Number field search results

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

Results (25 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
22.16.871...207.1	$x^{22} - 8 x^{21} + 18 x^{20} + 40 x^{19} - 297 x^{18} + 513 x^{17} + 450 x^{16} - 3255 x^{15} + 4443 x^{14} + 2314 x^{13} - 13613 x^{12} + 11338 x^{11} + 9530 x^{10} - 21040 x^{9} + 5227 x^{8} + 11912 x^{7} - 8172 x^{6} - 1577 x^{5} + 2749 x^{4} - 372 x^{3} - 267 x^{2} + 66 x + 1$	$22$	[16,3]	$-\,23^{21}\cdot 47^{2}$	$2$	$28.3034914521$	$136.73511025656717$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$18$	$177605096.839$
22.16.178...423.1	$x^{22} - 11 x^{21} + 51 x^{20} - 125 x^{19} + 128 x^{18} + 216 x^{17} - 1077 x^{16} + 1782 x^{15} - 804 x^{14} - 2284 x^{13} + 4953 x^{12} - 3588 x^{11} - 1546 x^{10} + 5279 x^{9} - 3904 x^{8} - 185 x^{7} + 2226 x^{6} - 1217 x^{5} - 74 x^{4} + 213 x^{3} - 24 x^{2} - 10 x + 1$	$22$	[16,3]	$-\,23^{20}\cdot 47^{3}$	$2$	$29.2380053103$	$118.57232216797493$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$18$	$238425084.122$
22.16.178...423.2	$x^{22} - 4 x^{21} - 9 x^{20} + 52 x^{19} + x^{18} - 163 x^{17} - 117 x^{16} + 266 x^{15} + 1582 x^{14} - 1236 x^{13} - 6092 x^{12} + 5618 x^{11} + 10042 x^{10} - 10618 x^{9} - 7547 x^{8} + 8528 x^{7} + 2464 x^{6} - 2769 x^{5} - 255 x^{4} + 289 x^{3} + 24 x^{2} - 9 x - 1$	$22$	[16,3]	$-\,23^{20}\cdot 47^{3}$	$2$	$29.2380053103$	$118.57232216797493$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$18$	$245612379.311$
22.16.178...423.3	$x^{22} - 5 x^{21} - 11 x^{20} + 93 x^{19} - 25 x^{18} - 607 x^{17} + 616 x^{16} + 2224 x^{15} - 4041 x^{14} - 2772 x^{13} + 11203 x^{12} - 4782 x^{11} - 11283 x^{10} + 14512 x^{9} - 1218 x^{8} - 9343 x^{7} + 6225 x^{6} + 273 x^{5} - 1230 x^{4} + 85 x^{3} + 86 x^{2} + x - 1$	$22$	[16,3]	$-\,23^{20}\cdot 47^{3}$	$2$	$29.2380053103$	$118.57232216797493$			?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$18$	$262731486.109$
22.16.289...759.1	$x^{22} - 11 x^{21} + 43 x^{20} - 45 x^{19} - 152 x^{18} + 456 x^{17} - 114 x^{16} - 1026 x^{15} + 1114 x^{14} + 790 x^{13} - 1814 x^{12} + 120 x^{11} + 1304 x^{10} - 464 x^{9} - 493 x^{8} + 217 x^{7} + 170 x^{6} - 46 x^{5} - 77 x^{4} + 9 x^{3} + 18 x^{2} - 1$	$22$	[16,3]	$-\,809\cdot 4759\cdot 8674315276967^{2}$	$3$	$29.8911403195$	$5778960349.413772$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$18$	$334750790.993$
22.16.128...496.1	$x^{22} - 14 x^{20} + 84 x^{18} - 284 x^{16} + 596 x^{14} - 794 x^{12} + 632 x^{10} - 220 x^{8} - 53 x^{6} + 65 x^{4} - 15 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 17524013040643^{2}$	$2$	$31.9887068235$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$18$	$750154888.6$
