Number field search results

Results (18 matches)

  Download displayed columns for results to

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
12.0.271...125.1	$x^{12} - x^{11} + 53 x^{10} - 11 x^{9} + 1303 x^{8} + 438 x^{7} + 18804 x^{6} + 9784 x^{5} + 170686 x^{4} + 49088 x^{3} + 900838 x^{2} + 99987 x + 2139101$	$12$	[0,6]	$5^{9}\cdot 7^{8}\cdot 17^{6}$	$3$	$50.4487787342$	$50.448778734178404$	✓	✓	?	$C_{12}$ (as 12T1)	$[962]$	$2$	$5$	$104.882003477$
12.12.133...125.1	$x^{12} - x^{11} - 152 x^{10} + 151 x^{9} + 8594 x^{8} - 8443 x^{7} - 228593 x^{6} + 234291 x^{5} + 2932130 x^{4} - 3275066 x^{3} - 15786160 x^{2} + 17913708 x + 16784881$	$12$	[12,0]	$5^{9}\cdot 7^{10}\cdot 17^{6}$	$3$	$69.7750779953$	$69.77507799528695$		✓	?	$C_{12}$ (as 12T1)	$[2]$	$2$	$11$	$6790562.47053$
12.0.384...125.1	$x^{12} - x^{11} + 45 x^{10} - 15 x^{9} + 1141 x^{8} + 680 x^{7} + 18214 x^{6} + 13740 x^{5} + 178606 x^{4} + 104830 x^{3} + 1201400 x^{2} + 851959 x + 4264781$	$12$	[0,6]	$5^{9}\cdot 13^{8}\cdot 17^{6}$	$3$	$76.2220922079$	$76.22209220793223$	✓	✓	?	$C_{12}$ (as 12T1)	$[2, 10, 130]$	$2$	$5$	$615.54450504$
12.12.198...125.1	$x^{12} - x^{11} - 202 x^{10} + 74 x^{9} + 15753 x^{8} + 1798 x^{7} - 599316 x^{6} - 252696 x^{5} + 11554141 x^{4} + 6283413 x^{3} - 104562232 x^{2} - 45628823 x + 334724041$	$12$	[12,0]	$3^{6}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$	$4$	$87.3798479474$	$87.37984794739731$		✓	?	$C_{12}$ (as 12T1)	$[2]$	$2$	$11$	$18345440.8395$
12.0.800...125.1	$x^{12} - x^{11} + 37 x^{10} + 21 x^{9} + 997 x^{8} + 268 x^{7} + 16408 x^{6} + 7328 x^{5} + 208512 x^{4} - 219292 x^{3} + 2113070 x^{2} - 1950049 x + 6498881$	$12$	[0,6]	$5^{9}\cdot 17^{6}\cdot 19^{8}$	$3$	$98.164478691$	$98.16447869097495$	✓	✓	?	$C_{12}$ (as 12T1)	$[2834]$	$2$	$5$	$1234.55163261$
12.12.111...000.1	$x^{12} - 4 x^{11} - 257 x^{10} + 874 x^{9} + 25914 x^{8} - 71452 x^{7} - 1309383 x^{6} + 2723614 x^{5} + 34749905 x^{4} - 47923684 x^{3} - 453217430 x^{2} + 304232502 x + 2215713361$	$12$	[12,0]	$2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$	$4$	$100.897557468$	$100.89755746835681$		✓	?	$C_{12}$ (as 12T1)	$[2]$	$2$	$11$	$54495459.0657$
12.0.429...997.1	$x^{12} - x^{11} + 150 x^{10} + 168 x^{9} + 6499 x^{8} + 17779 x^{7} + 113305 x^{6} + 399401 x^{5} + 930866 x^{4} + 2425574 x^{3} + 5043531 x^{2} + 4720833 x + 2845051$	$12$	[0,6]	$17^{6}\cdot 37^{11}$	$2$	$112.912677966$	$112.9126779663512$	✓	✓		$C_{12}$ (as 12T1)	$[19546]$	$2$	$5$	$2518.23324049$
12.0.649...125.1	$x^{12} - x^{11} + 270 x^{10} - 275 x^{9} + 20801 x^{8} - 24235 x^{7} + 615964 x^{6} - 658945 x^{5} + 8871411 x^{4} - 3368575 x^{3} + 65405755 x^{2} + 15856409 x + 249089881$	$12$	[0,6]	$5^{9}\cdot 13^{10}\cdot 17^{6}$	$3$	$116.87943159$	$116.87943159008147$	✓	✓	?	$C_{12}$ (as 12T1)	$[2, 2, 2, 5746]$	$2$	$5$	$615.54450504$
12.0.970...125.1	$x^{12} - x^{11} + 443 x^{10} - 444 x^{9} + 72854 x^{8} - 73298 x^{7} + 5685112 x^{6} - 6113764 x^{5} + 223464715 x^{4} - 256778386 x^{3} + 4246142315 x^{2} - 4044668347 x + 31633408171$	$12$	[0,6]	$3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6}$	$4$	$120.85398019$	$120.85398018991815$	✓	✓	?	$C_{12}$ (as 12T1)	$[2, 2, 35906]$	$2$	$5$	$104.882003477$
12.12.280...125.1	$x^{12} - x^{11} - 210 x^{10} + 70 x^{9} + 16611 x^{8} + 1360 x^{7} - 624896 x^{6} - 200970 x^{5} + 11417901 x^{4} + 4551265 x^{3} - 90501020 x^{2} - 23480651 x + 233001991$	$12$	[12,0]	$3^{6}\cdot 5^{9}\cdot 13^{8}\cdot 17^{6}$	$4$	$132.020536363$	$132.02053636333846$		✓	?	$C_{12}$ (as 12T1)	$[2]$	$2$	$11$	$427202136.726$
