| 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 |
| 15.15.192...521.1 |
$x^{15} - 2 x^{14} - 43 x^{13} + 100 x^{12} + 622 x^{11} - 1668 x^{10} - 3380 x^{9} + 11013 x^{8} + 4836 x^{7} - 27366 x^{6} + 3839 x^{5} + 23300 x^{4} - 6520 x^{3} - 6663 x^{2} + 1723 x + 197$ |
$15$ |
[15,0] |
$11^{12}\cdot 19^{10}$ |
$2$ |
$48.4860213922$ |
$48.486021392203654$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$39634245.0922$ |
| 15.15.365...625.1 |
$x^{15} - 5 x^{14} - 50 x^{13} + 260 x^{12} + 745 x^{11} - 4439 x^{10} - 2980 x^{9} + 29685 x^{8} - 4955 x^{7} - 81705 x^{6} + 43089 x^{5} + 82545 x^{4} - 55625 x^{3} - 17710 x^{2} + 9800 x + 2401$ |
$15$ |
[15,0] |
$5^{24}\cdot 19^{10}$ |
$2$ |
$93.5092142286$ |
$93.50921422862552$ |
|
✓ |
|
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$47458423135.208374$ |
| 15.15.482...561.1 |
$x^{15} - 2 x^{14} - 67 x^{13} + 102 x^{12} + 1524 x^{11} - 1830 x^{10} - 13856 x^{9} + 15183 x^{8} + 52210 x^{7} - 55028 x^{6} - 78181 x^{5} + 76130 x^{4} + 39828 x^{3} - 32647 x^{2} - 2587 x + 1303$ |
$15$ |
[15,0] |
$19^{10}\cdot 31^{12}$ |
$2$ |
$111.068717133$ |
$111.0687171326238$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$25852132818.113102$ |
| 15.15.138...881.1 |
$x^{15} - 2 x^{14} - 79 x^{13} + 208 x^{12} + 1972 x^{11} - 5720 x^{10} - 21178 x^{9} + 65923 x^{8} + 100680 x^{7} - 350546 x^{6} - 168943 x^{5} + 826932 x^{4} - 86756 x^{3} - 658269 x^{2} + 294489 x - 7213$ |
$15$ |
[15,0] |
$19^{10}\cdot 41^{12}$ |
$2$ |
$138.908712505$ |
$138.90871250452423$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$131418258185.00424$ |
| 15.1.105...907.1 |
$x^{15} - 2 x^{14} - 67 x^{13} + 7 x^{12} + 1862 x^{11} + 955 x^{10} - 22649 x^{9} + 15594 x^{8} + 130731 x^{7} - 339219 x^{6} - 186642 x^{5} + 1010637 x^{4} - 79380 x^{3} - 5426676 x^{2} + 9739440 x - 7873200$ |
$15$ |
[1,7] |
$-\,3^{7}\cdot 19^{10}\cdot 31^{12}$ |
$3$ |
$185.45918256313396$ |
$192.37666120520026$ |
|
|
|
$D_{15}$ (as 15T2) |
$[15]$ |
$2$ |
$7$ |
$1961515997574.46$ |
| 15.1.355...627.1 |
$x^{15} - 2 x^{14} - 103 x^{13} + 103 x^{12} + 4058 x^{11} - 2741 x^{10} - 71257 x^{9} + 89626 x^{8} + 596495 x^{7} - 1199059 x^{6} - 1908582 x^{5} + 3149229 x^{4} + 9123660 x^{3} - 14027508 x^{2} - 365904 x - 8624880$ |
$15$ |
[1,7] |
$-\,3^{7}\cdot 19^{10}\cdot 61^{12}$ |
$3$ |
$318.7299350073537$ |
$330.6183057395496$ |
|
|
|
$D_{15}$ (as 15T2) |
$[15]$ |
$2$ |
$7$ |
$113537367910376.89$ |
| 15.15.127...625.1 |
$x^{15} - 315 x^{13} - 745 x^{12} + 37950 x^{11} + 176688 x^{10} - 1972965 x^{9} - 14864145 x^{8} + 25709865 x^{7} + 496900305 x^{6} + 1090111281 x^{5} - 3949621080 x^{4} - 24504535850 x^{3} - 49854595680 x^{2} - 45194702610 x - 14819426693$ |
$15$ |
[15,0] |
$3^{20}\cdot 5^{24}\cdot 19^{10}$ |
$3$ |
$404.590872123$ |
$404.59087212305565$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
$[3]$ |
$2$ |
$14$ |
$136262050544131.52$ |
