Number field search results

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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	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
10.0.859773123.1	$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 12 x^{6} - 15 x^{5} + 18 x^{4} - 18 x^{3} + 15 x^{2} - 9 x + 3$	$10$	(0, 5)	$-\,3^{9}\cdot 11^{2}\cdot 19^{2}$	$3$	$7.82417195355$	$38.85816359107818$			✓	$S_5\times C_2$ (as 10T22)	trivial	trivial	$6$	$4$	$5.08034052289$	$0$	$19$
10.0.949763799.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 6 x^{6} - 9 x^{5} + 12 x^{4} - 12 x^{3} + 9 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 73\cdot 661$	$3$	$7.90244644331$	$590.4339058832476$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$5.43744318757$	$0$	$661$
10.0.978815907.1	$x^{10} - x^{9} + 3 x^{5} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 223^{2}$	$2$	$7.92629262797$	$40.13853901741795$			✓	$S_5\times C_2$ (as 10T22)	trivial	trivial	$6$	$4$	$5.57252177932$	$0$	$223$
10.0.1276422867.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 18 x^{6} - 18 x^{5} + 15 x^{4} - 9 x^{3} + 6 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 64849$	$2$	$8.13953242521$	$684.4800127449324$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$6.75237227686$	$0$	$64849$
10.0.1587552048.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 21 x^{6} - 21 x^{5} + 21 x^{4} - 15 x^{3} + 9 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,2^{4}\cdot 3^{9}\cdot 71^{2}$	$3$	$8.31903204595$	$45.29688103897607$			?	$S_5\times C_2$ (as 10T22)	trivial	trivial	$6$	$4$	$8.39732339411$	$0$	$71$
10.0.1626465339.1	$x^{10} - 2 x^{9} + 3 x^{7} - 3 x^{6} - 3 x^{5} + 6 x^{4} - 3 x^{2} + x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 82633$	$2$	$8.33920175823$	$772.6554803121494$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$7.83417125177$	$0$	$82633$
10.0.1813532571.1	$x^{10} - x^{9} - 3 x^{8} + 3 x^{6} + 6 x^{3} + 9 x^{2} + 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 199\cdot 463$	$3$	$8.43048453381$	$815.8797665606871$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$8.38843194319$	$0$	$463$
10.0.1890532467.1	$x^{10} - x^{9} + 3 x^{7} - 3 x^{6} + 3 x^{4} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 139\cdot 691$	$3$	$8.4656130567$	$833.0202388835313$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$8.90687836208$	$0$	$691$
10.0.2129562819.1	$x^{10} - 2 x^{9} + 6 x^{8} - 12 x^{7} + 18 x^{6} - 24 x^{5} + 27 x^{4} - 21 x^{3} + 12 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 108193$	$2$	$8.56700549701$	$884.114902104767$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$9.23438677283$	$0$	$108193$
10.0.2351350863.1	$x^{10} - x^{9} + 3 x^{6} - 3 x^{5} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 67\cdot 1783$	$3$	$8.65230347799$	$929.0138790055562$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$9.43463887767$	$0$	$1783$
10.0.2415832371.1	$x^{10} - 2 x^{9} + 6 x^{6} - 6 x^{5} - 3 x^{3} + 3 x^{2} + x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 139\cdot 883$	$3$	$8.67574302251$	$941.665980903998$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$10.000783607$	$0$	$883$
10.0.2593687959.1	$x^{10} - x^{9} + 6 x^{8} - 3 x^{7} + 9 x^{6} + 3 x^{3} - 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 313\cdot 421$	$3$	$8.73759222186$	$975.713571884945$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$11.3275532593$	$0$	$421$
10.0.2652028371.1	$x^{10} - 2 x^{9} + 6 x^{7} - 3 x^{6} - 9 x^{5} + 6 x^{4} + 6 x^{3} - 3 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 67\cdot 2011$	$3$	$8.75704974146$	$986.6260224938292$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$10.177720801$	$0$	$2011$
10.0.2765874843.1	$x^{10} - 2 x^{9} + 6 x^{7} - 6 x^{6} - 6 x^{5} + 18 x^{4} - 15 x^{3} + 6 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 140521$	$2$	$8.79393502419$	$1007.5804796645201$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$10.9226667523$	$0$	$140521$
10.0.2845236699.1	$x^{10} - 2 x^{9} + 6 x^{7} - 6 x^{6} - 3 x^{5} + 6 x^{4} - 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 31\cdot 4663$	$3$	$8.81884765331$	$1021.9336127137318$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$12.051187577$	$0$	$4663$
10.0.2941840863.1	$x^{10} - x^{9} + 6 x^{5} + 9 x^{4} + 9 x^{3} + 9 x^{2} + 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 13\cdot 11497$	$3$	$8.84834235205$	$1039.1376275836674$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$12.4336498925$	$0$	$11497$