22.16.127...624.1	$x^{22} - 15 x^{20} + 91 x^{18} - 278 x^{16} + 410 x^{14} - 123 x^{12} - 404 x^{10} + 417 x^{8} - 19 x^{6} - 77 x^{4} - 3 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 55029067682009^{2}$	$2$	$35.495617601$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$18$	$2278524879.23$
22.16.138...424.1	$x^{22} - 11 x^{20} + 43 x^{18} - 52 x^{16} - 96 x^{14} + 332 x^{12} - 229 x^{10} - 230 x^{8} + 408 x^{6} - 186 x^{4} + 20 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 233^{2}\cdot 246572816873^{2}$	$3$	$35.6349006082$				✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$18$	$2425829745.46$
22.16.165...392.1	$x^{22} - 46 x^{18} + 92 x^{16} + 529 x^{14} - 2070 x^{12} + 966 x^{10} + 6141 x^{8} - 12213 x^{6} + 9039 x^{4} - 2461 x^{2} + 23$	$22$	[16,3]	$-\,2^{22}\cdot 23^{21}$	$2$	$39.88973139007569$				?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$18$	$9045022668.50669$
22.16.565...896.1	$x^{22} - 17 x^{20} + 76 x^{18} + 4 x^{16} - 654 x^{14} + 958 x^{12} + 990 x^{10} - 2740 x^{8} + 855 x^{6} + 1065 x^{4} - 556 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$18$	$196538278464$
22.16.565...896.2	$x^{22} - 17 x^{20} + 74 x^{18} + 62 x^{16} - 919 x^{14} + 1316 x^{12} + 196 x^{10} - 1389 x^{8} + 887 x^{6} - 194 x^{4} + 7 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$18$	$239801436281$
22.16.565...896.3	$x^{22} - 17 x^{20} + 56 x^{18} + 103 x^{16} - 578 x^{14} + 31 x^{12} + 1647 x^{10} - 963 x^{8} - 1208 x^{6} + 1034 x^{4} - 112 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$18$	$278020997097$
22.16.565...896.4	$x^{22} - 14 x^{20} + 39 x^{18} + 167 x^{16} - 805 x^{14} - 22 x^{12} + 3282 x^{10} - 2173 x^{8} - 3246 x^{6} + 3447 x^{4} - 852 x^{2} + 25$	$22$	[16,3]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$18$	$146702035559$
22.16.565...896.5	$x^{22} - 3 x^{20} - 47 x^{18} + 206 x^{16} + 339 x^{14} - 2659 x^{12} + 2037 x^{10} + 6243 x^{8} - 9656 x^{6} + 3512 x^{4} - 381 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.999924379508414$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$18$	$240322279806.1655$
22.16.484...288.1	$x^{22} - 4 x^{21} - 14 x^{20} + 64 x^{19} + 85 x^{18} - 434 x^{17} - 310 x^{16} + 1626 x^{15} + 804 x^{14} - 3674 x^{13} - 1589 x^{12} + 5118 x^{11} + 2305 x^{10} - 4288 x^{9} - 2238 x^{8} + 1974 x^{7} + 1299 x^{6} - 372 x^{5} - 387 x^{4} - 22 x^{3} + 42 x^{2} + 12 x + 1$	$22$	[16,3]	$-\,2^{33}\cdot 31\cdot 2287\cdot 372719\cdot 21364574876217246673$	$5$	$63.6641813966$				✓	$S_{11}\wr C_2$ (as 22T57)	trivial	$2$	$18$	$1742672113670$
