Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 1092035 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
8.0.64000000.3	$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 11 x^{4} - 10 x^{3} + 2 x^{2} + 2 x + 1$	$8$	[0,4]	$2^{12}\cdot 5^{6}$	$2$	$9.45741609003$	$9.457416090031758$		✓		$D_4$ (as 8T4)	$[2]$	$4$	$3$	$5.03238945812$
8.0.76488065.1	$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 7 x^{4} - 2 x^{3} + x^{2} - x + 1$	$8$	[0,4]	$5\cdot 37\cdot 643^{2}$	$3$	$9.67050623513$	$344.8985358043725$			✓	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$2.63992822816$
8.0.81000000.1	$x^{8} - 3 x^{7} + 6 x^{6} - 9 x^{5} + 14 x^{4} - 27 x^{3} + 39 x^{2} - 36 x + 16$	$8$	[0,4]	$2^{6}\cdot 3^{4}\cdot 5^{6}$	$3$	$9.74003746425$	$16.3807251762544$				$D_4\times C_2$ (as 8T9)	$[2]$	$6$	$3$	$9.16000707431$
8.0.81450625.1	$x^{8} - x^{7} + 8 x^{6} + 7 x^{5} + 19 x^{4} + 7 x^{3} + 8 x^{2} - x + 1$	$8$	[0,4]	$5^{4}\cdot 19^{4}$	$2$	$9.74679434481$	$9.746794344808963$		✓	?	$D_4$ (as 8T4)	$[2]$	$2$	$3$	$2.76676434196$
8.0.93000677.1	$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 5 x^{4} - 7 x^{3} + 7 x^{2} - 4 x + 1$	$8$	[0,4]	$7^{3}\cdot 11\cdot 157^{2}$	$3$	$9.90970585565$	$178.84207446644047$			✓	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$2.79447033323$
8.0.96059601.1	$x^{8} - x^{7} - 2 x^{6} - 5 x^{5} + 11 x^{4} + x^{3} + 4 x^{2} - x + 1$	$8$	[0,4]	$3^{8}\cdot 11^{4}$	$2$	$9.94987437107$	$17.819817582388065$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$11.2924984888$
8.0.97831881.1	$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 6 x^{4} - 13 x^{3} + 16 x^{2} - 7 x + 1$	$8$	[0,4]	$3^{4}\cdot 7^{2}\cdot 157^{2}$	$3$	$9.97263790206$	$184.4558452935264$			?	$A_4\wr C_2$ (as 8T42)	$[2]$	$6$	$3$	$8.80125352986$
8.0.100618240.2	$x^{8} - 2 x^{7} + 8 x^{6} - 4 x^{5} + 13 x^{4} + 8 x^{3} + 10 x^{2} + 6 x + 1$	$8$	[0,4]	$2^{12}\cdot 5\cdot 17^{3}$	$3$	$10.0077071777$	$62.9686214593809$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$4$	$3$	$6.4517413252$
8.0.101875968.1	$x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{4} + 8 x^{3} + 15 x^{2} + 6 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 17^{3}$	$3$	$10.0232593672$	$29.001957651613843$			?	$C_4\wr C_2$ (as 8T17)	$[2]$	$4$	$3$	$6.34325059$
8.0.102468645.1	$x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{2} + 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 5\cdot 503^{2}$	$3$	$10.0305298381$	$86.86195945291587$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.02461741259$
8.0.104934441.1	$x^{8} - 3 x^{7} + 4 x^{6} - 10 x^{5} + 21 x^{4} - 20 x^{3} + 20 x^{2} - 27 x + 15$	$8$	[0,4]	$3\cdot 23\cdot 29\cdot 229^{2}$	$4$	$10.0603886056$	$676.9261407273323$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$3.47058377371$
8.0.106172416.1	$x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 8 x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1$	$8$	[0,4]	$2^{12}\cdot 7^{2}\cdot 23^{2}$	$3$	$10.0751486502$	$35.888716889852724$				$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$2$	$3$	$3.18896209766$