| 15.15.127...625.2 |
$x^{15} - 315 x^{13} - 80 x^{12} + 37950 x^{11} + 21078 x^{10} - 2210370 x^{9} - 1840785 x^{8} + 64187430 x^{7} + 64678900 x^{6} - 853162359 x^{5} - 801830280 x^{4} + 4137592700 x^{3} + 2003192925 x^{2} - 4152200025 x - 1849757995$ |
$15$ |
[15,0] |
$3^{20}\cdot 5^{24}\cdot 19^{10}$ |
$3$ |
$404.590872123$ |
$404.59087212305565$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
$[3]$ |
$2$ |
$14$ |
$248565525516001.56$ |
| 15.11.624...000.1 |
$x^{15} - 126 x^{13} - 1008 x^{12} - 47968 x^{11} - 737248 x^{10} - 5886360 x^{9} - 48520512 x^{8} - 378179296 x^{7} - 1954203776 x^{6} - 6255936640 x^{5} - 12603064320 x^{4} - 16068774400 x^{3} - 12611020800 x^{2} - 5569536000 x - 1060864000$ |
$15$ |
[11,2] |
$2^{18}\cdot 5^{6}\cdot 7^{4}\cdot 19^{10}\cdot 37^{4}\cdot 1481^{2}\cdot 158699^{2}$ |
$7$ |
$1790.70302565$ |
$98971312.27079217$ |
|
|
|
$A_5^3.A_4$ (as 15T98) |
trivial |
$2$ |
$12$ |
$33525688191400000000$ |
| 18.6.923...000.1 |
$x^{18} - 6 x^{17} + 37 x^{16} + 1152 x^{15} - 2974 x^{14} - 61244 x^{13} + 63744 x^{12} + 1762820 x^{11} - 4220923 x^{10} - 105291314 x^{9} - 553291175 x^{8} - 1505443500 x^{7} - 2155351755 x^{6} - 597301914 x^{5} + 3497241885 x^{4} + 6307802100 x^{3} + 4180439259 x^{2} + 98536770 x - 901812307$ |
$18$ |
[6,6] |
$2^{30}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12}\cdot 37^{4}\cdot 1481^{2}\cdot 158699^{2}$ |
$7$ |
$1131.41874588$ |
|
|
|
? |
$A_5^3.A_4$ (as 18T947) |
$[4]$ |
$2$ |
$11$ |
$218193846262000000000$ |
| 30.0.531...987.1 |
$x^{30} - 2 x^{29} + 47 x^{28} - 114 x^{27} + 1427 x^{26} - 3480 x^{25} + 26650 x^{24} - 63475 x^{23} + 359456 x^{22} - 789995 x^{21} + 3308817 x^{20} - 6363338 x^{19} + 21511529 x^{18} - 35718619 x^{17} + 94175646 x^{16} - 122059475 x^{15} + 264589630 x^{14} - 276325829 x^{13} + 505658662 x^{12} - 373829032 x^{11} + 543289539 x^{10} - 279319089 x^{9} + 400075917 x^{8} - 146956412 x^{7} + 180361499 x^{6} - 36092757 x^{5} + 51039429 x^{4} - 8911469 x^{3} + 4281340 x^{2} + 339431 x + 38809$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 11^{24}\cdot 19^{20}$ |
$3$ |
$83.9802525082$ |
$83.9802525081682$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 9726]$ |
$6$ |
$14$ |
$649367471590.597$ |
| 30.30.166...125.1 |
$x^{30} - 10 x^{29} - 45 x^{28} + 770 x^{27} - 295 x^{26} - 23359 x^{25} + 54455 x^{24} + 343495 x^{23} - 1367800 x^{22} - 2206505 x^{21} + 16375169 x^{20} - 1779305 x^{19} - 105182980 x^{18} + 113166050 x^{17} + 352596515 x^{16} - 673853726 x^{15} - 510001700 x^{14} + 1806739850 x^{13} - 24401545 x^{12} - 2533215115 x^{11} + 932296342 x^{10} + 1947745695 x^{9} - 1109021840 x^{8} - 807666870 x^{7} + 580613385 x^{6} + 155752170 x^{5} - 145475345 x^{4} - 4452115 x^{3} + 14710785 x^{2} - 1634025 x - 127301$ |
$30$ |
[30,0] |
$5^{51}\cdot 19^{20}$ |
$2$ |
$109.837694386$ |
$109.83769438621925$ |
|
✓ |
? |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$1260010579074621600000$ |
