Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (26 matches)

 

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
21.11.391...159.1	$x^{21} - 2 x^{20} - 9 x^{19} + 12 x^{18} + 25 x^{17} + 8 x^{16} - 79 x^{15} + 7 x^{14} + 170 x^{13} - 132 x^{12} - 294 x^{11} - 136 x^{10} + 534 x^{9} + 158 x^{8} - 345 x^{7} + 242 x^{6} + 243 x^{5} - 58 x^{4} - 53 x^{3} - 6 x^{2} + 2 x + 1$	$21$	[11,5]	$-\,7^{5}\cdot 17^{8}\cdot 2017^{5}$	$3$	$28.6279996321$	$489.9214222709597$			?	$S_7$ (as 21T38)	trivial	$2$	$15$	$47695486.7102$
21.11.344...967.1	$x^{21} - 6 x^{20} - x^{19} + 71 x^{18} - 93 x^{17} - 305 x^{16} + 665 x^{15} + 567 x^{14} - 2100 x^{13} - 214 x^{12} + 3718 x^{11} - 982 x^{10} - 3941 x^{9} + 1934 x^{8} + 2506 x^{7} - 1669 x^{6} - 928 x^{5} + 820 x^{4} + 128 x^{3} - 214 x^{2} + 45 x - 1$	$21$	[11,5]	$-\,3^{9}\cdot 280909^{5}$	$2$	$31.751048717$	$918.0016339854739$			?	$S_7$ (as 21T38)	trivial	$2$	$15$	$130916585.101$
21.11.210...648.1	$x^{21} - 21 x^{19} - 14 x^{18} + 162 x^{17} + 216 x^{16} - 495 x^{15} - 1134 x^{14} + 54 x^{13} + 1992 x^{12} + 2889 x^{11} + 3390 x^{10} - 974 x^{9} - 15336 x^{8} - 26253 x^{7} - 15618 x^{6} + 7452 x^{5} + 19224 x^{4} + 14736 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3}$	$4$	$38.619258655$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$15$	$818153590.884$
21.11.227...336.1	$x^{21} - 21 x^{19} - 16 x^{18} + 189 x^{17} + 288 x^{16} - 873 x^{15} - 2160 x^{14} + 1755 x^{13} + 8584 x^{12} + 1377 x^{11} - 18768 x^{10} - 14529 x^{9} + 20304 x^{8} + 28701 x^{7} - 5168 x^{6} - 22680 x^{5} - 7224 x^{4} + 4800 x^{3} + 4032 x^{2} + 1152 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3}$	$5$	$38.7672942778$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$15$	$1042636001.55$
21.11.139...064.1	$x^{21} - 3 x^{19} - 2 x^{18} - 54 x^{17} - 72 x^{16} + 111 x^{15} + 270 x^{14} + 828 x^{13} + 1768 x^{12} + 513 x^{11} - 3282 x^{10} - 6730 x^{9} - 9432 x^{8} - 8733 x^{7} + 1406 x^{6} + 16092 x^{5} + 21528 x^{4} + 14992 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3}$	$4$	$52.629314108$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$15$	$23183036666.8$
21.11.139...064.2	$x^{21} - 3 x^{19} - 2 x^{18} - 54 x^{17} - 72 x^{16} + 84 x^{15} + 216 x^{14} + 954 x^{13} + 2192 x^{12} + 1188 x^{11} - 2280 x^{10} - 7076 x^{9} - 14544 x^{8} - 18213 x^{7} - 7202 x^{6} + 11772 x^{5} + 20376 x^{4} + 14864 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3}$	$4$	$52.629314108$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$15$	$24612590782.3$
21.11.539...479.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 60 x^{16} - 892 x^{15} - 480 x^{14} + 2445 x^{13} + 1949 x^{12} - 3615 x^{11} - 4188 x^{10} + 2119 x^{9} + 4464 x^{8} + 627 x^{7} - 1945 x^{6} - 1065 x^{5} + 75 x^{4} + 180 x^{3} + 27 x^{2} - 6 x - 1$	$21$	[11,5]	$-\,7^{14}\cdot 13\cdot 97\cdot 10039\cdot 628578004368802949$	$5$	$56.1241005889$	$10322408779712.084$			?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$15$	$59912281265.3$
