Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (16 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
16.2.172...420.1	$x^{16} - 3 x^{15} + 5 x^{14} - 2 x^{13} - 6 x^{12} + 23 x^{11} - 34 x^{10} + 51 x^{9} - 50 x^{8} + 51 x^{7} - 34 x^{6} + 23 x^{5} - 6 x^{4} - 2 x^{3} + 5 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,2^{2}\cdot 5\cdot 37^{4}\cdot 463^{4}$	$4$	$13.7962181676$				?	$C_2\wr C_2^3.\GL(3,2)$ (as 16T1916)	trivial	$2$	$8$	$766.941029606$
16.10.871...840.1	$x^{16} - 2 x^{15} - 11 x^{14} + 17 x^{13} + 29 x^{12} - 43 x^{11} - 7 x^{10} + 35 x^{9} - 18 x^{8} + 35 x^{7} - 7 x^{6} - 43 x^{5} + 29 x^{4} + 17 x^{3} - 11 x^{2} - 2 x + 1$	$16$	[10,3]	$-\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4}$	$5$	$27.1488687087$	$6300.929112547363$			?	$C_2^7.C_{3276}$ (as 16T1944)	trivial	$2$	$12$	$1099555.69048$
16.6.871...840.1	$x^{16} - 6 x^{15} + 4 x^{14} + 39 x^{13} - 95 x^{12} + 73 x^{11} - 11 x^{10} + 4 x^{9} - 54 x^{8} + 95 x^{7} + 114 x^{6} - 22 x^{5} - 3 x^{4} - 313 x^{3} - 443 x^{2} - 280 x - 36$	$16$	[6,5]	$-\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4}$	$5$	$27.1488687087$	$6300.929112547363$			?	$C_2^7.C_{3276}$ (as 16T1944)	$[2]$	$2$	$10$	$453969.698903$
16.6.993...240.1	$x^{16} - 8 x^{15} + 34 x^{14} - 98 x^{13} + 194 x^{12} - 254 x^{11} + 156 x^{10} + 166 x^{9} - 536 x^{8} + 642 x^{7} - 340 x^{6} - 120 x^{5} + 351 x^{4} - 280 x^{3} + 106 x^{2} - 14 x - 1$	$16$	[6,5]	$-\,2^{24}\cdot 3\cdot 5\cdot 4457^{4}$	$4$	$27.3723040651$				?	$C_2\wr C_2^3.\GL(3,2)$ (as 16T1916)	trivial	$2$	$10$	$331631.005917$
16.8.122...960.1	$x^{16} - 4 x^{15} - 2 x^{14} + 16 x^{13} - 6 x^{12} + 36 x^{11} - 6 x^{10} - 224 x^{9} - 64 x^{8} - 68 x^{7} + 10 x^{6} + 936 x^{5} + 1822 x^{4} + 1172 x^{3} - 2162 x^{2} - 3720 x - 1465$	$16$	[8,4]	$2^{24}\cdot 5\cdot 37\cdot 4457^{4}$	$4$	$32.0260874389$				?	$C_2\wr C_2^3.\GL(3,2)$ (as 16T1916)	trivial	$2$	$11$	$1794573.42714$
16.8.268...040.1	$x^{16} - 2 x^{15} - 8 x^{14} + 34 x^{13} - 116 x^{12} + 72 x^{11} + 216 x^{10} - 836 x^{9} + 842 x^{8} + 3836 x^{7} - 13376 x^{6} + 21488 x^{5} - 14992 x^{4} - 2520 x^{3} + 6112 x^{2} - 1440 x - 40$	$16$	[8,4]	$2^{24}\cdot 5\cdot 13\cdot 199^{8}$	$4$	$51.7939003034$	$837.1891731578766$			?	$C_2^7.F_8:C_6$ (as 16T1841)	trivial	$2$	$11$	$373613664.709$
16.8.268...040.2	$x^{16} - 8 x^{15} + 38 x^{14} - 126 x^{13} + 194 x^{12} + 110 x^{11} - 1928 x^{10} + 6582 x^{9} - 10673 x^{8} + 7842 x^{7} + 23992 x^{6} - 76574 x^{5} + 118206 x^{4} - 110390 x^{3} + 6506 x^{2} + 36228 x - 2493$	$16$	[8,4]	$2^{24}\cdot 5\cdot 13\cdot 199^{8}$	$4$	$51.7939003034$				?	$C_2^7.F_8:C_6$ (as 16T1841)	trivial	$2$	$11$	$170592407.997$
16.2.522...280.1	$x^{16} - 2 x^{15} + 16 x^{14} - 24 x^{13} + 94 x^{12} - 54 x^{11} + 456 x^{10} + 634 x^{9} + 2217 x^{8} + 2102 x^{7} + 20 x^{6} - 7022 x^{5} - 15214 x^{4} - 20300 x^{3} - 4816 x^{2} + 5082 x + 29437$	$16$	[2,7]	$-\,2^{28}\cdot 5\cdot 11\cdot 29^{12}$	$4$	$53.9975007209$				?	$C_2^8.F_8$ (as 16T1768)	$[2, 2]$	$2$	$8$	$12512095.2581$