8.0.106770069.1	$x^{8} - 2 x^{7} + 7 x^{5} - 11 x^{4} - 3 x^{3} + 30 x^{2} - 42 x + 21$	$8$	[0,4]	$3^{6}\cdot 7^{4}\cdot 61$	$3$	$10.0822204795$	$47.1036844046804$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$11.8707758759$
8.0.110502144.1	$x^{8} - 4 x^{7} + 11 x^{6} - 14 x^{5} + 7 x^{4} + 18 x^{3} - 18 x^{2} - 36 x + 36$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 73^{2}$	$3$	$10.125613312$	$29.597297173897484$	✓			$D_4\times C_2$ (as 8T9)	$[2]$	$12$	$3$	$19.3523747957$
8.0.110502144.2	$x^{8} - 9 x^{6} + 29 x^{4} - 36 x^{2} + 16$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 73^{2}$	$3$	$10.125613312$	$29.597297173897484$				$D_4\times C_2$ (as 8T9)	$[2]$	$12$	$3$	$19.0522081113$
8.0.110502144.3	$x^{8} + x^{6} - 8 x^{5} - 4 x^{4} - 4 x^{3} + 21 x^{2} + 20 x + 25$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 73^{2}$	$3$	$10.125613312$	$29.597297173897484$				$D_4\times C_2$ (as 8T9)	$[2]$	$12$	$3$	$19.5375267096$
8.0.111017597.1	$x^{8} - 5 x^{6} - 2 x^{5} + 12 x^{4} + 5 x^{3} - 9 x^{2} - 10 x + 9$	$8$	[0,4]	$29\cdot 73\cdot 229^{2}$	$3$	$10.1315053439$	$696.2707806593638$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.40648157267$
8.0.112021056.1	$x^{8} - x^{7} - x^{6} - 7 x^{5} + 22 x^{4} - 23 x^{3} + 11 x^{2} - 2 x + 1$	$8$	[0,4]	$2^{6}\cdot 3^{6}\cdot 7^{4}$	$3$	$10.1429073345$	$17.058268835716344$			?	$Q_8:C_2$ (as 8T11)	$[2]$	$6$	$3$	$9.55171500307$
8.0.113396024.1	$x^{8} - 3 x^{7} + 8 x^{6} - 10 x^{5} + 12 x^{4} - 10 x^{3} + 8 x^{2} - 3 x + 1$	$8$	[0,4]	$2^{3}\cdot 7\cdot 1423^{2}$	$3$	$10.1583864023$	$282.2906303794017$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.57099257852$
8.0.119771136.5	$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{4} - 6 x^{3} + 8 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{12}\cdot 3^{4}\cdot 19^{2}$	$3$	$10.228077759$	$22.623940727226856$			?	$S_4\times C_2$ (as 8T24)	$[2]$	$4$	$3$	$9.82105065874$
8.0.121999616.1	$x^{8} - 4 x^{7} + 7 x^{6} - 6 x^{5} - 4 x^{4} + 4 x^{3} + 11 x^{2} + 6 x + 1$	$8$	[0,4]	$2^{8}\cdot 17^{3}\cdot 97$	$3$	$10.2516744877$	$164.91211206753155$				$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$4$	$3$	$7.55707962189$
8.0.123183909.1	$x^{8} - 3 x^{7} + 6 x^{6} - 4 x^{5} + 5 x^{4} - 15 x^{3} + 25 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 29\cdot 229^{2}$	$3$	$10.2640615499$	$141.1488575936766$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$3.73236551376$
8.0.125333229.1	$x^{8} + 4 x^{6} - 3 x^{5} + 5 x^{4} - 3 x^{3} + 4 x^{2} + 1$	$8$	[0,4]	$3\cdot 7^{3}\cdot 349^{2}$	$3$	$10.286278499$	$139.2505345009217$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$5.46771162562$
8.0.126376848.1	$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 5 x^{4} - 10 x^{3} + 2 x^{2} + 1$	$8$	[0,4]	$2^{4}\cdot 3^{4}\cdot 13^{2}\cdot 577$	$4$	$10.296946112$	$238.1260312766512$				$S_4\wr C_2$ (as 8T47)	$[2]$	$6$	$3$	$12.9682171918$
