Number field search results

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

Results (31 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
22.18.276...125.1	$x^{22} - x^{21} - 19 x^{20} + 14 x^{19} + 121 x^{18} - 78 x^{17} - 261 x^{16} + 287 x^{15} - 160 x^{14} - 852 x^{13} + 1239 x^{12} + 1601 x^{11} - 1405 x^{10} - 1576 x^{9} + 348 x^{8} + 692 x^{7} + 274 x^{6} - 60 x^{5} - 159 x^{4} - 32 x^{3} + 22 x^{2} + 4 x - 1$	$22$	[18,2]	$5^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2}$	$5$	$33.1212683614$	$6136288.465987807$			?	$C_2\times S_{11}$ (as 22T47)	trivial	$2$	$19$	$1570808982.29$
22.18.367...125.1	$x^{22} - x^{21} - 22 x^{20} + 5 x^{19} + 191 x^{18} + 88 x^{17} - 819 x^{16} - 753 x^{15} + 1905 x^{14} + 2178 x^{13} - 2680 x^{12} - 3041 x^{11} + 2570 x^{10} + 2301 x^{9} - 1770 x^{8} - 1001 x^{7} + 811 x^{6} + 259 x^{5} - 211 x^{4} - 38 x^{3} + 25 x^{2} + 2 x - 1$	$22$	[18,2]	$5^{11}\cdot 8674315276967^{2}$	$2$	$33.5496661146$	$6585710.013721755$			?	$C_2\times S_{11}$ (as 22T47)	trivial	$2$	$19$	$2040269368.26$
22.18.409...729.1	$x^{22} - 3 x^{21} - 14 x^{20} + 42 x^{19} + 35 x^{18} - 82 x^{17} - 76 x^{16} - 508 x^{15} + 1938 x^{14} - 984 x^{13} - 5144 x^{12} + 9774 x^{11} + 1291 x^{10} - 17627 x^{9} + 8445 x^{8} + 12822 x^{7} - 10291 x^{6} - 3443 x^{5} + 4487 x^{4} - 121 x^{3} - 672 x^{2} + 130 x + 1$	$22$	[18,2]	$23^{21}\cdot 47^{3}$	$2$	$33.7166533192$	$136.73511025656717$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$19$	$1999453068.78$
22.18.719...104.1	$x^{22} - 14 x^{20} + 64 x^{18} - 52 x^{16} - 451 x^{14} + 1535 x^{12} - 2054 x^{10} + 1332 x^{8} - 396 x^{6} + 30 x^{4} + 7 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 23^{20}$	$2$	$34.5911015298$				?	$C_2^{10}:C_{11}$ (as 22T23)	trivial	$2$	$19$	$2743636898.8$
22.18.719...104.2	$x^{22} - 10 x^{20} + 12 x^{18} + 145 x^{16} - 502 x^{14} + 434 x^{12} + 331 x^{10} - 775 x^{8} + 484 x^{6} - 139 x^{4} + 19 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 23^{20}$	$2$	$34.5911015298$				?	$C_2^{10}:C_{11}$ (as 22T23)	trivial	$2$	$19$	$2666560227.43$
22.18.101...661.1	$x^{22} - 11 x^{21} + 40 x^{20} - 15 x^{19} - 254 x^{18} + 519 x^{17} + 310 x^{16} - 1970 x^{15} + 1107 x^{14} + 2977 x^{13} - 3993 x^{12} - 1171 x^{11} + 5121 x^{10} - 1997 x^{9} - 2876 x^{8} + 2700 x^{7} + 340 x^{6} - 1207 x^{5} + 283 x^{4} + 173 x^{3} - 80 x^{2} + 3 x + 1$	$22$	[18,2]	$3363181\cdot 55029067682009^{2}$	$2$	$35.1410882696$	$13604143298.12233$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$19$	$3109721457.4$
