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 (1-50 of )

  To download results, . 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
8.2.71762455.1	$x^{8} - x^{7} - 3 x^{6} + 5 x^{4} + 6 x^{3} - 4 x^{2} - 8 x - 1$	$8$	[2,3]	$-\,5\cdot 131\cdot 331^{2}$	$3$	$9.59372269154$	$465.6232382517007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$4.87436409009$
8.2.73884131.1	$x^{8} - x^{7} - 2 x^{6} + 6 x^{5} - 2 x^{4} - 5 x^{3} + 3 x - 2$	$8$	[2,3]	$-\,131\cdot 751^{2}$	$2$	$9.62872750396$	$313.65745647122753$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$12.2061818613$
8.0.94744833.1	$x^{8} - 2 x^{7} + 3 x^{6} - 6 x^{5} + 16 x^{4} - 24 x^{3} + 22 x^{2} - 12 x + 3$	$8$	[0,4]	$3\cdot 131\cdot 491^{2}$	$3$	$9.9327485612$	$439.27553995186213$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$4.86619493452$
8.2.186582383.1	$x^{8} - x^{7} + 3 x^{6} + 2 x^{5} - 9 x^{4} + 18 x^{3} - 24 x^{2} + 14 x - 5$	$8$	[2,3]	$-\,13\cdot 131\cdot 331^{2}$	$3$	$10.810824805$	$750.7949120765271$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$9.46346973524$
8.0.330107293.1	$x^{8} + 6 x^{6} - x^{5} + 22 x^{4} - 5 x^{3} + 31 x^{2} - 2 x + 13$	$8$	[0,4]	$23\cdot 131\cdot 331^{2}$	$3$	$11.6099911825$	$998.6505895457129$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$9.4645904982$
8.4.347397721.1	$x^{8} - 3 x^{7} + 16 x^{5} - 29 x^{4} + 12 x^{3} + 20 x^{2} - 31 x + 13$	$8$	[4,2]	$11\cdot 131\cdot 491^{2}$	$3$	$11.6843180653$	$841.1486194484302$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$15.5045937074$
8.2.350006455.1	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 17 x^{4} - 12 x^{3} + 3 x^{2} + x - 3$	$8$	[2,3]	$-\,5\cdot 17^{2}\cdot 43^{2}\cdot 131$	$4$	$11.6952499173$	$691.9573686290219$			✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$20.5864161951$
8.2.501710219.1	$x^{8} - 4 x^{7} + 11 x^{6} - 19 x^{5} + 21 x^{4} - 15 x^{3} + 4 x^{2} + x - 1$	$8$	[2,3]	$-\,19^{2}\cdot 103^{2}\cdot 131$	$3$	$12.2336659727$	$506.32696945748404$			✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$10.6704851287$
8.2.560237744.1	$x^{8} - x^{7} - x^{6} - x^{5} + 11 x^{4} - 4 x^{3} - 2 x^{2} - 4$	$8$	[2,3]	$-\,2^{4}\cdot 11^{2}\cdot 47^{2}\cdot 131$	$4$	$12.4035655336$	$520.488232335756$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$15.3898015369$
8.2.591073048.1	$x^{8} - 2 x^{7} + 6 x^{6} - 21 x^{5} + 34 x^{4} - 43 x^{3} + 29 x^{2} - 14 x + 2$	$8$	[2,3]	$-\,2^{3}\cdot 131\cdot 751^{2}$	$3$	$12.4869146881$	$887.1572577621174$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$27.3267453319$
8.2.624279059.1	$x^{8} - 2 x^{7} - 6 x^{6} + 12 x^{5} + 11 x^{4} - 23 x^{3} + x^{2} + 5 x - 7$	$8$	[2,3]	$-\,37^{2}\cdot 59^{2}\cdot 131$	$3$	$12.5725203106$	$534.7644341202956$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$21.7802807431$
8.4.674567077.1	$x^{8} - 3 x^{7} - 4 x^{6} + 9 x^{5} + 23 x^{4} - 22 x^{3} - 40 x^{2} + 18 x + 23$	$8$	[4,2]	$47\cdot 131\cdot 331^{2}$	$3$	$12.6948666309$	$1427.5738159548878$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$26.2806708204$