10.0.3015297819.1	$x^{10} - 2 x^{9} + 6 x^{8} - 9 x^{7} + 15 x^{6} - 15 x^{5} + 18 x^{4} - 12 x^{3} + 9 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 307\cdot 499$	$3$	$8.87019201819$	$1052.031127218494$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$11.2589823469$	$0$	$499$
10.0.3219371163.1	$x^{10} - 4 x^{9} + 9 x^{8} - 12 x^{7} + 12 x^{6} - 9 x^{5} + 9 x^{4} - 9 x^{3} + 9 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 163561$	$2$	$8.9284712591$	$1087.0487170534657$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$11.2626362495$	$0$	$163561$
10.0.3311723799.1	$x^{10} - 3 x^{9} + 6 x^{8} - 12 x^{7} + 21 x^{6} - 27 x^{5} + 30 x^{4} - 30 x^{3} + 24 x^{2} - 12 x + 3$	$10$	(0, 5)	$-\,3^{9}\cdot 168253$	$2$	$8.95375921028$	$1102.5303097500753$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$13.3832441428$	$0$	$168253$
10.0.3377622483.1	$x^{10} - x^{9} + 3 x^{7} - 3 x^{5} + 3 x^{4} + 3 x^{3} - 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 157\cdot 1093$	$3$	$8.97141838648$	$1113.4456846458907$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$12.2462368487$	$0$	$1093$
10.0.3488870799.1	$x^{10} - x^{9} + 3 x^{5} - 3 x^{3} + 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 157\cdot 1129$	$3$	$9.00053839084$	$1131.6338411430509$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$13.6263763631$	$0$	$1129$
10.0.3589254099.1	$x^{10} - 2 x^{9} + 6 x^{8} - 9 x^{7} + 9 x^{6} - 9 x^{5} + 3 x^{4} + x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 182353$	$2$	$9.02610581417$	$1147.7983220518186$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$12.4933348891$	$0$	$182353$
10.0.3679953363.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 6 x^{6} - 6 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 31\cdot 37\cdot 163$	$4$	$9.04865919598$	$1162.2100869267529$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$11.9323211636$	$0$	$163$
10.0.4049836299.1	$x^{10} - x^{9} - 3 x^{8} + 6 x^{6} - 3 x^{4} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 61\cdot 3373$	$3$	$9.13574032944$	$1219.2203906643272$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.2181720116$	$0$	$3373$
10.0.4162501791.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 21 x^{6} - 21 x^{5} + 18 x^{4} - 12 x^{3} + 6 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 7\cdot 30211$	$3$	$9.16084306626$	$1236.0632650909558$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.0766042744$	$0$	$30211$
10.0.4178090727.1	$x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 6 x^{6} - 3 x^{5} - 6 x^{4} + 3 x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 37\cdot 5737$	$3$	$9.16426811447$	$1238.37568498398$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.403572085$	$0$	$5737$
10.0.4237671168.1	$x^{10} - x^{9} - 3 x^{8} + 6 x^{7} + 3 x^{6} - 9 x^{5} + 3 x^{4} + 6 x^{3} - 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,2^{8}\cdot 3^{9}\cdot 29^{2}$	$3$	$9.17725343929$	$32.49449483995461$				$S_5\times C_2$ (as 10T22)	trivial	trivial	$6$	$4$	$17.448078285$	$0$	$29$
10.0.4277765439.1	$x^{10} - x^{9} - 3 x^{6} + 3 x^{5} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 217333$	$2$	$9.18589965036$	$1253.0602884850855$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.5837257768$	$0$	$217333$
10.0.4287213279.1	$x^{10} - x^{9} + 6 x^{8} - 6 x^{7} + 12 x^{6} - 12 x^{5} + 9 x^{4} - 9 x^{3} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 139\cdot 1567$	$3$	$9.1879264276$	$1254.4432749730577$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$16.0655986809$	$0$	$1567$
10.0.4369645683.1	$x^{10} - x^{9} + 3 x^{8} + 3 x^{5} - 3 x^{4} - 3 x^{3} + 6 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 13\cdot 17077$	$3$	$9.20544149759$	$1266.4457608089645$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$13.6314559514$	$0$	$17077$
10.0.4427277507.1	$x^{10} - x^{9} + 6 x^{5} + 3 x^{4} + 3 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 224929$	$2$	$9.21751121087$	$1274.7700618960669$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.9031200734$	$0$	$224929$
10.0.4556476719.1	$x^{10} - x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 9 x^{5} + 9 x^{4} - 6 x^{3} + 6 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 231493$	$2$	$9.2440634033$	$1293.2368194607861$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$14.3929250402$	$0$	$231493$
10.0.4851249327.1	$x^{10} - x^{9} + 3 x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{3} + 6 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 246469$	$2$	$9.3021932919$	$1334.4130506965753$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$15.3331153059$	$0$	$246469$