12.0.402...125.1	$x^{12} - x^{11} + 21 x^{10} + 33 x^{9} + 898 x^{8} + 137 x^{7} + 14950 x^{6} + 14307 x^{5} + 235426 x^{4} - 424511 x^{3} + 3757769 x^{2} - 2920010 x + 16177451$	$12$	[0,6]	$5^{9}\cdot 17^{6}\cdot 31^{8}$	$3$	$136.048291783$	$136.04829178250532$	✓	✓	?	$C_{12}$ (as 12T1)	$[11714]$	$2$	$5$	$4882.16021651$
12.0.545...000.1	$x^{12} + 595 x^{10} + 131495 x^{8} + 13756400 x^{6} + 716192575 x^{4} + 17393248250 x^{2} + 147842610125$	$12$	[0,6]	$2^{12}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6}$	$4$	$139.550155991$	$139.5501559905739$	✓	✓	?	$C_{12}$ (as 12T1)	$[2, 2, 201994]$	$2$	$5$	$104.882003477$
12.0.712...000.1	$x^{12} - 4 x^{11} + 508 x^{10} - 1676 x^{9} + 104199 x^{8} - 273412 x^{7} + 10968102 x^{6} - 21538616 x^{5} + 623909300 x^{4} - 819565924 x^{3} + 18410523340 x^{2} - 12257477028 x + 222965992201$	$12$	[0,6]	$2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$	$4$	$142.690694182$	$142.69069418206897$	✓	✓	?	$C_{12}$ (as 12T1)	$[18, 16866]$	$2$	$5$	$104.882003477$
12.12.712...000.1	$x^{12} - 4 x^{11} - 512 x^{10} + 1724 x^{9} + 103859 x^{8} - 281572 x^{7} - 10644338 x^{6} + 21700544 x^{5} + 578712080 x^{4} - 784199124 x^{3} - 15736799340 x^{2} + 10519199812 x + 166108823761$	$12$	[12,0]	$2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$	$4$	$142.690694182$	$142.69069418206897$		✓	?	$C_{12}$ (as 12T1)	$[2]$	$2$	$11$	$320040330.009$
12.12.844...625.1	$x^{12} - x^{11} - 285 x^{10} + 285 x^{9} + 27236 x^{8} - 33450 x^{7} - 1015091 x^{6} + 1882750 x^{5} + 13705706 x^{4} - 36747465 x^{3} - 37348115 x^{2} + 178599199 x - 130101919$	$12$	[12,0]	$5^{9}\cdot 13^{11}\cdot 17^{6}$	$3$	$144.732713189$	$144.7327131886099$		✓	?	$C_{12}$ (as 12T1)	$[2, 2]$	$2$	$11$	$544261614.045$
12.12.844...625.2	$x^{12} - x^{11} - 285 x^{10} + 285 x^{9} + 27236 x^{8} - 6930 x^{7} - 1152111 x^{6} - 702950 x^{5} + 20667206 x^{4} + 25065130 x^{3} - 101392810 x^{2} - 59815601 x + 123164081$	$12$	[12,0]	$5^{9}\cdot 13^{11}\cdot 17^{6}$	$3$	$144.732713189$	$144.7327131886099$		✓		$C_{12}$ (as 12T1)	$[2, 10]$	$2$	$11$	$101052811.273$
20.10.447...552.1	$x^{20} - 4 x^{19} - 192 x^{18} - 368 x^{17} + 5900 x^{16} + 11612 x^{15} - 82376 x^{14} - 147412 x^{13} + 496249 x^{12} + 5837552 x^{11} + 28472784 x^{10} + 9581508 x^{9} - 257955946 x^{8} - 848288280 x^{7} - 488954264 x^{6} + 5231676656 x^{5} + 10164474572 x^{4} - 6966146992 x^{3} - 22153914848 x^{2} - 5610833232 x + 1443605144$	$20$	[10,5]	$-\,2^{38}\cdot 17^{8}\cdot 23^{5}\cdot 881^{8}$	$4$	$382.436101742$	$11049.38055118573$			?	$C_2^8.(S_3\times A_5)$ (as 20T754)	trivial	$2$	$14$	$12096615465700000000$
24.0.177...625.3	$x^{24} - x^{23} - 20 x^{22} + 20 x^{21} + 320 x^{20} - 219 x^{19} - 4901 x^{18} + 14901 x^{17} + 60299 x^{16} - 248180 x^{15} - 836019 x^{14} + 3276519 x^{13} + 13401461 x^{12} - 39585781 x^{11} - 30241579 x^{10} + 249183880 x^{9} - 136356881 x^{8} - 463267559 x^{7} + 1148300059 x^{6} - 13723758699 x^{5} + 13110121180 x^{4} + 71729555620 x^{3} - 174821473680 x^{2} - 220712110521 x + 1061520150601$	$24$	[0,12]	$5^{18}\cdot 7^{20}\cdot 17^{12}$	$3$	$69.7750779953$	$69.77507799528695$	✓	✓	?	$C_2\times C_{12}$ (as 24T2)	not computed	$14$	$11$

  Download displayed columns for results to