22.18.338...896.1	$x^{22} - 16 x^{20} + 105 x^{18} - 363 x^{16} + 700 x^{14} - 709 x^{12} + 248 x^{10} + 146 x^{8} - 135 x^{6} + 20 x^{4} + 5 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 2053^{2}\cdot 43747835269^{2}$	$3$	$37.112136067$				✓	$C_2^{10}.S_{11}$ (as 22T51)	trivial	$2$	$19$	$6802460318.29$
22.18.390...976.1	$x^{22} - 15 x^{20} + 91 x^{18} - 279 x^{16} + 417 x^{14} - 130 x^{12} - 453 x^{10} + 544 x^{8} - 66 x^{6} - 185 x^{4} + 75 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}$	$5$	$37.3541218434$				✓	$C_2^{10}.S_{11}$ (as 22T51)	trivial	$2$	$19$	$7576192193.94$
22.18.165...392.1	$x^{22} - 23 x^{20} + 184 x^{18} - 598 x^{16} + 437 x^{14} + 1840 x^{12} - 4324 x^{10} + 2875 x^{8} + 253 x^{6} - 828 x^{4} + 253 x^{2} - 23$	$22$	[18,2]	$2^{22}\cdot 23^{21}$	$2$	$39.8897313901$				?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$19$	$12568639506.3$
22.18.108...901.1	$x^{22} - 11 x^{21} + 40 x^{20} - 15 x^{19} - 254 x^{18} + 519 x^{17} + 309 x^{16} - 1962 x^{15} + 1086 x^{14} + 2984 x^{13} - 3923 x^{12} - 1318 x^{11} + 5184 x^{10} - 1751 x^{9} - 3296 x^{8} + 2717 x^{7} + 803 x^{6} - 1525 x^{5} + 161 x^{4} + 436 x^{3} - 110 x^{2} - 75 x - 1$	$22$	[18,2]	$137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 116499629$	$5$	$43.4469856952$	$106013022279.75117$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$19$	$26299120217.5$
22.18.154...049.1	$x^{22} - 11 x^{21} + 39 x^{20} - 5 x^{19} - 289 x^{18} + 549 x^{17} + 438 x^{16} - 2382 x^{15} + 1432 x^{14} + 3832 x^{13} - 6324 x^{12} - 692 x^{11} + 9779 x^{10} - 5877 x^{9} - 7100 x^{8} + 8177 x^{7} + 1805 x^{6} - 4599 x^{5} + 512 x^{4} + 1102 x^{3} - 307 x^{2} - 80 x + 29$	$22$	[18,2]	$1297^{10}\cdot 115001$	$2$	$44.1575132655$	$12212.956112260455$			?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$19$	$71513086940.5$
22.18.228...581.1	$x^{22} - 11 x^{21} + 30 x^{20} + 85 x^{19} - 518 x^{18} + 45 x^{17} + 3394 x^{16} - 2978 x^{15} - 12837 x^{14} + 16021 x^{13} + 32642 x^{12} - 44805 x^{11} - 60933 x^{10} + 75322 x^{9} + 86609 x^{8} - 74536 x^{7} - 89913 x^{6} + 34489 x^{5} + 58999 x^{4} + 3076 x^{3} - 17033 x^{2} - 7149 x - 883$	$22$	[18,2]	$131\cdot 2297\cdot 71647\cdot 10298992926983^{2}$	$4$	$44.946078922$	$471207864818.8128$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$19$	$37601816880.6$
22.18.373...301.1	$x^{22} - 11 x^{21} + 30 x^{20} + 85 x^{19} - 516 x^{18} + 27 x^{17} + 3420 x^{16} - 2778 x^{15} - 13418 x^{14} + 15160 x^{13} + 36613 x^{12} - 43034 x^{11} - 75553 x^{10} + 73248 x^{9} + 119719 x^{8} - 70453 x^{7} - 136889 x^{6} + 22305 x^{5} + 97142 x^{4} + 21717 x^{3} - 29073 x^{2} - 17742 x - 2953$	$22$	[18,2]	$29\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681$	$5$	$45.9575047733$	$655155090331.9882$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$19$	$74620353201.4$
