x18 + 62091x17 + 423768x16 + 53105x15 + 415071x14 + 105954x13 + 408896x12 + 148752x11 + 103692x10 + 47916x9 + 30861x8 + 10350x7 + 8009x6 - 1710x5 + 372x4 - 77x3 + 18x2 - 3x + 1 |
$36$ |
[0,18] |
$3^{48}\cdot 5^{18}\cdot 7^{30}$ |
$3$ |
$48.966046629$ |
✓ |
✓ |
not computed |
$C_6^2$ (as 36T4) |
$[18, 126]$ |
$14$ |
$17$ |
$13624539961495.691$ |
| 36.0.722...125.1 |
x36 + 9x34 + 54x32 + 273x30 + 1260x28 - x27 + 4374x26 - 18x25 + 13050x24 - 189x23 + 34695x22 - 153x21 + 79785x20 + 1935x19 + 133435x18 + 11664x17 + 197460x16 + 36792x15 + 255879x14 + 40932x13 + 256629x12 + 26649x11 + 121878x10 + 26x9 + 55485x8 - 19917x7 + 22041x6 - 4752x5 + 6021x4 - 699x3 + 81x2 - 9x + 1 |
$36$ |
[0,18] |
$3^{88}\cdot 5^{27}$ |
$2$ |
$49.0370012138$ |
✓ |
✓ |
not computed |
$C_{36}$ (as 36T1) |
$[2053]$ |
$10$ |
$17$ |
$6550249244897.024$ |
| 36.0.786...544.1 |
x36 - x35 + x34 - x33 + x32 - 5x31 + x30 - 24x29 + 20x28 - 16x27 + 28x26 + 8x25 + 80x24 + 32x23 + 208x22 - 192x21 - 64x20 - 320x19 - 448x18 - 640x17 - 256x16 - 1536x15 + 3328x14 + 1024x13 + 5120x12 + 1024x11 + 7168x10 - 8192x9 + 20480x8 - 49152x7 + 4096x6 - 40960x5 + 16384x4 - 32768x3 + 65536x2 - 131072x + 262144 |
$36$ |
[0,18] |
$2^{24}\cdot 7^{30}\cdot 229^{12}$ |
$3$ |
$49.1526410239$ |
✓ |
|
|
$C_2\times C_6\times S_4$ (as 36T330) |
$[3, 3, 18]$ |
$14$ |
$17$ |
$290558369176692.94$ |
| 36.0.186...849.1 |
x36 - 9x35 + 84x34 - 474x33 + 2544x32 - 10560x31 + 40809x30 - 131799x29 + 391791x28 - 999422x27 + 2325150x26 - 4660386x25 + 8396052x24 - 12580209x23 + 15643398x22 - 11729097x21 - 3258969x20 + 36356592x19 - 76149739x18 + 110085921x17 - 89826543x16 - 1425666x15 + 198417867x14 - 384743850x13 + 432712269x12 - 69755586x11 - 550371321x10 + 1063020818x9 - 679694445x8 - 366468081x7 + 1347871539x6 - 962673774x5 - 198005841x4 + 1059232617x3 - 493446843x2 - 181048875x + 361488133 |
$36$ |
[0,18] |
$3^{62}\cdot 31^{12}\cdot 199^{6}$ |
$3$ |
$50.3467651299$ |
✓ |
|
not computed |
$C_2^2\times S_3\times A_4$ (as 36T334) |
not computed |
$18$ |
$17$ |
$$ |
| 36.0.343...529.1 |
x36 - 4x35 + 29x34 - 102x33 + 387x32 - 1124x31 + 3306x30 - 8114x29 + 22893x28 - 48914x27 + 130172x26 - 236820x25 + 491340x24 - 771909x23 + 1556952x22 - 2575973x21 + 9578578x20 - 17316065x19 + 51912793x18 - 76656575x17 + 141757837x16 - 135159634x15 + 136402715x14 - 44564002x13 - 58867556x12 + 59049233x11 - 7027542x10 - 75995389x9 + 25472394x8 + 135493988x7 + 125206304x6 + 59315184x5 + 16879200x4 + 3007232x3 + 327552x2 + 19712x + 512 |
