Number field search results

Results (6 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
18.6.270...481.1	$x^{18} - 6 x^{17} + 13 x^{16} - 5 x^{15} - 50 x^{14} + 186 x^{13} - 408 x^{12} + 671 x^{11} - 888 x^{10} + 973 x^{9} - 888 x^{8} + 671 x^{7} - 408 x^{6} + 186 x^{5} - 50 x^{4} - 5 x^{3} + 13 x^{2} - 6 x + 1$	$18$	[6,6]	$37^{4}\cdot 229^{6}$	$2$	$13.6490083503$	$168.0295085661925$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$1221.91254415$
18.6.322...824.1	$x^{18} - 5 x^{16} + 11 x^{14} - 25 x^{12} + 51 x^{10} - 65 x^{8} + 59 x^{6} - 40 x^{4} + 13 x^{2} - 1$	$18$	[6,6]	$2^{18}\cdot 31^{6}\cdot 61^{4}$	$3$	$15.6635617531$	$244.0314106543862$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$4930.83963215$
18.6.343...496.1	$x^{18} - 7 x^{16} + 26 x^{14} - 68 x^{12} + 122 x^{10} - 137 x^{8} + 86 x^{6} - 26 x^{4} + 5 x^{2} - 1$	$18$	[6,6]	$2^{18}\cdot 23^{6}\cdot 97^{4}$	$3$	$15.7196945928$	$286.36728431179296$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$4765.9503312$
18.6.123...321.1	$x^{18} - 9 x^{17} + 40 x^{16} - 116 x^{15} + 226 x^{14} - 266 x^{13} + 44 x^{12} + 568 x^{11} - 1371 x^{10} + 1839 x^{9} - 1517 x^{8} + 528 x^{7} + 458 x^{6} - 864 x^{5} + 686 x^{4} - 326 x^{3} + 94 x^{2} - 15 x + 1$	$18$	[6,6]	$3^{6}\cdot 7^{4}\cdot 643^{6}$	$3$	$19.1827252704$	$160.71810651253818$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$27272.1993456$
18.18.708...264.1	$x^{18} - 17 x^{16} + 115 x^{14} - 404 x^{12} + 802 x^{10} - 911 x^{8} + 568 x^{6} - 176 x^{4} + 24 x^{2} - 1$	$18$	[18,0]	$2^{18}\cdot 37^{4}\cdot 229^{6}$	$3$	$27.2980167006$	$475.2592197863912$			✓	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$17$	$9691749.65253$
18.6.305...129.1	$x^{18} - 8 x^{17} + 46 x^{16} - 191 x^{15} + 523 x^{14} - 1064 x^{13} + 1207 x^{12} + 396 x^{11} - 3837 x^{10} + 9146 x^{9} - 10595 x^{8} + 6262 x^{7} - 10121 x^{6} + 18076 x^{5} - 8612 x^{4} + 9310 x^{3} + 89808 x^{2} - 100347 x + 10447$	$18$	[6,6]	$3^{18}\cdot 31^{12}$	$2$	$29.60481720965692$	$98.45631355516282$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$1576232.3501902334$
18.18.324...224.1	$x^{18} - 27 x^{16} + 293 x^{14} - 1668 x^{12} + 5427 x^{10} - 10303 x^{8} + 11189 x^{6} - 6448 x^{4} + 1584 x^{2} - 49$	$18$	[18,0]	$2^{18}\cdot 3^{6}\cdot 7^{4}\cdot 643^{6}$	$4$	$38.3654505407$	$454.5794518979103$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$17$	$440520753.884$
18.6.508...944.1	$x^{18} - 6 x^{17} - 52 x^{16} + 342 x^{15} + 1181 x^{14} - 8316 x^{13} - 17918 x^{12} + 119992 x^{11} + 213812 x^{10} - 1162938 x^{9} - 1943296 x^{8} + 7746998 x^{7} + 12374734 x^{6} - 33785802 x^{5} - 51586375 x^{4} + 85546866 x^{3} + 127358505 x^{2} - 90676766 x - 133896661$	$18$	[6,6]	$2^{18}\cdot 23^{12}\cdot 97^{4}$	$3$	$44.70472038568142$	$627.1267992145598$			?	$C_3^3:S_4$ (as 18T203)	trivial	$2$	$11$	$78344894.5489731$
18.6.389...201.1	$x^{18} - 8 x^{17} + 13 x^{16} + 95 x^{15} - 1077 x^{14} + 5587 x^{13} - 14159 x^{12} - 563 x^{11} + 218936 x^{10} - 1325395 x^{9} + 4074285 x^{8} - 6871493 x^{7} - 2162692 x^{6} + 88206112 x^{5} - 296071885 x^{4} + 714861729 x^{3} - 1605471655 x^{2} + 2718086673 x - 4243463647$	$18$	[6,6]	$37^{4}\cdot 229^{12}$	$2$	$83.50508586064281$	$653.6487391674256$			?	$C_3^3:S_4$ (as 18T203)	$[4]$	$2$	$11$	$6408697035.0850725$
18.6.389...201.2	$x^{18} - 4 x^{17} - 9 x^{16} - 13 x^{15} - 597 x^{14} + 2122 x^{13} - 7515 x^{12} + 36890 x^{11} + 9479 x^{10} + 172142 x^{9} + 1166220 x^{8} - 1283327 x^{7} + 12280651 x^{6} - 20991582 x^{5} + 44901835 x^{4} - 106011501 x^{3} - 30282926 x^{2} - 208666042 x - 477834611$	$18$	[6,6]	$37^{4}\cdot 229^{12}$	$2$	$83.50508586064281$	$653.6487391674256$			?	$C_3^3:S_4$ (as 18T203)	$[4]$	$2$	$11$	$4071256535.465879$
18.18.235...481.1	$x^{18} - 2 x^{17} - 249 x^{16} + 851 x^{15} + 23568 x^{14} - 109309 x^{13} - 1045799 x^{12} + 6273890 x^{11} + 20735572 x^{10} - 176507738 x^{9} - 92596625 x^{8} + 2367361083 x^{7} - 1962014393 x^{6} - 13323698337 x^{5} + 18612154293 x^{4} + 28498795308 x^{3} - 42099533188 x^{2} - 18289720992 x + 8721539523$	$18$	[18,0]	$11^{12}\cdot 37^{4}\cdot 43^{12}$	$3$	$135.43472570515786$	$1126.1951989947609$				$C_3^3:S_4$ (as 18T203)	$[2]$	$2$	$17$	$17707561154638.71$

  Download displayed columns for results to