21.11.145...400.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 56 x^{16} - 896 x^{15} - 424 x^{14} + 2509 x^{13} + 1657 x^{12} - 4006 x^{11} - 3526 x^{10} + 3229 x^{9} + 3977 x^{8} - 757 x^{7} - 2159 x^{6} - 441 x^{5} + 389 x^{4} + 167 x^{3} - 6 x^{2} - 10 x - 1$	$21$	[11,5]	$-\,2^{14}\cdot 3^{3}\cdot 5^{2}\cdot 37^{7}\cdot 138252302841813371149$	$5$	$65.6491276822$	$439713037181.062$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$15$	$382144312660$
21.11.152...867.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 57 x^{16} - 895 x^{15} - 438 x^{14} + 2493 x^{13} + 1730 x^{12} - 3915 x^{11} - 3705 x^{10} + 2992 x^{9} + 4200 x^{8} - 438 x^{7} - 2312 x^{6} - 744 x^{5} + 312 x^{4} + 200 x^{3} + 9 x^{2} - 9 x - 1$	$21$	[11,5]	$-\,7^{15}\cdot 223\cdot 80317\cdot 1789163334752592959$	$4$	$65.7963145502$	$28650323637858.58$			?	$S_7\wr C_3$ (as 21T159)	trivial	$2$	$15$	$346568702169$
21.11.121...024.1	$x^{21} - 21 x^{19} - 12 x^{18} + 189 x^{17} + 216 x^{16} - 925 x^{15} - 1620 x^{14} + 2535 x^{13} + 6616 x^{12} - 3303 x^{11} - 16212 x^{10} - 665 x^{9} + 24840 x^{8} + 9225 x^{7} - 23660 x^{6} - 14796 x^{5} + 12360 x^{4} + 11024 x^{3} - 2016 x^{2} - 3264 x - 640$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 577^{9}$	$3$	$72.638853571$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$15$	$1014045893980$
21.11.607...120.1	$x^{21} - 6 x^{19} - 4 x^{18} - 63 x^{17} - 84 x^{16} + 242 x^{15} + 540 x^{14} + 1413 x^{13} + 2888 x^{12} + 378 x^{11} - 6852 x^{10} - 11321 x^{9} - 10116 x^{8} - 5073 x^{7} + 5566 x^{6} + 18252 x^{5} + 22104 x^{4} + 15056 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 5\cdot 577^{9}$	$4$	$78.4247724381$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$15$	$2114267781900$
21.11.103...792.1	$x^{21} - 21 x^{19} - x^{18} + 189 x^{17} + 18 x^{16} - 1101 x^{15} - 135 x^{14} + 5175 x^{13} + 1640 x^{12} - 19143 x^{11} - 14415 x^{10} + 45479 x^{9} + 60858 x^{8} - 49671 x^{7} - 122905 x^{6} - 9180 x^{5} + 109356 x^{4} + 53424 x^{3} - 30384 x^{2} - 19008 x + 6208$	$21$	[11,5]	$-\,2^{10}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}$	$4$	$80.4377539978$					$C_3^7.(C_2^7.A_7)$ (as 21T151)	trivial	$2$	$15$	$15413558494200$
21.11.219...411.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 45 x^{16} - 907 x^{15} - 270 x^{14} + 2685 x^{13} + 854 x^{12} - 5050 x^{11} - 1643 x^{10} + 6094 x^{9} + 2169 x^{8} - 4438 x^{7} - 1895 x^{6} + 1645 x^{5} + 935 x^{4} - 110 x^{3} - 128 x^{2} - 21 x - 1$	$21$	[11,5]	$-\,53\cdot 229^{7}\cdot 12555396112941725258843$	$3$	$83.3768455645$	$12344425568764.783$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$15$	$2673532080110$