| 30.30.529...104.1 |
$x^{30} - 10 x^{29} - 48 x^{28} + 798 x^{27} - 179 x^{26} - 25184 x^{25} + 55078 x^{24} + 388292 x^{23} - 1455894 x^{22} - 2722082 x^{21} + 17930760 x^{20} + 1193082 x^{19} - 117262612 x^{18} + 101641726 x^{17} + 406752755 x^{16} - 619828244 x^{15} - 714475932 x^{14} + 1645150938 x^{13} + 547043802 x^{12} - 2315092560 x^{11} - 21631829 x^{10} + 1848879120 x^{9} - 221907026 x^{8} - 847752374 x^{7} + 136822096 x^{6} + 214129196 x^{5} - 35280309 x^{4} - 26358916 x^{3} + 4144395 x^{2} + 1133136 x - 166099$ |
$30$ |
[30,0] |
$2^{30}\cdot 11^{27}\cdot 19^{20}$ |
$3$ |
$123.249683568$ |
$123.24968356835286$ |
|
✓ |
? |
$C_{30}$ (as 30T1) |
$[3]$ |
$2$ |
$29$ |
$1831400752076153000000$ |
| 30.0.694...311.1 |
$x^{30} - 7 x^{29} - 35 x^{28} + 329 x^{27} + 476 x^{26} - 8204 x^{25} + 6275 x^{24} + 108347 x^{23} - 300328 x^{22} - 521806 x^{21} + 4169141 x^{20} - 5708315 x^{19} - 18480310 x^{18} + 86896620 x^{17} - 99437268 x^{16} - 274995417 x^{15} + 1281190811 x^{14} - 1736964517 x^{13} - 2181788246 x^{12} + 12507403922 x^{11} - 17508111675 x^{10} - 8179320955 x^{9} + 70004837147 x^{8} - 123106228978 x^{7} + 108558174307 x^{6} - 25035649243 x^{5} - 59213494009 x^{4} + 73519564340 x^{3} - 22272346010 x^{2} - 18605014849 x + 14435554493$ |
$30$ |
[0,15] |
$-\,19^{20}\cdot 31^{27}$ |
$2$ |
$156.576984612$ |
$156.57698461157645$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
not computed |
$2$ |
$14$ |
|
| 30.0.191...875.1 |
$x^{30} - 5 x^{29} + 75 x^{28} - 270 x^{27} + 3055 x^{26} - 9989 x^{25} + 76695 x^{24} - 205615 x^{23} + 1268270 x^{22} - 3053520 x^{21} + 14250607 x^{20} - 27692045 x^{19} + 104312915 x^{18} - 173603960 x^{17} + 543871790 x^{16} - 734070323 x^{15} + 1890612890 x^{14} - 2123594530 x^{13} + 4685722525 x^{12} - 4212224975 x^{11} + 7313798610 x^{10} - 5139923735 x^{9} + 7595115415 x^{8} - 3877959200 x^{7} + 3741392965 x^{6} - 529306561 x^{5} + 660578555 x^{4} + 93553250 x^{3} + 138561710 x^{2} + 23529800 x + 5764801$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 5^{48}\cdot 19^{20}$ |
$3$ |
$161.96271002$ |
$161.962710019822$ |
✓ |
✓ |
|
$C_{30}$ (as 30T1) |
$[137576373]$ |
$6$ |
$14$ |
$777558804647254.0$ |
| 30.0.239...375.1 |
$x^{30} - 10 x^{29} + 15 x^{28} + 195 x^{27} - 785 x^{26} - 2050 x^{25} + 16355 x^{24} + 14795 x^{23} - 300570 x^{22} + 326125 x^{21} + 3471424 x^{20} - 9647025 x^{19} - 30129000 x^{18} + 186863060 x^{17} - 85243185 x^{16} - 1703212137 x^{15} + 5383819095 x^{14} - 2765019025 x^{13} - 21367269535 x^{12} + 53877887060 x^{11} - 10021139591 x^{10} - 201635430090 x^{9} + 460629082720 x^{8} - 376877431190 x^{7} - 104271426180 x^{6} + 215033546696 x^{5} + 411885074405 x^{4} - 732002348645 x^{3} + 338412410830 x^{2} - 59713329110 x + 41068326751$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 5^{51}\cdot 19^{20}$ |
$3$ |
$190.244467263$ |