22.18.565...896.1	$x^{22} - 16 x^{20} + 46 x^{18} + 155 x^{16} - 748 x^{14} + 688 x^{12} + 579 x^{10} - 1382 x^{8} + 904 x^{6} - 253 x^{4} + 28 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{11}$ (as 22T30)	trivial	$2$	$19$	$356788225608$
22.18.565...896.2	$x^{22} - 19 x^{20} + 110 x^{18} - 228 x^{16} - 81 x^{14} + 1073 x^{12} - 1656 x^{10} + 934 x^{8} - 71 x^{6} - 67 x^{4} + 16 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{11}$ (as 22T30)	trivial	$2$	$19$	$244248936396$
22.18.285...232.1	$x^{22} - 22 x^{20} + 207 x^{18} - 2 x^{17} - 1092 x^{16} + 28 x^{15} + 3559 x^{14} - 156 x^{13} - 7445 x^{12} + 450 x^{11} + 10059 x^{10} - 736 x^{9} - 8611 x^{8} + 714 x^{7} + 4442 x^{6} - 426 x^{5} - 1238 x^{4} + 152 x^{3} + 140 x^{2} - 24 x - 1$	$22$	[18,2]	$2^{33}\cdot 79\cdot 3767\cdot 449833\cdot 2443537\cdot 1016137678657$	$6$	$62.1495474636$				✓	$S_{11}\wr C_2$ (as 22T57)	trivial	$2$	$19$	$1871979355040$
22.18.429...609.1	$x^{22} - 5 x^{21} - 49 x^{20} + 149 x^{19} + 1117 x^{18} - 1000 x^{17} - 12006 x^{16} - 3533 x^{15} + 64273 x^{14} + 63958 x^{13} - 171145 x^{12} - 263217 x^{11} + 207316 x^{10} + 471355 x^{9} - 84325 x^{8} - 394692 x^{7} + 1221 x^{6} + 166543 x^{5} + 881 x^{4} - 34179 x^{3} + 1826 x^{2} + 2665 x - 347$	$22$	[18,2]	$19^{11}\cdot 211^{11}$	$2$	$63.3166644731$	$503.8219009458458$			?	$C_2^{10}.D_{11}$ (as 22T29)	trivial	$2$	$19$	$3627901913190$
22.18.395...936.1	$x^{22} - 33 x^{20} + 429 x^{18} - 2673 x^{16} + 6578 x^{14} + 12122 x^{12} - 121726 x^{10} + 319682 x^{8} - 379335 x^{6} + 172667 x^{4} + 11253 x^{2} - 20449$	$22$	[18,2]	$2^{34}\cdot 7^{10}\cdot 11^{22}$	$3$	$77.7600145192$				?	$C_2^{10}.F_{11}$ (as 22T34)	trivial	$2$	$19$	$84012537963800$
22.18.158...744.1	$x^{22} - 11 x^{20} - 319 x^{18} + 7183 x^{16} - 57794 x^{14} + 234762 x^{12} - 526174 x^{10} + 651002 x^{8} - 398827 x^{6} + 67529 x^{4} + 26565 x^{2} - 3721$	$22$	[18,2]	$2^{36}\cdot 7^{10}\cdot 11^{22}$	$3$	$82.8176105784$				?	$C_2^{10}.F_{11}$ (as 22T34)	trivial	$2$	$19$	$178623184551000$
22.18.276...552.1	$x^{22} - 22 x^{20} - 88 x^{18} + 3520 x^{16} - 4576 x^{14} - 99132 x^{12} + 468424 x^{10} - 870980 x^{8} + 806696 x^{6} - 380600 x^{4} + 81092 x^{2} - 4732$	$22$	[18,2]	$2^{34}\cdot 7^{11}\cdot 11^{22}$	$3$	$84.9512708677$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$19$	$275497411266000$