10.0.4904865819.1	$x^{10} - 4 x^{9} + 9 x^{8} - 12 x^{7} + 12 x^{6} - 6 x^{5} + 3 x^{3} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 7\cdot 97\cdot 367$	$4$	$9.3124233925$	$1341.7668210227343$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$16.0429548952$	$0$	$367$
10.0.5070911607.1	$x^{10} - 4 x^{9} + 9 x^{8} - 12 x^{7} + 12 x^{6} - 9 x^{5} + 6 x^{4} - 3 x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 241\cdot 1069$	$3$	$9.34347878909$	$1364.2893946419647$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$17.7177434107$	$0$	$1069$
10.0.5202708975.1	$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 9 x^{5} - 3 x^{4} - 6 x^{3} + 3 x^{2} + 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 5^{2}\cdot 97\cdot 109$	$4$	$9.36748385677$	$618.0067911941513$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$17.9598588323$	$0$	$109$
10.0.5216172147.1	$x^{10} - 4 x^{9} + 12 x^{8} - 21 x^{7} + 27 x^{6} - 24 x^{5} + 18 x^{4} - 12 x^{3} + 9 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 43\cdot 6163$	$3$	$9.36990508441$	$1383.6920346900363$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$15.3090297009$	$0$	$6163$
10.0.5261521779.1	$x^{10} - 5 x^{9} + 12 x^{8} - 18 x^{7} + 21 x^{6} - 18 x^{5} + 12 x^{4} - 9 x^{3} + 9 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 31\cdot 8623$	$3$	$9.37801962515$	$1389.6939576357497$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$15.5772597455$	$0$	$8623$
10.0.5435834427.1	$x^{10} - 2 x^{9} + 3 x^{7} - 6 x^{4} + 3 x^{3} + 6 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 277\cdot 997$	$3$	$9.40863502624$	$1412.5264632309904$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$16.6598555973$	$0$	$997$
10.0.5462760771.1	$x^{10} - x^{9} + 3 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 13\cdot 37\cdot 577$	$4$	$9.41328522667$	$1416.0206084080282$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$16.2034361981$	$0$	$577$
10.0.5518798272.1	$x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 3 x^{6} - 3 x^{5} - 3 x^{4} + 3 x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,2^{6}\cdot 3^{9}\cdot 13\cdot 337$	$4$	$9.4228971739$	$503.200135442304$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$18.0156073796$	$0$	$337$
10.0.5537162511.1	$x^{10} - 2 x^{9} + 6 x^{8} - 9 x^{7} + 12 x^{6} - 15 x^{5} + 15 x^{4} - 15 x^{3} + 12 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 281317$	$2$	$9.42602803235$	$1425.630959037901$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$15.4013284155$	$0$	$281317$
10.0.5537871099.1	$x^{10} - 2 x^{9} - 3 x^{8} + 9 x^{7} - 12 x^{5} + 6 x^{4} + 6 x^{3} - 3 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 281353$	$2$	$9.42614864983$	$1425.7221747708547$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$15.9307700506$	$0$	$281353$
10.0.5586055083.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 6 x^{6} + 6 x^{4} + 3 x^{3} + 3 x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 7\cdot 40543$	$3$	$9.43431822994$	$1431.9112129325747$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$17.1897439668$	$0$	$40543$
10.0.5654847168.1	$x^{10} - 2 x^{9} + 3 x^{7} - 6 x^{3} + 9 x^{2} - 5 x + 1$	$10$	(0, 5)	$-\,2^{6}\cdot 3^{9}\cdot 67^{2}$	$3$	$9.44587267389$	$62.22881401675073$			?	$S_5\times C_2$ (as 10T22)	trivial	trivial	$6$	$4$	$19.8004026763$	$0$	$67$
10.0.5666125527.1	$x^{10} - 3 x^{9} + 6 x^{8} - 12 x^{7} + 18 x^{6} - 21 x^{5} + 24 x^{4} - 21 x^{3} + 15 x^{2} - 9 x + 3$	$10$	(0, 5)	$-\,3^{9}\cdot 19\cdot 109\cdot 139$	$4$	$9.44775492545$	$1442.1371972808977$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$16.5258680567$	$0$	$139$
10.0.5734622367.1	$x^{10} - 3 x^{9} + 9 x^{8} - 15 x^{7} + 24 x^{6} - 27 x^{5} + 30 x^{4} - 24 x^{3} + 18 x^{2} - 9 x + 3$	$10$	(0, 5)	$-\,3^{9}\cdot 291349$	$2$	$9.45911449808$	$1450.8278883091314$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$18.1979721904$	$0$	$291349$
10.0.5898069999.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{6} + 6 x^{5} - 6 x^{4} + 6 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 299653$	$2$	$9.48573509859$	$1471.3583026765593$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$18.5191296321$	$0$	$299653$
10.0.5908462623.1	$x^{10} - 4 x^{9} + 6 x^{8} - 3 x^{7} - 3 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - x + 1$	$10$	(0, 5)	$-\,3^{9}\cdot 7\cdot 19\cdot 37\cdot 61$	$5$	$9.48740519742$	$1472.6540268361507$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$19.3703940878$	$0$	$61$
10.0.6040259991.1	$x^{10} - 3 x^{6} - 3 x^{3} + 6 x^{2} - 3 x + 3$	$10$	(0, 5)	$-\,3^{9}\cdot 306877$	$2$	$9.50835883665$	$1488.988347917689$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	trivial	$6$	$4$	$17.023508801$	$0$	$306877$

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