Number field search results

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

Results (13 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
22.20.719...104.1	$x^{22} - 24 x^{20} + 220 x^{18} - 980 x^{16} + 2267 x^{14} - 2696 x^{12} + 1324 x^{10} + 265 x^{8} - 563 x^{6} + 215 x^{4} - 29 x^{2} + 1$	$22$	[20,1]	$-\,2^{22}\cdot 23^{20}$	$2$	$34.5911015298$				?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$20$	$3758789855.24$
22.20.158...999.1	$x^{22} - 11 x^{21} + 41 x^{20} - 25 x^{19} - 223 x^{18} + 525 x^{17} + 92 x^{16} - 1654 x^{15} + 1480 x^{14} + 1772 x^{13} - 3759 x^{12} + 506 x^{11} + 3901 x^{10} - 2800 x^{9} - 1867 x^{8} + 2565 x^{7} + 335 x^{6} - 1066 x^{5} - 4 x^{4} + 202 x^{3} + 3 x^{2} - 14 x - 1$	$22$	[20,1]	$-\,79\cdot 1451^{2}\cdot 18521\cdot 71823490019^{2}$	$4$	$35.8589982125$	$12348457743.510412$			?	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$20$	$6449194007.94$
22.20.411...831.1	$x^{22} - 11 x^{21} + 39 x^{20} - 5 x^{19} - 285 x^{18} + 513 x^{17} + 519 x^{16} - 2214 x^{15} + 571 x^{14} + 4063 x^{13} - 3308 x^{12} - 3539 x^{11} + 4878 x^{10} + 1039 x^{9} - 3472 x^{8} + 490 x^{7} + 1272 x^{6} - 427 x^{5} - 239 x^{4} + 95 x^{3} + 25 x^{2} - 5 x - 1$	$22$	[20,1]	$-\,151\cdot 2053^{2}\cdot 33769\cdot 43747835269^{2}$	$4$	$37.4431259863$	$21400323203.48444$			✓	$C_2^{10}.(C_2\times S_{11})$ (as 22T53)	trivial	$2$	$20$	$10091571218.1$
22.20.165...392.1	$x^{22} - 23 x^{20} + 207 x^{18} - 897 x^{16} + 1679 x^{14} + 483 x^{12} - 7636 x^{10} + 13041 x^{8} - 9660 x^{6} + 3312 x^{4} - 483 x^{2} + 23$	$22$	[20,1]	$-\,2^{22}\cdot 23^{21}$	$2$	$39.8897313901$				?	$C_{15}\times C_{420}$ (as 22T28)	trivial	$2$	$20$	$20563977553.4$
22.20.565...896.1	$x^{22} - 25 x^{20} + 250 x^{18} - 1243 x^{16} + 2879 x^{14} - 334 x^{12} - 14126 x^{10} + 33691 x^{8} - 35857 x^{6} + 18585 x^{4} - 4105 x^{2} + 289$	$22$	[20,1]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$20$	$624846806003$
22.20.565...896.2	$x^{22} - 28 x^{20} + 296 x^{18} - 1503 x^{16} + 3716 x^{14} - 3348 x^{12} - 2647 x^{10} + 7446 x^{8} - 5457 x^{6} + 1686 x^{4} - 192 x^{2} + 1$	$22$	[20,1]	$-\,2^{22}\cdot 1297^{10}$	$2$	$51.9999243795$				?	$C_2^{10}.D_{22}$ (as 22T32)	trivial	$2$	$20$	$442787807470$
22.20.282...876.1	$x^{22} - 3 x^{21} - 17 x^{20} + 53 x^{19} + 120 x^{18} - 388 x^{17} - 461 x^{16} + 1529 x^{15} + 1071 x^{14} - 3536 x^{13} - 1601 x^{12} + 4931 x^{11} + 1610 x^{10} - 4134 x^{9} - 1099 x^{8} + 2031 x^{7} + 485 x^{6} - 555 x^{5} - 128 x^{4} + 76 x^{3} + 18 x^{2} - 4 x - 1$	$22$	[20,1]	$-\,2^{2}\cdot 5647\cdot 36767\cdot 31618751\cdot 10757635112949841811531$	$5$	$55.9464601959$				✓	$S_{22}$ (as 22T59)	trivial	$2$	$20$	$2102811538580$
