Number field search results

Results (1-50 of 384 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
8.0.95879424.1	$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} - 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 3\cdot 131\cdot 953$	$4$	$9.94753960785$	$1318.3354639380366$			?	$S_8$ (as 8T50)	trivial	$2$	$3$	$8.85373574119$
8.2.227604224.1	$x^{8} - 2 x - 1$	$8$	[2,3]	$-\,2^{8}\cdot 631\cdot 1409$	$3$	$11.0827500764$	$2031.2032636030215$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$16.0898223295$
8.4.797497600.1	$x^{8} - 4 x^{6} - 4 x^{5} + 8 x^{4} + 8 x^{3} - 2 x^{2} - 10 x + 2$	$8$	[4,2]	$2^{8}\cdot 5^{2}\cdot 353^{2}$	$3$	$12.9633179511$	$90.50145560316005$			✓	$A_8$ (as 8T49)	trivial	$2$	$5$	$39.81410124055594$
8.2.1284568832.1	$x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} - 2 x + 1$	$8$	[2,3]	$-\,2^{8}\cdot 2111\cdot 2377$	$3$	$13.759247176$	$4825.495522723284$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$51.3931808021$
8.0.1936656640.1	$x^{8} - 2 x + 2$	$8$	[0,4]	$2^{8}\cdot 5\cdot 1513013$	$3$	$14.4837686319$	$5925.016190597873$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$30.8182807458$
8.2.2358310656.1	$x^{8} - 2 x - 2$	$8$	[2,3]	$-\,2^{8}\cdot 3\cdot 13\cdot 236209$	$4$	$14.844826519$	$6538.283286871174$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$79.3019753896$
8.0.2916000000.11	$x^{8} - 2 x^{7} + 6 x^{6} - 12 x^{5} + 30 x^{4} - 38 x^{3} + 36 x^{2} - 18 x + 6$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 5^{6}$	$3$	$15.2439824446$	$102.75927104246999$			?	$A_8$ (as 8T49)	trivial	$2$	$3$	$107.44581306$
8.2.9500000000.1	$x^{8} - 2 x^{7} - 2 x^{6} - 4 x^{5} + 20 x^{4} - 4 x^{3} - 12 x^{2} - 2 x + 6$	$8$	[2,3]	$-\,2^{8}\cdot 5^{9}\cdot 19$	$3$	$17.6691415789$	$120.05009742168745$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$218.225762726$
8.0.28943536384.2	$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - 8 x^{4} + 4 x^{3} + 16 x^{2} - 16 x + 8$	$8$	[0,4]	$2^{8}\cdot 7^{6}\cdot 31^{2}$	$3$	$20.3092529689$	$51.616385159869715$			?	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$3$	$102.688218432$
8.2.30780000000.6	$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 40 x^{4} - 44 x^{3} + 36 x^{2} - 18 x + 3$	$8$	[2,3]	$-\,2^{8}\cdot 3^{4}\cdot 5^{7}\cdot 19$	$4$	$20.4660286116$	$227.20400310274306$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$494.443096399$
8.0.36480944384.1	$x^{8} - 2 x + 3$	$8$	[0,4]	$2^{8}\cdot 5623\cdot 25343$	$3$	$20.9053892836$	$25715.57638826155$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$292.945547863$
8.0.72313663744.1	$x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 7^{10}$	$2$	$22.7720718638$	$41.78800629070284$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$	$2$	$3$	$124.833646442$
8.2.74956969728.1	$x^{8} - 6 x - 9$	$8$	[2,3]	$-\,2^{8}\cdot 3^{6}\cdot 71\cdot 5657$	$4$	$22.8744943525$	$3500.793941211008$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$863.180506844$
8.2.121500000000.2	$x^{8} - 2 x^{7} + 6 x^{6} - 10 x^{5} + 10 x^{4} - 16 x^{3} - 8 x^{2} - 6 x - 25$	$8$	[2,3]	$-\,2^{8}\cdot 3^{5}\cdot 5^{9}$	$3$	$24.298084315$	$249.03163342635705$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$1219.1546939$
8.8.181912486144.1	$x^{8} - 2 x^{7} - 14 x^{6} + 40 x^{5} + 10 x^{4} - 106 x^{3} + 68 x^{2} + 26 x - 21$	$8$	[8,0]	$2^{8}\cdot 19^{2}\cdot 23^{2}\cdot 61^{2}$	$4$	$25.5554076862$	$351.7133437722911$			?	$C_2^3:\GL(3,2)$ (as 8T48)	trivial	$2$	$7$	$2279.4264387992516$
8.2.393660000000.2	$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} + 66 x^{3} + 68 x^{2} + 68 x - 79$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$	$3$	$28.1442811796$	$138.4034641689339$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$3136.20698725$
8.2.393660000000.3	$x^{8} - 4 x^{7} + 2 x^{6} - 2 x^{5} + 20 x^{4} - 4 x^{3} - 44 x^{2} - 88 x - 52$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$	$3$	$28.1442811796$	$75.17606627073587$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2043.67571568$