22.18.434...296.1	$x^{22} - 44 x^{20} + 660 x^{18} - 2640 x^{16} - 27456 x^{14} + 312576 x^{12} - 1046848 x^{10} + 991232 x^{8} + 892672 x^{6} - 1402368 x^{4} + 259072 x^{2} - 11264$	$22$	[18,2]	$2^{34}\cdot 7^{10}\cdot 11^{23}$	$3$	$86.7146277629$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$19$	$515955293802000$
22.18.113...984.1	$x^{22} - 33 x^{20} - 473 x^{18} - 1562 x^{17} + 23265 x^{16} + 76296 x^{15} - 108526 x^{14} - 1090342 x^{13} - 1720004 x^{12} + 3925524 x^{11} + 11886094 x^{10} - 3917782 x^{9} - 28429720 x^{8} - 3261940 x^{7} + 31213369 x^{6} + 8149526 x^{5} - 15186435 x^{4} - 4824908 x^{3} + 2175415 x^{2} + 1066868 x + 115123$	$22$	[18,2]	$2^{22}\cdot 7^{16}\cdot 11^{22}$	$3$	$90.58148519459012$				?	$C_2^{10}.F_{11}$ (as 22T34)	trivial	$2$	$19$	$519373019408642.56$
22.18.156...000.1	$x^{22} - 36 x^{20} + 45 x^{18} + 7290 x^{16} - 90045 x^{14} + 482778 x^{12} - 1333233 x^{10} + 1837620 x^{8} - 984150 x^{6} - 46170 x^{4} + 102141 x^{2} - 1296$	$22$	[18,2]	$2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$	$4$	$91.9141100158$	$292.8999259369444$			?	$C_2^{10}:C_{11}:C_5$ (as 22T33)	trivial	$2$	$19$	$760178630770000$
22.18.178...832.1	$x^{22} - 88 x^{20} - 198 x^{19} + 2024 x^{18} + 6270 x^{17} - 19580 x^{16} - 78364 x^{15} + 78408 x^{14} + 496276 x^{13} + 7304 x^{12} - 1707542 x^{11} - 1055472 x^{10} + 3197810 x^{9} + 3138322 x^{8} - 3066712 x^{7} - 3678862 x^{6} + 1424742 x^{5} + 1891010 x^{4} - 280808 x^{3} - 376200 x^{2} + 13574 x + 18010$	$22$	[18,2]	$2^{22}\cdot 7^{15}\cdot 11^{23}$	$3$	$92.4617099971$				?	$C_2^{10}.F_{11}$ (as 22T35)	trivial	$2$	$19$	$1417836653750000$
22.18.625...000.1	$x^{22} - 29 x^{20} - 35 x^{18} + 7965 x^{16} - 79140 x^{14} + 140187 x^{12} + 1374597 x^{10} - 6587220 x^{8} + 8430720 x^{6} - 2011840 x^{4} + 141056 x^{2} - 1024$	$22$	[18,2]	$2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$	$4$	$97.8923038661$	$305.86771353088227$			?	$C_2^{10}:C_{11}:C_5$ (as 22T33)	trivial	$2$	$19$	$3681360209630000$
22.18.172...000.1	$x^{22} - 19 x^{20} - 35 x^{18} + 2820 x^{16} - 19335 x^{14} + 18417 x^{12} + 263922 x^{10} - 1087185 x^{8} + 1651980 x^{6} - 1077890 x^{4} + 270611 x^{2} - 11264$	$22$	[18,2]	$2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17}$	$4$	$102.498667026$	$388.75224058411334$			?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	trivial	$2$	$19$	$4215018604390000$