8.2.789540275.1	$x^{8} - 2 x^{7} + 13 x^{5} - 19 x^{4} + 21 x^{3} - 19 x^{2} - x - 3$	$8$	[2,3]	$-\,5^{2}\cdot 131\cdot 491^{2}$	$3$	$12.9470786452$	$567.1022835432776$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$28.3650617758$
8.2.789540275.2	$x^{8} - 12 x^{5} - 13 x^{4} - 35 x^{3} - 14 x^{2} - 27 x - 1$	$8$	[2,3]	$-\,5^{2}\cdot 131\cdot 491^{2}$	$3$	$12.9470786452$	$567.1022835432776$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$14.0354011417$
8.2.791109655.1	$x^{8} - 2 x^{7} + 2 x^{6} - 10 x^{5} + 12 x^{4} - 12 x^{3} + 19 x^{2} - 18 x + 1$	$8$	[2,3]	$-\,5\cdot 7^{2}\cdot 131\cdot 157^{2}$	$4$	$12.9502927369$	$848.4367978818458$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$25.723037605$
8.0.851546112.1	$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 29 x^{4} - 26 x^{3} + 14 x^{2} - 4 x + 2$	$8$	[0,4]	$2^{12}\cdot 3\cdot 23^{2}\cdot 131$	$4$	$13.0700130526$	$268.90890650924894$			✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$50.6156126708$
8.0.871328553.1	$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 12 x^{4} - 12 x^{3} + 8 x^{2} - 3 x + 2$	$8$	[0,4]	$3\cdot 131\cdot 1489^{2}$	$3$	$13.1075868269$	$764.968626807662$			✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$68.021334251$
8.4.1019026861.1	$x^{8} - x^{7} - 3 x^{6} + 2 x^{5} - 17 x^{4} - 12 x^{3} - x^{2} - 5 x + 23$	$8$	[4,2]	$71\cdot 131\cdot 331^{2}$	$3$	$13.3666693163$	$1754.6028040556644$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$26.5008720649$
8.2.1044721856.1	$x^{8} - 2 x^{7} - x^{6} + x^{5} + x^{4} + 13 x^{3} + 11 x^{2} + 6 x + 2$	$8$	[2,3]	$-\,2^{6}\cdot 131\cdot 353^{2}$	$3$	$13.4083421941$	$608.230219571504$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$57.0799647832$
8.2.1047731843.1	$x^{8} - 2 x^{7} - 5 x^{6} + x^{5} + 17 x^{4} + 36 x^{3} - 33 x^{2} - 61 x - 19$	$8$	[2,3]	$-\,73\cdot 131\cdot 331^{2}$	$3$	$13.4131650274$	$1779.1438952484984$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$25.9171258885$
8.0.1107553517.1	$x^{8} - 3 x^{7} + 11 x^{6} - 19 x^{5} + 34 x^{4} - 36 x^{3} + 37 x^{2} - 25 x + 7$	$8$	[0,4]	$7^{3}\cdot 131\cdot 157^{2}$	$3$	$13.506586058$	$379.43247093521137$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$16.921368308$
8.4.1231682829.1	$x^{8} - x^{7} - 2 x^{6} + 12 x^{5} + 6 x^{4} - 5 x^{3} - 24 x^{2} - x + 11$	$8$	[4,2]	$3\cdot 13\cdot 131\cdot 491^{2}$	$4$	$13.6871290127$	$1583.830483353569$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$40.7533906095$
8.2.1294846051.1	$x^{8} - x^{7} - 2 x^{6} + 6 x^{5} - 12 x^{4} - 19 x^{3} + 23 x^{2} - 20 x - 13$	$8$	[2,3]	$-\,41\cdot 131\cdot 491^{2}$	$3$	$13.7729593938$	$1623.9338040696116$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$24.4871525592$
8.2.1310598539.1	$x^{8} - 4 x^{7} + 13 x^{6} - 25 x^{5} + 38 x^{4} - 39 x^{3} + 26 x^{2} - 10 x - 3$	$8$	[2,3]	$-\,131\cdot 3163^{2}$	$2$	$13.7937931773$	$643.7025710683467$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$37.5471915469$
8.2.1320561875.1	$x^{8} - x^{7} - 5 x^{6} + x^{5} + 11 x^{4} + 2 x^{3} - 10 x^{2} - 5 x + 2$	$8$	[2,3]	$-\,5^{4}\cdot 127^{2}\cdot 131$	$3$	$13.806857558$	$377.1529518965761$			✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$63.296221545$