22.16.432...368.1	$x^{22} - 33 x^{20} - 66 x^{19} + 231 x^{18} + 1144 x^{17} + 1529 x^{16} - 4928 x^{15} - 22154 x^{14} - 1936 x^{13} + 88242 x^{12} - 17636 x^{11} - 365706 x^{10} + 218944 x^{9} + 1743610 x^{8} + 775632 x^{7} - 2869999 x^{6} - 3158496 x^{5} + 575311 x^{4} + 2206182 x^{3} + 942403 x^{2} + 77528 x + 1789$	$22$	[16,3]	$-\,2^{28}\cdot 7^{11}\cdot 11^{22}$	$3$	$70.3186930912$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$18$	$31449293670700$
22.16.471...888.1	$x^{22} - 4 x^{21} - 16 x^{20} + 70 x^{19} + 116 x^{18} - 516 x^{17} - 533 x^{16} + 2066 x^{15} + 1752 x^{14} - 4808 x^{13} - 4036 x^{12} + 6422 x^{11} + 5961 x^{10} - 4476 x^{9} - 5101 x^{8} + 1158 x^{7} + 2240 x^{6} + 184 x^{5} - 405 x^{4} - 106 x^{3} + 19 x^{2} + 10 x + 1$	$22$	[16,3]	$-\,2^{33}\cdot 7^{3}\cdot 31\cdot 89\cdot 1033\cdot 5613742962947696588359$	$6$	$70.5976731739$				?	$S_{11}\wr C_2$ (as 22T57)	trivial	$2$	$18$	$9412688089530$
22.16.678...864.1	$x^{22} - 55 x^{20} - 22 x^{19} + 957 x^{18} + 198 x^{17} - 7293 x^{16} + 1914 x^{15} + 24794 x^{14} - 25828 x^{13} - 28380 x^{12} + 85584 x^{11} - 13596 x^{10} - 105028 x^{9} + 73260 x^{8} + 53592 x^{7} - 84535 x^{6} - 11374 x^{5} + 43571 x^{4} + 264 x^{3} - 10241 x^{2} + 572 x + 1115$	$22$	[16,3]	$-\,2^{28}\cdot 7^{10}\cdot 11^{23}$	$3$	$71.7783175447$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$18$	$29456905708500$
22.16.987...984.1	$x^{22} - 44 x^{20} + 814 x^{18} - 8426 x^{16} - 176 x^{15} + 54912 x^{14} + 4752 x^{13} - 239844 x^{12} - 52324 x^{11} + 715836 x^{10} + 302192 x^{9} - 1393920 x^{8} - 959640 x^{7} + 1505240 x^{6} + 1551528 x^{5} - 514272 x^{4} - 984368 x^{3} - 174856 x^{2} + 115280 x + 32136$	$22$	[16,3]	$-\,2^{32}\cdot 7^{10}\cdot 11^{22}$	$3$	$73.0112812456$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$18$	$35285362544300$
22.16.168...875.1	$x^{22} - 7 x^{21} - 35 x^{20} + 270 x^{19} + 645 x^{18} - 4209 x^{17} - 9252 x^{16} + 31050 x^{15} + 96990 x^{14} - 65105 x^{13} - 614131 x^{12} - 561998 x^{11} + 1988085 x^{10} + 4067340 x^{9} - 2442075 x^{8} - 9864030 x^{7} - 410850 x^{6} + 10078335 x^{5} + 2192040 x^{4} - 3755745 x^{3} - 571725 x^{2} + 123390 x - 4545$	$22$	[16,3]	$-\,3^{20}\cdot 5^{20}\cdot 11^{17}$	$3$	$74.797382692$	$101.490943175476$			?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	trivial	$2$	$18$	$67003658567600$
22.16.172...472.1	$x^{22} - 33 x^{20} + 429 x^{18} - 176 x^{17} - 4081 x^{16} + 5852 x^{15} + 47674 x^{14} - 68332 x^{13} - 459998 x^{12} + 333988 x^{11} + 2587090 x^{10} - 470580 x^{9} - 7832726 x^{8} - 1357004 x^{7} + 11956197 x^{6} + 4761548 x^{5} - 7915633 x^{4} - 4092132 x^{3} + 1244177 x^{2} + 607860 x + 45207$	$22$	[16,3]	$-\,2^{30}\cdot 7^{11}\cdot 11^{22}$	$3$	$74.8922974978$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$18$	$80132486392700$