$190.2444672631546$ |
✓ |
✓ |
? |
$C_{30}$ (as 30T1) |
not computed |
$2$ |
$14$ |
|
| 30.2.287...549.1 |
$x^{30} - x^{29} - 72 x^{28} - 205 x^{27} + 2584 x^{26} + 11451 x^{25} - 36944 x^{24} - 311605 x^{23} - 5112 x^{22} + 6317427 x^{21} + 15943968 x^{20} - 85013349 x^{19} - 366333630 x^{18} + 204864321 x^{17} + 3097331184 x^{16} - 4063681215 x^{15} - 22809127224 x^{14} + 33952616553 x^{13} - 60808473112 x^{12} - 639238464143 x^{11} + 1242657239592 x^{10} + 2512031633641 x^{9} - 8763515984464 x^{8} - 4861966491711 x^{7} + 19283565609125 x^{6} + 6836079708868 x^{5} - 102389597598552 x^{4} + 137727803098992 x^{3} + 709824917823696 x^{2} - 1050477386704704 x + 790353944398080$ |
$30$ |
[2,14] |
$3^{14}\cdot 19^{20}\cdot 61^{27}$ |
$3$ |
$480.7904555853967$ |
$498.72355364965205$ |
|
|
|
$D_{30}$ (as 30T14) |
$[15]$ |
$2$ |
$15$ |
$75868378065549830000000000000000$ |
| 30.0.862...647.1 |
$x^{30} - 2 x^{29} - 98 x^{28} + 370 x^{27} + 5098 x^{26} - 23054 x^{25} - 115285 x^{24} + 490400 x^{23} + 2152520 x^{22} - 8012060 x^{21} - 19006172 x^{20} + 174692788 x^{19} + 264268799 x^{18} - 3832119922 x^{17} + 5081291822 x^{16} + 53250182362 x^{15} - 167220694622 x^{14} - 305735993894 x^{13} + 2457098926357 x^{12} - 4700691473708 x^{11} - 13281144500756 x^{10} + 52460559105360 x^{9} + 17282035893840 x^{8} - 342271867420800 x^{7} + 755782408529856 x^{6} + 621613814194944 x^{5} - 3212077691342592 x^{4} - 505480648946688 x^{3} + 11186896011992064 x^{2} - 14028645053546496 x + 5481313354579968$ |
$30$ |
[0,15] |
$-\,3^{15}\cdot 19^{20}\cdot 61^{27}$ |
$3$ |
$498.72355364965205$ |
$498.72355364965205$ |
|
|
|
$D_{30}$ (as 30T14) |
$[3, 120]$ |
$2$ |
$14$ |
$6901733514290882000000000000000$ |
| 45.45.206...625.1 |
$x^{45} - 15 x^{44} - 120 x^{43} + 2785 x^{42} + 2040 x^{41} - 222342 x^{40} + 420425 x^{39} + 10024590 x^{38} - 35069730 x^{37} - 280556895 x^{36} + 1389459441 x^{35} + 4980489270 x^{34} - 34327919505 x^{33} - 52485204525 x^{32} + 576080544270 x^{31} + 196092367854 x^{30} - 6820772763030 x^{29} + 3051952728270 x^{28} + 57922300812880 x^{27} - 59937846525180 x^{26} - 353495076875202 x^{25} + 542694665981220 x^{24} + 1531071286376460 x^{23} - 3131712122030760 x^{22} - 4545064586341055 x^{21} + 12339167509476885 x^{20} + 8461213880546430 x^{19} - 33709107574234355 x^{18} - 6968642817313350 x^{17} + 63373889569191960 x^{16} - 7076452922900098 x^{15} - 80218608988132905 x^{14} + 26470314281644410 x^{13} + 66243722166245240 x^{12} - 32060240741785995 x^{11} - 34356066621763764 x^{10} + 20781515138515650 x^{9} + 10477766738441505 x^{8} - 7675031336820660 x^{7} - 1594722107742745 x^{6} + 1559444254090284 x^{5} + 49643486026125 x^{4} - 150881459933485 x^{3} + 10931860799430 x^{2} + 4297070637735 x - 401780151251$ |
$45$ |
[45,0] |
$3^{60}\cdot 5^{72}\cdot 19^{30}$ |
$3$ |
$404.590872123$ |
$404.59087212305565$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
