Number field search results

Results (22 matches)

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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
18.0.138...168.1	$x^{18} - x^{16} + 6 x^{14} + 52 x^{12} + 45 x^{10} + 45 x^{8} + 90 x^{6} - 9 x^{4} - 27 x^{2} + 27$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 107^{8}$	$3$	$21.9379295141$	$86.48963648013812$			?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$8$	$21360.6745425$
18.4.138...168.1	$x^{18} - 4 x^{16} + 6 x^{14} - 26 x^{12} + 96 x^{10} - 18 x^{8} + 9 x^{6} + 81 x^{4} - 108 x^{2} + 27$	$18$	[4,7]	$-\,2^{12}\cdot 3^{9}\cdot 107^{8}$	$3$	$21.9379295141$	$86.48963648013812$			?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$10$	$86889.1930703$
18.4.138...168.2	$x^{18} - 8 x^{16} + 5 x^{14} + 31 x^{12} + 48 x^{10} + 45 x^{8} + 27 x^{6} + 99 x^{4} + 54 x^{2} + 27$	$18$	[4,7]	$-\,2^{12}\cdot 3^{9}\cdot 107^{8}$	$3$	$21.9379295141$	$86.48963648013812$			?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$10$	$92625.9187567$
18.2.353...184.2	$x^{18} - 6 x^{17} + 18 x^{16} - 54 x^{15} + 200 x^{14} - 600 x^{13} + 1076 x^{12} - 1696 x^{11} + 4184 x^{10} - 6100 x^{9} - 1848 x^{8} + 13896 x^{7} - 8780 x^{6} - 7384 x^{5} + 9112 x^{4} + 288 x^{3} - 3680 x^{2} + 1568 x - 208$	$18$	[2,8]	$2^{24}\cdot 11^{9}\cdot 19^{7}$	$3$	$26.2641129343$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$9$	$701772.458618$
18.2.353...184.3	$x^{18} - 6 x^{17} + 4 x^{16} + 36 x^{15} - 49 x^{14} - 42 x^{13} - 52 x^{12} - 38 x^{11} + 1991 x^{10} - 4774 x^{9} + 4818 x^{8} - 4812 x^{7} + 7345 x^{6} - 5806 x^{5} - 48 x^{4} + 2346 x^{3} - 3244 x^{2} + 5320 x - 3154$	$18$	[2,8]	$2^{24}\cdot 11^{9}\cdot 19^{7}$	$3$	$26.2641129343$	$83.58685284594152$			?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$9$	$381440.226813$
18.0.886...752.3	$x^{18} + 8 x^{16} + 25 x^{14} + 31 x^{12} - 20 x^{10} - 81 x^{8} + 25 x^{6} + 237 x^{4} + 234 x^{2} + 27$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 107^{8}$	$3$	$27.6400591859$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$8$	$207771.196757$
18.0.886...752.4	$x^{18} + 2 x^{16} - 5 x^{14} + 13 x^{12} + 64 x^{10} + 45 x^{8} + 97 x^{6} + 153 x^{4} + 27$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 107^{8}$	$3$	$27.6400591859$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$8$	$126720.97831$
18.0.886...752.5	$x^{18} + 5 x^{16} + 4 x^{14} - 29 x^{12} - 66 x^{10} + 33 x^{8} + 288 x^{6} + 387 x^{4} + 189 x^{2} + 27$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 107^{8}$	$3$	$27.6400591859$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$8$	$124213.471524$
18.6.181...000.3	$x^{18} - 5 x^{17} - 3 x^{16} + 16 x^{15} + 22 x^{14} + 38 x^{13} + 30 x^{12} - 12 x^{11} - 45 x^{10} - 59 x^{9} - 45 x^{8} - 12 x^{7} + 30 x^{6} + 38 x^{5} + 22 x^{4} + 16 x^{3} - 3 x^{2} - 5 x + 1$	$18$	[6,6]	$2^{12}\cdot 5^{9}\cdot 197^{8}$	$3$	$37.147914143$	$74.49845739530615$			?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$11$	$15163425.8657$
18.6.181...000.4	$x^{18} + 2 x^{16} - 49 x^{14} - 155 x^{12} + 359 x^{10} + 1400 x^{8} + 80 x^{6} - 1725 x^{4} - 1025 x^{2} - 125$	$18$	[6,6]	$2^{12}\cdot 5^{9}\cdot 197^{8}$	$3$	$37.147914143$	$74.49845739530615$			?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$11$	$21822320.5615$
18.14.464...000.1	$x^{18} - 10 x^{16} + 15 x^{14} + 149 x^{12} - 713 x^{10} + 1236 x^{8} - 880 x^{6} + 131 x^{4} + 71 x^{2} - 5$	$18$	[14,2]	$2^{18}\cdot 5^{7}\cdot 197^{8}$	$3$	$39.1394241061$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$15$	$255852977.198$