8.2.393660000000.4	$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} - 24 x^{3} + 8 x^{2} + 8 x - 4$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$	$3$	$28.1442811796$	$84.26189250994942$			?	$S_8$ (as 8T50)	$[2]$	$2$	$4$	$1393.99808903$
8.2.393660000000.10	$x^{8} - 2 x^{7} - 2 x^{6} + 16 x^{5} + 40 x^{4} + 16 x^{3} + 28 x^{2} - 2 x - 14$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$	$3$	$28.1442811796$	$125.5267203836957$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2378.48944333$
8.2.393660000000.11	$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} - 12 x^{3} + 24 x^{2} + 24 x - 12$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$	$3$	$28.1442811796$	$95.96360229071443$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2697.27559266$
8.0.401469235456.1	$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} - 8 x^{4} + 4 x^{3} + 16 x^{2} - 14 x + 6$	$8$	[0,4]	$2^{8}\cdot 199^{4}$	$2$	$28.2134719593$	$73.42634779951366$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	trivial	$2$	$3$	$1372.0493131$
8.0.401469235456.2	$x^{8} - 2 x^{7} - 4 x^{6} + 4 x^{5} + 12 x^{4} - 16 x^{3} + 68 x + 52$	$8$	[0,4]	$2^{8}\cdot 199^{4}$	$2$	$28.2134719593$	$73.42634779951366$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	trivial	$2$	$3$	$902.529001489$
8.0.497340911872.1	$x^{8} - 6 x + 7$	$8$	[0,4]	$2^{8}\cdot 7^{8}\cdot 337$	$3$	$28.9788917975$	$439.9567842119033$			?	$S_8$ (as 8T50)	trivial	$2$	$3$	$603.77233519$
8.4.567647723776.3	$x^{8} - 2 x^{7} - 8 x^{6} + 4 x^{5} + 12 x^{4} + 28 x^{3} - 56 x + 56$	$8$	[4,2]	$2^{8}\cdot 7^{4}\cdot 31^{4}$	$3$	$29.4618397253$	$51.616385159869715$			?	$C_2^3:\GL(3,2)$ (as 8T48)	trivial	$2$	$5$	$3004.84581333$
8.2.743580000000.1	$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} + 6 x^{3} + 18 x^{2} + 18 x - 9$	$8$	[2,3]	$-\,2^{8}\cdot 3^{7}\cdot 5^{7}\cdot 17$	$4$	$30.4730526842$	$167.02244360673245$			?	$S_8$ (as 8T50)	$[2]$	$2$	$4$	$834.083569136$
8.2.1093500000000.1	$x^{8} - 30 x^{4} - 36 x^{3} - 60 x^{2} - 180 x - 135$	$8$	[2,3]	$-\,2^{8}\cdot 3^{7}\cdot 5^{9}$	$3$	$31.9780773315$	$99.22638744343617$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2969.61571734$
8.2.1093500000000.2	$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} + 84 x^{3} + 72 x^{2} + 72 x - 36$	$8$	[2,3]	$-\,2^{8}\cdot 3^{7}\cdot 5^{9}$	$3$	$31.9780773315$	$228.52995139973822$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2320.49602936$
8.2.1296540000000.3	$x^{8} - 4 x^{7} + 12 x^{6} - 12 x^{5} - 8 x^{3} + 32 x^{2} + 4 x - 4$	$8$	[2,3]	$-\,2^{8}\cdot 3^{3}\cdot 5^{7}\cdot 7^{4}$	$4$	$32.6661716631$	$247.23935985987188$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$3593.27660997$
8.2.1296540000000.4	$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 40 x^{4} - 44 x^{3} + 16 x^{2} + 2 x - 2$	$8$	[2,3]	$-\,2^{8}\cdot 3^{3}\cdot 5^{7}\cdot 7^{4}$	$4$	$32.6661716631$	$247.23935985987188$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$2949.01034517$
8.2.1310930827008.1	$x^{8} - 2 x - 5$	$8$	[2,3]	$-\,2^{8}\cdot 3\cdot 11\cdot 155176471$	$4$	$32.7112749927$	$154153.4024739655$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$2748.31820802$
8.2.1346544228096.1	$x^{8} - 6 x + 3$	$8$	[2,3]	$-\,2^{8}\cdot 3^{7}\cdot 2405093$	$3$	$32.8210580931$	$8736.354423320454$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$2029.79089502$
8.2.1381088515840.1	$x^{8} - 6 x + 2$	$8$	[2,3]	$-\,2^{8}\cdot 5\cdot 11\cdot 163\cdot 601771$	$5$	$32.92514447$	$158224.59176526917$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$4318.92815324$
8.2.1383252776704.1	$x^{8} - 6 x - 1$	$8$	[2,3]	$-\,2^{8}\cdot 683\cdot 7911173$	$3$	$32.9315895489$	$158348.5176528123$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$3952.42106798$