21.11.103...336.1	$x^{21} - 72 x^{17} - 96 x^{16} - 86 x^{15} - 108 x^{14} + 1143 x^{13} + 3224 x^{12} + 4212 x^{11} + 4680 x^{10} + 186 x^{9} - 14616 x^{8} - 32574 x^{7} - 46204 x^{6} - 53784 x^{5} - 48816 x^{4} - 30624 x^{3} - 12096 x^{2} - 2688 x - 256$	$21$	[11,5]	$-\,2^{45}\cdot 3^{21}\cdot 809^{6}$	$3$	$89.7486585247$					$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147)	trivial	$2$	$15$	$100808157432000$
21.11.237...000.1	$x^{21} - 3 x^{19} - 2 x^{18} - 90 x^{17} - 120 x^{16} + 68 x^{15} + 216 x^{14} + 1521 x^{13} + 3704 x^{12} + 2700 x^{11} - 1608 x^{10} - 9151 x^{9} - 23292 x^{8} - 32793 x^{7} - 20162 x^{6} + 5292 x^{5} + 18648 x^{4} + 14672 x^{3} + 6048 x^{2} + 1344 x + 128$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 6679^{6}$	$4$	$93.3874102746$				?	$C_3^7.(C_2^7.A_7)$ (as 21T151)	trivial	$2$	$15$	$12200061834400$
21.11.482...872.1	$x^{21} - 12 x^{19} - 14 x^{18} - 171 x^{17} + 762 x^{16} + 2775 x^{15} - 11556 x^{14} - 7095 x^{13} + 67730 x^{12} - 4464 x^{11} - 219000 x^{10} - 105816 x^{9} + 1080900 x^{8} - 492591 x^{7} - 3230200 x^{6} + 5102568 x^{5} - 1202184 x^{4} - 1646784 x^{3} + 1253952 x^{2} - 358272 x + 39808$	$21$	[11,5]	$-\,2^{14}\cdot 3^{28}\cdot 23^{3}\cdot 239^{3}\cdot 311^{2}\cdot 431^{3}$	$6$	$96.5854395362$				?	$C_3^7.(C_2^6.S_7)$ (as 21T149)	trivial	$2$	$15$	$9904428893780$
21.11.756...911.1	$x^{21} - x^{20} - 10 x^{19} + 40 x^{18} - 74 x^{17} + 11 x^{16} + 323 x^{15} - 1158 x^{14} + 2738 x^{13} - 4870 x^{12} + 7701 x^{11} - 11657 x^{10} + 15330 x^{9} - 18587 x^{8} + 21309 x^{7} - 19493 x^{6} + 16136 x^{5} - 15807 x^{4} + 11731 x^{3} - 3775 x^{2} + 70 x + 41$	$21$	[11,5]	$-\,29^{18}\cdot 41^{3}\cdot 3671\cdot 3769^{2}$	$4$	$98.6793533428$	$5807824.654789286$			?	$C_3^7:C_2\wr C_7$ (as 21T123)	trivial	$2$	$15$	$21791741670400$
21.11.514...240.1	$x^{21} - 72 x^{17} - 96 x^{16} - 86 x^{15} - 108 x^{14} + 1224 x^{13} + 3440 x^{12} + 4914 x^{11} + 6396 x^{10} + 2362 x^{9} - 13176 x^{8} - 32094 x^{7} - 46140 x^{6} - 53784 x^{5} - 48816 x^{4} - 30624 x^{3} - 12096 x^{2} - 2688 x - 256$	$21$	[11,5]	$-\,2^{32}\cdot 3^{21}\cdot 5\cdot 73^{12}$	$4$	$108.111983439$				?	$C_3^7.C_2\wr C_7:C_3$ (as 21T137)	trivial	$2$	$15$	$317515413729000$
21.11.866...696.1	$x^{21} - 3 x^{20} - 13 x^{19} + 37 x^{18} + 80 x^{17} - 188 x^{16} - 321 x^{15} + 511 x^{14} + 910 x^{13} - 802 x^{12} - 1758 x^{11} + 703 x^{10} + 2157 x^{9} - 238 x^{8} - 1551 x^{7} - 113 x^{6} + 576 x^{5} + 112 x^{4} - 83 x^{3} - 20 x^{2} + 4 x + 1$	$21$	[11,5]	$-\,2^{4}\cdot 757\cdot 21211\cdot 754931\cdot 44661826147142180133953570063$	$5$	$110.827773067$	$1.2810744695827034e+21$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$15$	$116125611721000$
21.11.236...536.1	$x^{21} - 21 x^{19} - 14 x^{18} - 54 x^{17} - 72 x^{16} + 1947 x^{15} + 3942 x^{14} - 1098 x^{13} - 9352 x^{12} + 129303 x^{11} + 459714 x^{10} + 249230 x^{9} - 1062936 x^{8} - 7283943 x^{7} - 25324998 x^{6} - 47407788 x^{5} - 51752376 x^{4} - 34339664 x^{3} - 13722912 x^{2} - 3049536 x - 290432$	$21$	[11,5]	$-\,2^{14}\cdot 3^{28}\cdot 107^{3}\cdot 2269^{2}\cdot 21557^{3}$	$5$	$116.264635999$				?	$C_3^7.(C_2^6.S_7)$ (as 21T149)	trivial	$2$	$15$	$94973411061400$