8.0.126773829.1	$x^{8} - x^{7} - 2 x^{6} - 4 x^{5} + 7 x^{4} + 5 x^{3} + 7 x^{2} + 2 x + 1$	$8$	[0,4]	$3^{7}\cdot 7^{3}\cdot 13^{2}$	$3$	$10.3009837239$	$40.57666075681575$				$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$13.3183414934$
8.0.127828125.1	$x^{8} - 2 x^{7} + 12 x^{6} - 20 x^{5} + 51 x^{4} - 65 x^{3} + 83 x^{2} - 66 x + 31$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 101$	$3$	$10.3116532919$	$58.20346197531708$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$10$	$3$	$15.7875080169$
8.0.128307240.1	$x^{8} - 3 x^{7} + 6 x^{6} - 6 x^{5} + 8 x^{4} - 6 x^{3} + 6 x^{2} - 3 x + 1$	$8$	[0,4]	$2^{3}\cdot 3^{4}\cdot 5\cdot 199^{2}$	$4$	$10.316476551$	$154.53155017665486$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.92079408999$
8.0.128777104.2	$x^{8} - x^{7} + 2 x^{6} - x^{5} + 6 x^{4} + x^{3} + 2 x^{2} + x + 1$	$8$	[0,4]	$2^{4}\cdot 2837^{2}$	$2$	$10.3211913985$	$84.55052949037936$				$C_2^3:S_4$ (as 8T39)	$[2]$	$2$	$3$	$5.4558810725$
8.0.128799801.1	$x^{8} - 2 x^{7} - 4 x^{6} + 29 x^{4} + 6 x^{3} - 43 x^{2} - 35 x + 49$	$8$	[0,4]	$3^{4}\cdot 13^{2}\cdot 97^{2}$	$3$	$10.3214187701$	$61.506097258727124$			?	$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$6$	$3$	$9.54693389748$
8.0.129267065.1	$x^{8} - x^{7} + x^{6} + 3 x^{5} + 2 x^{4} + 3 x^{3} + 13 x^{2} + 20 x + 9$	$8$	[0,4]	$5\cdot 17\cdot 29\cdot 229^{2}$	$4$	$10.3260919043$	$751.3221679146703$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.50440049239$
8.0.131974144.1	$x^{8} + x^{6} + 4 x^{4} - 3 x^{2} + 1$	$8$	[0,4]	$2^{10}\cdot 359^{2}$	$2$	$10.3528782498$	$53.59104402789705$			?	$C_2^3:S_4$ (as 8T39)	$[2]$	$2$	$3$	$5.34214964994$
8.0.132710400.3	$x^{8} - 4 x^{5} + 13 x^{4} - 24 x^{3} + 22 x^{2} - 8 x + 1$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 5^{2}$	$3$	$10.3600802564$	$15.491933384829668$			?	$Q_8:C_2$ (as 8T11)	$[2]$	$6$	$3$	$9.97462313965$
8.0.132917841.2	$x^{8} - x^{7} - 6 x^{6} + 11 x^{5} + 37 x^{4} + 9 x^{3} - 30 x^{2} - 9 x + 9$	$8$	[0,4]	$3^{6}\cdot 7^{2}\cdot 61^{2}$	$3$	$10.3621031171$	$47.1036844046804$			?	$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$6$	$3$	$13.1080925522$
8.0.135644301.1	$x^{8} - x^{7} + x^{6} - 8 x^{5} + 5 x^{4} - 2 x^{3} + 7 x^{2} + 5 x + 1$	$8$	[0,4]	$3^{7}\cdot 13^{2}\cdot 367$	$3$	$10.3884366081$	$256.5662581317608$			?	$S_4\wr C_2$ (as 8T47)	$[2]$	$6$	$3$	$13.53660976$
8.0.138515453.1	$x^{8} - 3 x^{7} + 5 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} + 5 x + 1$	$8$	[0,4]	$19\cdot 23\cdot 563^{2}$	$3$	$10.4156715987$	$496.0151207372614$			✓	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$4.46964733731$
8.0.140955633.1	$x^{8} - x^{7} - 5 x^{6} + 10 x^{5} - 19 x^{3} + 22 x^{2} - 8 x + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 13^{2}\cdot 1471$	$4$	$10.4384329165$	$633.7057676871815$			✓	$S_4\wr C_2$ (as 8T47)	$[2]$	$6$	$3$	$10.0612068115$
8.0.142850304.2	$x^{8} + 3 x^{6} - 4 x^{5} + 8 x^{4} - 6 x^{3} + 7 x^{2} + 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 83^{2}$	$3$	$10.4558693063$	$31.559467676119$				$S_4\times C_2$ (as 8T24)	$[2]$	$6$	$3$	$14.2632940037$