8.2.1385383483136.1	$x^{8} - 6 x - 2$	$8$	[2,3]	$-\,2^{8}\cdot 7867\cdot 687893$	$3$	$32.9379260903$	$158470.42753928667$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$1568.88355058$
8.2.1680700000000.1	$x^{8} - 2 x^{7} + 70 x^{3} - 140 x^{2} + 100 x - 25$	$8$	[2,3]	$-\,2^{8}\cdot 5^{8}\cdot 7^{5}$	$3$	$33.7432006957$	$132.10981453984164$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$3348.16501166$
8.0.2101386547456.12	$x^{8} - 2 x^{7} + 2 x^{6} - 16 x^{5} + 34 x^{4} + 4 x^{3} - 94 x^{2} + 16 x + 153$	$8$	[0,4]	$2^{8}\cdot 7^{4}\cdot 43^{4}$	$3$	$34.6987031458$	$96.75220539252781$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$	$2$	$3$	$574.051605692$
8.2.2693955999488.1	$x^{8} - 6 x - 5$	$8$	[2,3]	$-\,2^{8}\cdot 13\cdot 20173\cdot 40127$	$4$	$35.793058667$	$220982.8019336467$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$2815.70995221$
8.2.3294172000000.4	$x^{8} - 4 x^{7} + 14 x^{5} - 28 x^{3} - 28 x^{2} - 10 x - 2$	$8$	[2,3]	$-\,2^{8}\cdot 5^{6}\cdot 7^{7}$	$3$	$36.7044130824$	$154.0455526727784$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$6460.34536915$
8.0.3313310738688.1	$x^{8} - 6 x + 6$	$8$	[0,4]	$2^{8}\cdot 3^{7}\cdot 167\cdot 35437$	$4$	$36.7310015946$	$13704.115719890828$			✓	$S_8$ (as 8T50)	$[4]$	$2$	$3$	$436.458795749$
8.2.3542940000000.5	$x^{8} - 4 x^{7} - 8 x^{6} + 28 x^{5} + 50 x^{4} - 92 x^{3} - 32 x^{2} - 124 x - 11$	$8$	[2,3]	$-\,2^{8}\cdot 3^{11}\cdot 5^{7}$	$3$	$37.0399570736$	$142.692231128093$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$6646.76218873$
8.0.4543718560000.9	$x^{8} + 4 x^{6} - 2 x^{5} + 52 x^{4} - 124 x^{3} + 352 x^{2} - 58 x + 91$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 73^{4}$	$3$	$38.2099463491$	$84.13630819106092$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$	$2$	$3$	$845.863359859$
8.0.4543718560000.10	$x^{8} - 2 x^{6} - 8 x^{5} - 16 x^{4} - 2 x^{3} + 58 x^{2} + 88 x + 171$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 73^{4}$	$3$	$38.2099463491$	$84.13630819106092$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[4]$	$2$	$3$	$751.513061741$
8.0.4696335911168.1	$x^{8} - 2 x + 6$	$8$	[0,4]	$2^{8}\cdot 11\cdot 19\cdot 107\cdot 820331$	$5$	$38.3680647291$	$291771.4564149819$			✓	$S_8$ (as 8T50)	$[2]$	$2$	$3$	$2654.37656588$
8.2.4696757565184.1	$x^{8} - 2 x - 6$	$8$	[2,3]	$-\,2^{8}\cdot 1747\cdot 10501837$	$3$	$38.3684953152$	$291784.5542690706$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$5530.22575654$
8.0.5857406763264.1	$x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 18 x + 121$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 7^{10}$	$3$	$39.4423854617$	$72.37895004250518$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2, 2]$	$2$	$3$	$1208.01278238$
8.0.5904900000000.1	$x^{8} - 8 x^{6} - 2 x^{5} + 30 x^{4} + 10 x^{3} - 50 x^{2} - 30 x + 55$	$8$	[0,4]	$2^{8}\cdot 3^{10}\cdot 5^{8}$	$3$	$39.4822203886$	$279.0216036308045$			?	$A_8$ (as 8T49)	$[2]$	$2$	$3$	$2683.86166284$
8.2.6079782737664.1	$x^{8} - 6 x - 6$	$8$	[2,3]	$-\,2^{8}\cdot 3^{7}\cdot 71\cdot 152947$	$4$	$39.6265266804$	$18563.67528537424$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$4461.53575236$
8.0.9682651996416.1	$x^{8} - 14 x^{6} + 168 x^{4} - 504 x^{3} + 616 x^{2} - 180 x + 28$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 7^{8}$	$3$	$42.0$	$103.69474346279736$			?	$C_2^3:(C_7: C_3)$ (as 8T36)	$[2]$	$2$	$3$	$2028.31714907$
8.2.9841500000000.3	$x^{8} - 2 x^{7} - 14 x^{6} - 26 x^{5} - 50 x^{4} - 98 x^{3} - 114 x^{2} - 78 x - 42$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{9}$	$3$	$42.0855165602$	$537.0780908962541$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$12119.1153798$
8.2.9841500000000.4	$x^{8} - 2 x^{7} - 2 x^{6} + 8 x^{5} - 70 x^{4} - 34 x^{3} + 558 x^{2} + 108 x - 27$	$8$	[2,3]	$-\,2^{8}\cdot 3^{9}\cdot 5^{9}$	$3$	$42.0855165602$	$431.13490547326217$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$12243.7994218$