21.11.139...600.1	$x^{21} + 12 x^{19} - 60 x^{18} - 288 x^{17} - 840 x^{16} - 3726 x^{15} + 594 x^{14} + 366 x^{13} + 17192 x^{12} + 75906 x^{11} - 86412 x^{10} + 32126 x^{9} + 10296 x^{8} - 447726 x^{7} + 531832 x^{6} - 214920 x^{5} + 43176 x^{4} - 2352 x^{3} - 5760 x^{2} + 1440 x + 160$	$21$	[11,5]	$-\,2^{26}\cdot 3^{21}\cdot 5^{2}\cdot 73^{12}\cdot 347$	$5$	$126.507892543$				?	$C_3^7.C_2\wr C_7:C_3$ (as 21T137)	trivial	$2$	$15$	$1482236780840000$
21.11.329...176.1	$x^{21} + 36 x^{19} - 24 x^{18} + 108 x^{17} - 144 x^{16} - 6648 x^{15} + 13392 x^{14} - 50400 x^{13} + 112576 x^{12} + 83808 x^{11} - 598848 x^{10} + 1555648 x^{9} - 3375360 x^{8} + 2618112 x^{7} + 6278144 x^{6} - 18828288 x^{5} + 22671360 x^{4} - 15421440 x^{3} + 6193152 x^{2} - 1376256 x + 131072$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 7^{12}\cdot 173^{9}$	$4$	$131.790376852$				?	$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$15$	$1077669342130000$
21.11.822...952.1	$x^{21} - 3 x^{20} - 8 x^{19} + 27 x^{18} + 21 x^{17} - 99 x^{16} - 11 x^{15} + 205 x^{14} - 54 x^{13} - 287 x^{12} + 157 x^{11} + 287 x^{10} - 235 x^{9} - 184 x^{8} + 218 x^{7} + 54 x^{6} - 122 x^{5} + 8 x^{4} + 37 x^{3} - 7 x^{2} - 4 x + 1$	$21$	[11,5]	$-\,2^{3}\cdot 10\!\cdots\!69$	$2$	$137.658775193$	$2.8670875967088593e+22$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$15$	$1161496769030000$
21.11.209...392.1	$x^{21} + 21 x^{19} - 14 x^{18} - 99 x^{17} + 132 x^{16} - 3851 x^{15} + 7614 x^{14} - 13905 x^{13} + 24672 x^{12} + 86535 x^{11} - 356466 x^{10} + 760871 x^{9} - 1419660 x^{8} + 1233567 x^{7} + 1621218 x^{6} - 5701428 x^{5} + 7018920 x^{4} - 4799280 x^{3} + 1929312 x^{2} - 428736 x + 40832$	$21$	[11,5]	$-\,2^{46}\cdot 3^{21}\cdot 11^{2}\cdot 29^{2}\cdot 809^{6}$	$5$	$160.627160857$					$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147)	trivial	$2$	$15$	$37316919733400000$
21.11.508...032.1	$x^{21} + 21 x^{19} - 14 x^{18} - 2457 x^{15} + 4914 x^{14} - 16884 x^{13} + 37016 x^{12} - 19278 x^{11} - 40572 x^{10} + 241311 x^{9} - 723996 x^{8} + 1097907 x^{7} - 806246 x^{6} + 111132 x^{5} + 297864 x^{4} - 272496 x^{3} + 114912 x^{2} - 25536 x + 2432$	$21$	[11,5]	$-\,2^{14}\cdot 3^{21}\cdot 7^{36}\cdot 19^{2}\cdot 31$	$5$	$208.617480665$				?	$C_3^7:C_2\wr C_7$ (as 21T123)	trivial	$2$	$15$	$80989570243700000$
21.11.517...264.1	$x^{21} - 3 x^{19} - 2 x^{18} - 207 x^{17} - 276 x^{16} + 745 x^{15} + 1674 x^{14} + 7029 x^{13} + 16016 x^{12} - 999 x^{11} - 48882 x^{10} - 79184 x^{9} - 73008 x^{8} - 35757 x^{7} + 55086 x^{6} + 166428 x^{5} + 199512 x^{4} + 135568 x^{3} + 54432 x^{2} + 12096 x + 1152$	$21$	[11,5]	$-\,2^{14}\cdot 3^{23}\cdot 13\cdot 31^{12}\cdot 41^{9}$	$5$	$208.781841182$				?	$C_3^7.C_2\wr F_7$ (as 21T142)	trivial	$2$	$15$	$71373275446700000$