22.18.924...581.1	$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 149 x^{18} + 714 x^{17} - 1042 x^{16} - 742 x^{15} + 5168 x^{14} - 5630 x^{13} - 5248 x^{12} + 15888 x^{11} - 6710 x^{10} - 12738 x^{9} + 15541 x^{8} - 1265 x^{7} - 8234 x^{6} + 5083 x^{5} + 294 x^{4} - 1334 x^{3} + 492 x^{2} - 67 x + 3$	$22$	[18,2]	$74843^{8}\cdot 939181$	$2$	$110.638739198$	$265124.73212244833$			?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$19$	$3410489314190000$
22.18.412...904.1	$x^{22} - 62 x^{20} + 1332 x^{18} - 12445 x^{16} + 46846 x^{14} - 17000 x^{12} - 234649 x^{10} + 219644 x^{8} + 210856 x^{6} - 218489 x^{4} + 42680 x^{2} - 81$	$22$	[18,2]	$2^{22}\cdot 74843^{8}$	$2$	$118.426422289$				?	$C_2^{10}.\PSL(2,11)$ (as 22T39)	trivial	$2$	$19$	$4003271696600000$
22.18.412...904.2	$x^{22} - 50 x^{20} + 967 x^{18} - 9172 x^{16} + 44799 x^{14} - 106893 x^{12} + 101941 x^{10} - 12539 x^{8} - 4786 x^{6} + 708 x^{4} + 4 x^{2} - 1$	$22$	[18,2]	$2^{22}\cdot 74843^{8}$	$2$	$118.426422289$				?	$C_2^{10}.\PSL(2,11)$ (as 22T39)	trivial	$2$	$19$	$6265992865560000$
22.18.412...904.3	$x^{22} - 37 x^{20} + 368 x^{18} + 466 x^{16} - 26158 x^{14} + 120420 x^{12} + 98802 x^{10} - 2086099 x^{8} + 5731387 x^{6} - 6492408 x^{4} + 3090478 x^{2} - 514089$	$22$	[18,2]	$2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$					$C_2^{10}.\PSL(2,11)$ (as 22T39)	trivial	$2$	$19$	$14238434942850328$
22.18.661...732.1	$x^{22} - 2 x^{21} - 22 x^{20} + 36 x^{19} + 205 x^{18} - 257 x^{17} - 1042 x^{16} + 939 x^{15} + 3122 x^{14} - 1916 x^{13} - 5652 x^{12} + 2249 x^{11} + 6166 x^{10} - 1525 x^{9} - 3959 x^{8} + 601 x^{7} + 1438 x^{6} - 143 x^{5} - 281 x^{4} + 19 x^{3} + 27 x^{2} - x - 1$	$22$	[18,2]	$2^{2}\cdot 23\cdot 43\cdot 2083\cdot 1669897\cdot 13592816541193\cdot 35388744506094820229$	$7$	$120.994069506$				?	$S_{22}$ (as 22T59)	trivial	$2$	$19$	$10819783392900000$
22.18.106...721.1	$x^{22} - 2 x^{21} - 22 x^{20} + 36 x^{19} + 205 x^{18} - 257 x^{17} - 1042 x^{16} + 939 x^{15} + 3122 x^{14} - 1916 x^{13} - 5652 x^{12} + 2249 x^{11} + 6168 x^{10} - 1525 x^{9} - 3960 x^{8} + 601 x^{7} + 1438 x^{6} - 143 x^{5} - 281 x^{4} + 19 x^{3} + 27 x^{2} - x - 1$	$22$	[18,2]	$3^{4}\cdot 29\cdot 1051\cdot 7796988506731\cdot 55511479826982340639646618909$	$5$	$152.449872359$	$4.138058921760083e+23$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$19$	$172338502843000000$
22.18.309...072.1	$x^{22} - 152 x^{20} + 8733 x^{18} - 236350 x^{16} + 3051787 x^{14} - 17399125 x^{12} + 47374033 x^{10} - 62687488 x^{8} + 35737999 x^{6} - 4125223 x^{4} - 1571703 x^{2} - 74843$	$22$	[18,2]	$2^{22}\cdot 74843^{9}$	$2$	$197.242698696$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$19$	$1132407889300000000$