22.16.426...448.1	$x^{22} - 4 x^{21} - 15 x^{20} + 67 x^{19} + 99 x^{18} - 474 x^{17} - 395 x^{16} + 1838 x^{15} + 1092 x^{14} - 4243 x^{13} - 2161 x^{12} + 5933 x^{11} + 2919 x^{10} - 4899 x^{9} - 2465 x^{8} + 2230 x^{7} + 1163 x^{6} - 500 x^{5} - 264 x^{4} + 52 x^{3} + 27 x^{2} - 2 x - 1$	$22$	[16,3]	$-\,2^{3}\cdot 7\cdot 13\cdot 109\cdot 947\cdot 211723\cdot 26\!\cdots\!79$	$7$	$106.817196858$	$2.0656319636854184e+22$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$18$	$1240777282540000$
22.16.818...532.1	$x^{22} - 4 x^{21} - 15 x^{20} + 67 x^{19} + 99 x^{18} - 474 x^{17} - 395 x^{16} + 1838 x^{15} + 1092 x^{14} - 4243 x^{13} - 2161 x^{12} + 5933 x^{11} + 2919 x^{10} - 4899 x^{9} - 2465 x^{8} + 2231 x^{7} + 1163 x^{6} - 501 x^{5} - 264 x^{4} + 52 x^{3} + 27 x^{2} - 2 x - 1$	$22$	[16,3]	$-\,2^{2}\cdot 878489\cdot 33910867246172209\cdot 6872776964574058806283$	$4$	$110.030264653$	$2.2713831581271657e+22$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$18$	$3605049445600000$
22.16.412...904.1	$x^{22} - 29 x^{20} + 57 x^{18} + 3633 x^{16} - 22667 x^{14} - 43524 x^{12} + 516399 x^{10} - 732335 x^{8} - 444902 x^{6} + 959879 x^{4} - 44962 x^{2} + 441$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$					$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$11066744298400000$
22.16.412...904.2	$x^{22} - 18 x^{20} - 120 x^{18} + 3945 x^{16} - 21338 x^{14} - 14989 x^{12} + 369623 x^{10} - 648901 x^{8} - 637282 x^{6} + 2623736 x^{4} - 2281873 x^{2} + 588289$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$					$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$14304052758800000$
22.16.412...904.3	$x^{22} - 6 x^{20} - 335 x^{18} + 5050 x^{16} - 18019 x^{14} - 101105 x^{12} + 982641 x^{10} - 2621147 x^{8} + 1562236 x^{6} + 2051432 x^{4} - 26350 x^{2} + 9$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$					$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$14577850456900000$
22.16.412...904.4	$x^{22} - 20 x^{20} - 141 x^{18} + 6373 x^{16} - 58122 x^{14} + 200198 x^{12} - 37877 x^{10} - 1451515 x^{8} + 3467174 x^{6} - 2913736 x^{4} + 806773 x^{2} + 3969$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$1974438631570000$
22.16.412...904.5	$x^{22} - 32 x^{20} - 168 x^{18} + 2283 x^{16} - 1247 x^{14} - 9167 x^{12} + 11205 x^{10} + 1913 x^{8} - 6708 x^{6} + 2037 x^{4} - 117 x^{2} + 1$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$2350031861945059.5$
22.16.412...904.6	$x^{22} - 15 x^{20} + 28 x^{18} + 466 x^{16} - 2589 x^{14} + 4395 x^{12} - 34 x^{10} - 7825 x^{8} + 8726 x^{6} - 3758 x^{4} + 559 x^{2} + 9$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$2345011634829391.0$
22.16.412...904.7	$x^{22} - 32 x^{20} + 145 x^{18} + 1137 x^{16} - 6304 x^{14} - 6338 x^{12} + 47806 x^{10} - 13890 x^{8} - 94169 x^{6} + 89514 x^{4} - 23298 x^{2} + 1849$	$22$	[16,3]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$18$	$4290105966579585.0$