22.20.245...088.1	$x^{22} - x^{21} - 22 x^{20} + 21 x^{19} + 204 x^{18} - 185 x^{17} - 1038 x^{16} + 888 x^{15} + 3162 x^{14} - 2526 x^{13} - 5908 x^{12} + 4344 x^{11} + 6683 x^{10} - 4429 x^{9} - 4388 x^{8} + 2536 x^{7} + 1577 x^{6} - 744 x^{5} - 294 x^{4} + 95 x^{3} + 28 x^{2} - 4 x - 1$	$22$	[20,1]	$-\,2^{4}\cdot 3^{4}\cdot 19^{2}\cdot 31\cdot 65380800771598157\cdot 258573494153022619$	$6$	$76.092399426$				?	$S_{22}$ (as 22T59)	trivial	$2$	$20$	$75826530958700$
22.20.158...744.1	$x^{22} - 55 x^{20} + 1199 x^{18} - 13299 x^{16} + 81114 x^{14} - 279642 x^{12} + 532422 x^{10} - 491194 x^{8} + 80201 x^{6} + 190157 x^{4} - 119053 x^{2} + 18225$	$22$	[20,1]	$-\,2^{36}\cdot 7^{10}\cdot 11^{22}$	$3$	$82.8176105784$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$20$	$398887974077000$
22.20.632...976.1	$x^{22} - 55 x^{20} + 1177 x^{18} - 12639 x^{16} + 73898 x^{14} - 237402 x^{12} + 390258 x^{10} - 246906 x^{8} - 33011 x^{6} + 40249 x^{4} - 451 x^{2} + 1$	$22$	[20,1]	$-\,2^{38}\cdot 7^{10}\cdot 11^{22}$	$3$	$88.2041581953$				?	$C_2\times C_2^{10}.F_{11}$ (as 22T37)	trivial	$2$	$20$	$655923805276000$
22.20.156...000.1	$x^{22} - 61 x^{20} + 1150 x^{18} - 7485 x^{16} - 13755 x^{14} + 419313 x^{12} - 2209803 x^{10} + 5513775 x^{8} - 7283940 x^{6} + 4978855 x^{4} - 1483189 x^{2} + 85264$	$22$	[20,1]	$-\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$	$4$	$91.9141100158$	$305.86771353088227$			?	$C_2^{10}.C_{11}:C_{10}$ (as 22T36)	trivial	$2$	$20$	$647594212316000$
22.20.412...904.1	$x^{22} - 68 x^{20} + 1749 x^{18} - 21878 x^{16} + 146579 x^{14} - 538577 x^{12} + 1028049 x^{10} - 796919 x^{8} - 100770 x^{6} + 299644 x^{4} - 34200 x^{2} + 729$	$22$	[20,1]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$20$	$7215216869150000$
22.20.412...904.2	$x^{22} - 48 x^{20} + 773 x^{18} - 5165 x^{16} + 14676 x^{14} - 11976 x^{12} - 15879 x^{10} + 31691 x^{8} - 16674 x^{6} + 3536 x^{4} - 313 x^{2} + 9$	$22$	[20,1]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.426422289$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$20$	$13513644657200000$
22.20.412...904.3	$x^{22} - 34 x^{20} + 329 x^{18} - 731 x^{16} - 4872 x^{14} + 32227 x^{12} - 75755 x^{10} + 83326 x^{8} - 40183 x^{6} + 6441 x^{4} - 409 x^{2} + 9$	$22$	[20,1]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$20$	$9399985256959050.0$
22.20.412...904.4	$x^{22} - 30 x^{20} + 232 x^{18} + 1520 x^{16} - 35215 x^{14} + 227693 x^{12} - 687645 x^{10} + 972686 x^{8} - 570782 x^{6} + 126658 x^{4} - 6592 x^{2} + 81$	$22$	[20,1]	$-\,2^{22}\cdot 74843^{8}$	$2$	$118.42642228905491$				?	$C_2^{11}.\PSL(2,11)$ (as 22T42)	trivial	$2$	$20$	$14909269333961354$