18.10.464...000.2	$x^{18} - 6 x^{17} + 10 x^{16} - 6 x^{15} + 23 x^{14} - 72 x^{13} + 9 x^{12} + 418 x^{11} - 683 x^{10} - 406 x^{9} + 2318 x^{8} - 626 x^{7} - 3636 x^{6} + 2020 x^{5} + 1939 x^{4} - 1380 x^{3} - 41 x^{2} + 160 x - 25$	$18$	[10,4]	$2^{18}\cdot 5^{7}\cdot 197^{8}$	$3$	$39.1394241061$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$13$	$107812312.373$
18.10.464...000.3	$x^{18} - 6 x^{17} - 6 x^{16} + 82 x^{15} - 85 x^{14} - 272 x^{13} + 513 x^{12} + 448 x^{11} - 1403 x^{10} - 618 x^{9} + 2864 x^{8} + 220 x^{7} - 3088 x^{6} - 696 x^{5} + 2897 x^{4} + 374 x^{3} - 1515 x^{2} + 90 x + 199$	$18$	[10,4]	$2^{18}\cdot 5^{7}\cdot 197^{8}$	$3$	$39.1394241061$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$13$	$119170187.228$
18.14.116...000.1	$x^{18} - 27 x^{16} + 229 x^{14} - 616 x^{12} - 1252 x^{10} + 10145 x^{8} - 19165 x^{6} + 12125 x^{4} - 1050 x^{2} - 125$	$18$	[14,2]	$2^{18}\cdot 5^{9}\cdot 197^{8}$	$3$	$46.8034389884$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$15$	$1473811757.81$
18.10.281...000.1	$x^{18} - 5 x^{17} + 9 x^{16} - 48 x^{15} + 73 x^{14} + 145 x^{13} + 1203 x^{12} - 3277 x^{11} - 6310 x^{10} + 11552 x^{9} + 15489 x^{8} - 3141 x^{7} - 50687 x^{6} + 11061 x^{5} + 68787 x^{4} - 56325 x^{3} - 6811 x^{2} + 15560 x - 2011$	$18$	[10,4]	$2^{12}\cdot 5^{7}\cdot 197^{10}$	$3$	$55.8742608666$	$186.64713826368123$			?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$13$	$1131227607.22$
18.10.743...000.1	$x^{18} + 10 x^{16} - 211 x^{14} - 67 x^{12} + 4419 x^{10} + 2820 x^{8} - 8170 x^{6} + 1375 x^{4} + 1225 x^{2} - 125$	$18$	[10,4]	$2^{24}\cdot 5^{9}\cdot 197^{8}$	$3$	$58.968637989$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$13$	$1785280249.31$
18.6.743...000.1	$x^{18} + 21 x^{16} - 49 x^{14} - 1384 x^{12} - 2214 x^{10} + 9865 x^{8} + 17635 x^{6} + 4025 x^{4} - 2900 x^{2} - 125$	$18$	[6,6]	$2^{24}\cdot 5^{9}\cdot 197^{8}$	$3$	$58.968637989$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$11$	$1281496763.35$
18.6.743...000.2	$x^{18} + 32 x^{16} + 296 x^{14} + 240 x^{12} - 5616 x^{10} - 4560 x^{8} + 19120 x^{6} + 14400 x^{4} - 14400 x^{2} - 8000$	$18$	[6,6]	$2^{24}\cdot 5^{9}\cdot 197^{8}$	$3$	$58.968637989$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$11$	$762638058.82$
18.6.475...000.1	$x^{18} + 11 x^{16} - 91 x^{14} - 1190 x^{12} + 94 x^{10} + 28335 x^{8} + 71685 x^{6} - 5075 x^{4} - 124900 x^{2} - 36125$	$18$	[6,6]	$2^{30}\cdot 5^{9}\cdot 197^{8}$	$3$	$74.295828286$				?	$C_2^6:S_3^2$ (as 18T371)	$[2]$	$2$	$11$	$8531249157.68$
18.6.475...000.2	$x^{18} + 26 x^{16} + 193 x^{14} - 73 x^{12} - 5017 x^{10} - 5952 x^{8} + 41070 x^{6} + 33595 x^{4} - 82425 x^{2} - 36125$	$18$	[6,6]	$2^{30}\cdot 5^{9}\cdot 197^{8}$	$3$	$74.295828286$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$11$	$10738775274.6$
18.18.475...000.3	$x^{18} - 39 x^{16} + 616 x^{14} - 5106 x^{12} + 24006 x^{10} - 64300 x^{8} + 92360 x^{6} - 59750 x^{4} + 10025 x^{2} - 125$	$18$	[18,0]	$2^{30}\cdot 5^{9}\cdot 197^{8}$	$3$	$74.295828286$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$17$	$186317980282$
18.18.475...000.4	$x^{18} - 45 x^{16} + 673 x^{14} - 4870 x^{12} + 19340 x^{10} - 44275 x^{8} + 59425 x^{6} - 45875 x^{4} + 18750 x^{2} - 3125$	$18$	[18,0]	$2^{30}\cdot 5^{9}\cdot 197^{8}$	$3$	$74.295828286$				?	$C_2^6:S_3^2$ (as 18T371)	trivial	$2$	$17$	$187495578831$

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