8.0.1335823768.1	$x^{8} - 3 x^{7} + 7 x^{6} - 13 x^{5} + 19 x^{4} - 33 x^{3} + 43 x^{2} - 30 x + 14$	$8$	[0,4]	$2^{3}\cdot 131\cdot 1129^{2}$	$3$	$13.826703369$	$1087.7462939490993$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$43.7394192283$
8.4.1484335717.1	$x^{8} - x^{7} - 6 x^{6} - x^{5} + 20 x^{4} + 23 x^{3} - 52 x^{2} - 18 x + 31$	$8$	[4,2]	$47\cdot 131\cdot 491^{2}$	$3$	$14.0101090993$	$1738.7026772855675$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$57.7610603418$
8.4.1505130657.1	$x^{8} - 3 x^{6} - 4 x^{5} + x^{4} - 4 x^{3} - 15 x^{2} - 4 x + 1$	$8$	[4,2]	$3\cdot 19^{2}\cdot 103^{2}\cdot 131$	$4$	$14.0344945178$	$876.9840363427376$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$47.6415443087$
8.0.1535716537.1	$x^{8} - 3 x^{7} + 4 x^{6} + 8 x^{5} - 40 x^{4} + 47 x^{3} + 34 x^{2} - 148 x + 113$	$8$	[0,4]	$107\cdot 131\cdot 331^{2}$	$3$	$14.0698310544$	$2153.9793406623007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$14.6946154176$
8.2.1546598576.1	$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 12 x^{4} - 17 x^{3} + 4 x^{2} + 4 x - 2$	$8$	[2,3]	$-\,2^{4}\cdot 131\cdot 859^{2}$	$3$	$14.0822548876$	$532.4991189168677$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$81.8926948149$
8.2.1570692751.1	$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 11 x^{4} - 16 x^{3} - 47 x^{2} + 97 x - 49$	$8$	[2,3]	$-\,29\cdot 131\cdot 643^{2}$	$3$	$14.1094928864$	$1562.9321802304794$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$34.611150269$
8.2.1571907776.1	$x^{8} - x^{7} - 3 x^{6} - 6 x^{5} - x^{4} - x^{3} - x^{2} + 2 x - 4$	$8$	[2,3]	$-\,2^{6}\cdot 131\cdot 433^{2}$	$3$	$14.1108567423$	$673.6349159596762$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$68.6776979344$
8.2.1621831483.2	$x^{8} - x^{7} + 5 x^{6} - 3 x^{4} - 18 x^{3} - 53 x^{2} - 35 x - 47$	$8$	[2,3]	$-\,113\cdot 131\cdot 331^{2}$	$3$	$14.1661134595$	$2213.5476050900734$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$20.1650671031$
8.4.1650626200.1	$x^{8} - 3 x^{7} + 5 x^{6} - x^{5} - 8 x^{4} + 28 x^{3} + 3 x^{2} - 20 x + 5$	$8$	[4,2]	$2^{3}\cdot 5^{2}\cdot 131\cdot 251^{2}$	$4$	$14.1973108655$	$1146.8391343165788$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$73.6109346094$
8.0.1679016389.1	$x^{8} - x^{7} + 2 x^{6} - 6 x^{5} + 9 x^{4} - 7 x^{3} + 27 x^{2} - 49 x + 53$	$8$	[0,4]	$31\cdot 131\cdot 643^{2}$	$3$	$14.2276072121$	$1615.9279068077265$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$15.9368334992$
8.2.1794061375.1	$x^{8} - 3 x^{7} - 2 x^{6} + 22 x^{5} - 31 x^{4} - 22 x^{3} + 88 x^{2} - 16 x - 80$	$8$	[2,3]	$-\,5^{3}\cdot 131\cdot 331^{2}$	$3$	$14.3459615342$	$465.6232382517007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$33.7125298381$
8.2.2003987303.1	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 11 x^{4} - 27 x^{2} + 25 x - 25$	$8$	[2,3]	$-\,37\cdot 131\cdot 643^{2}$	$3$	$14.545775176$	$1765.3954231276346$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$40.0233090217$
8.0.2028659712.1	$x^{8} + 4 x^{6} - 8 x^{5} + 6 x^{4} - 6 x^{3} + 13 x^{2} - 12 x + 6$	$8$	[0,4]	$2^{10}\cdot 3\cdot 71^{2}\cdot 131$	$4$	$14.568040849$	$668.16764363444$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$110.709025933$