16.6.522...280.2	$x^{16} - 2 x^{15} - 2 x^{14} + 22 x^{13} - 44 x^{12} - 120 x^{11} + 4 x^{10} + 22 x^{9} - 2489 x^{8} - 9660 x^{7} - 20952 x^{6} - 47430 x^{5} - 31344 x^{4} + 70854 x^{3} + 89246 x^{2} - 13784 x - 42953$	$16$	[6,5]	$-\,2^{28}\cdot 5\cdot 11\cdot 29^{12}$	$4$	$53.9975007209$				?	$C_2^8.F_8$ (as 16T1768)	trivial	$2$	$10$	$229098285.922$
16.12.617...240.1	$x^{16} - 28 x^{14} - 8 x^{13} + 200 x^{12} + 360 x^{11} - 612 x^{10} - 2432 x^{9} + 818 x^{8} + 4272 x^{7} + 1756 x^{6} - 1992 x^{5} - 2880 x^{4} - 1048 x^{3} + 164 x^{2} + 80 x + 5$	$16$	[12,2]	$2^{28}\cdot 5\cdot 13\cdot 29^{12}$	$4$	$54.5642356192$				?	$C_2^8.F_8$ (as 16T1768)	trivial	$2$	$13$	$1045107258.74$
16.4.617...240.1	$x^{16} - 8 x^{15} + 28 x^{14} - 48 x^{13} + 46 x^{12} - 124 x^{11} + 88 x^{10} + 548 x^{9} - 783 x^{8} - 1268 x^{7} + 3556 x^{6} - 1148 x^{5} - 3796 x^{4} + 3944 x^{3} - 288 x^{2} - 1352 x + 588$	$16$	[4,6]	$2^{28}\cdot 5\cdot 13\cdot 29^{12}$	$4$	$54.5642356192$	$486.1196414793201$			?	$C_2^8.F_8$ (as 16T1768)	$[2, 2]$	$2$	$9$	$107690211.184$
16.8.617...240.2	$x^{16} - 16 x^{14} - 48 x^{13} - 92 x^{12} - 144 x^{11} - 120 x^{10} + 928 x^{9} + 3924 x^{8} + 4784 x^{7} + 848 x^{6} - 3712 x^{5} - 7152 x^{4} - 6240 x^{3} - 11648 x^{2} - 13120 x + 2960$	$16$	[8,4]	$2^{28}\cdot 5\cdot 13\cdot 29^{12}$	$4$	$54.5642356192$				?	$C_2^8.F_8$ (as 16T1768)	trivial	$2$	$11$	$274158139.855$
16.8.433...040.1	$x^{16} - 4 x^{15} - 74 x^{14} + 434 x^{13} + 1071 x^{12} - 11844 x^{11} + 9828 x^{10} + 113658 x^{9} - 298329 x^{8} - 172098 x^{7} + 1759128 x^{6} - 2949968 x^{5} + 2069312 x^{4} - 291760 x^{3} - 438576 x^{2} + 252384 x - 43072$	$16$	[8,4]	$2^{8}\cdot 5\cdot 7^{16}\cdot 13\cdot 97^{8}$	$5$	$126.562775357$	$1402.3004335165967$				$C_2^8.\GL(3,2)$ (as 16T1844)	$[2]$	$2$	$11$	$351517564684$
16.8.433...040.2	$x^{16} + 24 x^{14} - 98 x^{12} - 84 x^{10} + 427 x^{8} + 140 x^{6} - 434 x^{4} - 88 x^{2} + 65$	$16$	[8,4]	$2^{8}\cdot 5\cdot 7^{16}\cdot 13\cdot 97^{8}$	$5$	$126.562775357$	$1402.3004335165967$			?	$C_2^8.\GL(3,2)$ (as 16T1844)	$[2]$	$2$	$11$	$79280763684.3$
16.12.566...360.2	$x^{16} - 4 x^{15} - 103 x^{14} + 553 x^{13} + 2632 x^{12} - 23149 x^{11} + 15722 x^{10} + 271683 x^{9} - 847969 x^{8} + 135637 x^{7} + 4009341 x^{6} - 9389184 x^{5} + 9932720 x^{4} - 4866876 x^{3} + 229276 x^{2} + 749932 x - 220196$	$16$	[12,2]	$2^{8}\cdot 5\cdot 7^{16}\cdot 17\cdot 97^{8}$	$5$	$128.702679242$	$1603.5918960809438$				$C_2^8.\GL(3,2)$ (as 16T1844)	$[2]$	$2$	$13$	$593414137902$
20.16.152...465.1	$x^{20} - 8 x^{19} + 11 x^{18} + 65 x^{17} - 182 x^{16} - 162 x^{15} + 879 x^{14} - 13 x^{13} - 2124 x^{12} + 731 x^{11} + 2905 x^{10} - 1328 x^{9} - 2313 x^{8} + 1032 x^{7} + 1043 x^{6} - 371 x^{5} - 245 x^{4} + 58 x^{3} + 26 x^{2} - 3 x - 1$	$20$	[16,2]	$5\cdot 4860586389913\cdot 6258165255430831836461$	$3$	$57.425566066$	$3.8998944130818157e+17$			✓	$S_{20}$ (as 20T1117)	trivial	$2$	$17$	$76899104558.8$