$36$ |
[0,18] |
$7^{30}\cdot 67^{12}\cdot 239^{6}$ |
$3$ |
$51.2082126583$ |
✓ |
|
|
$C_2^2\times S_3\times A_4$ (as 36T334) |
$[252]$ |
$14$ |
$17$ |
$338042130880954.0$ |
| 36.0.485...969.1 |
x36 - 136x27 - 1187x18 - 2676888x9 + 387420489 |
$36$ |
[0,18] |
$3^{90}\cdot 11^{18}$ |
$2$ |
$51.7010638188$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
not computed |
$54$ |
$17$ |
$$ |
| 36.36.650...125.1 |
x36 - 36x34 + 594x32 - 5952x30 + 40455x28 - x27 - 197316x26 + 27x25 + 712530x24 - 324x23 - 1937520x22 + 2277x21 + 3996135x20 - 10395x19 - 6249100x18 + 32319x17 + 7354710x16 - 69768x15 - 6418656x14 + 104652x13 + 4056234x12 - 107406x11 - 1790712x10 + 72931x9 + 523260x8 - 30897x7 - 93024x6 + 7398x5 + 8721x4 - 849x3 - 324x2 + 36x + 1 |
$36$ |
[36,0] |
$3^{90}\cdot 5^{27}$ |
$2$ |
$52.123148338$ |
|
✓ |
✓ |
$C_{36}$ (as 36T1) |
trivial |
$2$ |
$35$ |
$31157843880432600000$ |
| 36.0.774...632.1 |
x36 + 3 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{107}$ |
$2$ |
$52.3769724955$ |
|
|
|
$(C_2\times C_{18}):C_6$ (as 36T185) |
trivial |
$6$ |
$17$ |
$146190247413682400$ |
| 36.0.807...721.1 |
x36 - x35 + 18x34 - 15x33 + 185x32 - 137x31 + 1281x30 - 831x29 + 6616x28 - 3799x27 + 26339x26 - 13196x25 + 83006x24 - 36260x23 + 208286x22 - 77735x21 + 418163x20 - 132518x19 + 666068x18 - 173318x17 + 834766x16 - 177139x15 + 804267x14 - 129870x13 + 582511x12 - 73129x11 + 302060x10 - 23507x9 + 107217x8 - 7128x7 + 23244x6 - 78x5 + 2775x4 - 165x3 + 126x2 + 9x + 1 |
$36$ |
[0,18] |
$3^{18}\cdot 37^{34}$ |
$2$ |
$52.4372651879$ |
✓ |
✓ |
not computed |
$C_2\times C_{18}$ (as 36T2) |
$[19, 684]$ |
$6$ |
$17$ |
$3171872728760.222$ |
| 36.0.900...616.1 |
x36 + 36x34 + 594x32 + 5953x30 + 40485x28 + 197721x26 + 715780x24 + 1954770x22 + 4059891x20 + 6417344x18 + 7674462x16 + 6854571x14 + 4475587x12 + 2066547x10 + 640764x8 + 122466x6 + 12276x4 + 432x2 + 1 |
$36$ |
[0,18] |
$2^{36}\cdot 3^{54}\cdot 7^{30}$ |
$3$ |
$52.5969116658$ |
✓ |
✓ |
✓ |
$C_6^2$ (as 36T4) |
$[2, 28, 364]$ |
$4$ |
$17$ |
$816369751172.7767$ |
| 36.36.900...616.1 |
x36 - 36x34 + 594x32 - 5951x30 + 40425x28 - 196911x26 + 709280x24 - 1920270x22 + 3932379x20 - 6080856x18 + 7034958x16 - 5982741x14 + 3636879x12 - 1514853x10 + 405648x8 - 63358x6 + 4956x4 - 144x2 + 1 |
$36$ |
[36,0] |
$2^{36}\cdot 3^{54}\cdot 7^{30}$ |
$3$ |
$52.5969116658$ |
|
✓ |
✓ |
$C_6^2$ (as 36T4) |
trivial |
$2$ |
$35$ |
$33651165194729250000$ |