8.2.2124391499.1	$x^{8} - 2 x^{7} + 2 x^{6} + 5 x^{5} - 4 x^{4} - 9 x^{3} + 2 x^{2} + 7 x - 3$	$8$	[2,3]	$-\,131\cdot 4027^{2}$	$2$	$14.6522499755$	$726.3174237205108$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$52.9723548656$
8.0.2163608576.1	$x^{8} - 3 x^{7} - 5 x^{5} + 18 x^{4} - 3 x^{3} + 24 x^{2} - x + 1$	$8$	[0,4]	$2^{10}\cdot 127^{2}\cdot 131$	$3$	$14.6857907801$	$867.7007970437954$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$54.4993802271$
8.0.2167226141.1	$x^{8} - 3 x^{7} + 10 x^{6} - 4 x^{5} + 4 x^{4} + 34 x^{3} + 25 x^{2} - 25 x + 125$	$8$	[0,4]	$131\cdot 151\cdot 331^{2}$	$3$	$14.6888578772$	$2558.810465821961$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$15.9965790986$
8.2.2293267136.1	$x^{8} - 3 x^{7} + 3 x^{6} + 2 x^{5} - 2 x^{4} - 12 x^{3} - 2 x^{2} - 8 x - 2$	$8$	[2,3]	$-\,2^{6}\cdot 131\cdot 523^{2}$	$3$	$14.7930195405$	$587.6086142712594$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$63.6775503203$
8.4.2396865997.1	$x^{8} - 2 x^{7} - 7 x^{6} + 24 x^{5} - 2 x^{4} - 21 x^{3} - 21 x^{2} - 22 x + 67$	$8$	[4,2]	$131\cdot 167\cdot 331^{2}$	$3$	$14.8749484488$	$2690.963953679053$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$31.916130481$
8.4.2417107200.1	$x^{8} - 2 x^{7} - 2 x^{6} + 12 x^{5} - 7 x^{4} - 8 x^{3} - 4 x^{2} - 12 x - 3$	$8$	[4,2]	$2^{8}\cdot 3\cdot 5^{2}\cdot 31^{2}\cdot 131$	$5$	$14.8905928509$	$554.0689154043789$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$83.7692421224$
8.4.2545605493.1	$x^{8} - 3 x^{7} - 5 x^{6} + 13 x^{5} + 19 x^{4} - 16 x^{3} - 41 x^{2} + 25$	$8$	[4,2]	$47\cdot 131\cdot 643^{2}$	$3$	$14.9873167987$	$1989.711285588942$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$78.8747928268$
8.4.2695650273.1	$x^{8} - 4 x^{7} + 4 x^{6} - 12 x^{4} + 11 x^{2} - 2 x - 1$	$8$	[4,2]	$3^{7}\cdot 97^{2}\cdot 131$	$3$	$15.0949939537$	$406.1280433669487$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$104.424956051$
8.4.2730050349.1	$x^{8} - 3 x^{7} - 4 x^{6} + 16 x^{5} - 4 x^{4} - 2 x^{3} - x^{2} - 43 x + 43$	$8$	[4,2]	$3\cdot 13\cdot 17^{2}\cdot 43^{2}\cdot 131$	$5$	$15.1189396013$	$1932.5317591180747$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$56.4287015332$
8.4.2741325781.1	$x^{8} - x^{7} - 3 x^{6} + 19 x^{5} - 19 x^{4} - 48 x^{3} + 40 x^{2} - 11 x + 53$	$8$	[4,2]	$131\cdot 191\cdot 331^{2}$	$3$	$15.1267309108$	$2877.8379037047935$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$36.2936057855$
8.0.2807957097.2	$x^{8} - x^{7} - 2 x^{6} + 10 x^{5} + 8 x^{4} - 8 x^{3} + 14 x^{2} + 25 x + 17$	$8$	[0,4]	$3^{11}\cdot 11^{2}\cdot 131$	$3$	$15.172208718$	$284.4816712962022$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$3$	$115.904676759$
8.0.2817946764.1	$x^{8} - x^{7} + 2 x^{6} - 8 x^{5} + 5 x^{4} - 7 x^{3} + 11 x^{2} + 6$	$8$	[0,4]	$2^{2}\cdot 3^{2}\cdot 131\cdot 773^{2}$	$4$	$15.1789453741$	$1102.3411450181836$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$30.1906744825$

  To download results, . Download displayed columns for results to