8.0.144733797.1	$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} - 3 x^{4} + 13 x^{3} - 2 x^{2} - 5 x + 43$	$8$	[0,4]	$3^{4}\cdot 13^{2}\cdot 97\cdot 109$	$4$	$10.4730033985$	$642.1425075479741$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$9.42742058269$
8.0.144733797.2	$x^{8} - 2 x^{6} - 5 x^{5} - 7 x^{4} + 41 x^{3} - 76 x + 49$	$8$	[0,4]	$3^{4}\cdot 13^{2}\cdot 97\cdot 109$	$4$	$10.4730033985$	$642.1425075479741$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$9.86445425024$
8.0.146313216.1	$x^{8} - 2 x^{7} + 4 x^{5} + 10 x^{4} - 48 x^{3} + 72 x^{2} - 48 x + 12$	$8$	[0,4]	$2^{12}\cdot 3^{6}\cdot 7^{2}$	$3$	$10.4872215901$	$17.058268835716344$			?	$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$6$	$3$	$16.0343906042$
8.0.146313216.2	$x^{8} - 2 x^{7} - 4 x^{6} + 16 x^{5} - 14 x^{4} - 16 x^{3} + 56 x^{2} - 64 x + 28$	$8$	[0,4]	$2^{12}\cdot 3^{6}\cdot 7^{2}$	$3$	$10.4872215901$	$17.058268835716344$			?	$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$6$	$3$	$11.4081969523$
8.0.148777965.1	$x^{8} + 2 x^{6} - 3 x^{5} + 6 x^{4} - 3 x^{3} + 2 x^{2} + 3 x + 1$	$8$	[0,4]	$3^{6}\cdot 5\cdot 7^{4}\cdot 17$	$4$	$10.5091436086$	$55.60315361119768$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$2$	$3$	$5.7028013589$
8.0.151253973.1	$x^{8} - 3 x^{7} + 3 x^{6} - x^{4} + 3 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 13\cdot 379^{2}$	$3$	$10.5308481113$	$121.57713600837947$			✓	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$3.54920911894$
8.0.151725312.1	$x^{8} - 4 x^{7} + 13 x^{6} - 22 x^{5} + 28 x^{4} - 16 x^{3} - 2 x^{2} + 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{7}\cdot 271$	$3$	$10.5349445702$	$122.29521732022195$			?	$S_4\wr C_2$ (as 8T47)	$[2]$	$6$	$3$	$14.1462515874$
8.0.151807041.1	$x^{8} - 5 x^{6} + 28 x^{4} + 15 x^{2} + 9$	$8$	[0,4]	$3^{4}\cdot 37^{4}$	$2$	$10.5356537529$	$10.535653752852738$		✓		$D_4$ (as 8T4)	$[2]$	$6$	$3$	$21.2686658839$
8.0.153140625.1	$x^{8} - x^{7} - 9 x^{5} + 9 x^{4} - 4 x^{3} + 20 x^{2} - 16 x + 16$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 11^{2}$	$3$	$10.547178642$	$19.208102881010017$				$D_4\times C_2$ (as 8T9)	$[2]$	$6$	$3$	$14.2842011414$
8.0.153140625.2	$x^{8} - 3 x^{7} - x^{6} + 13 x^{5} + 6 x^{4} - 35 x^{3} - 15 x^{2} + 25 x + 25$	$8$	[0,4]	$3^{4}\cdot 5^{6}\cdot 11^{2}$	$3$	$10.547178642$	$19.208102881010017$			?	$C_2^2:C_4$ (as 8T10)	$[2]$	$10$	$3$	$17.9418504811$
8.0.153364736.1	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 16 x^{4} - 10 x^{3} + 5 x^{2} - 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 7\cdot 23\cdot 61^{2}$	$4$	$10.5491067936$	$280.2998394576779$			✓	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$3.47714438695$
8.0.153760000.1	$x^{8} + 7 x^{6} + 18 x^{4} + 17 x^{2} + 1$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 31^{2}$	$3$	$10.5525014692$	$35.21363372331802$				$C_2^2 \wr C_2$ (as 8T18)	$[2]$	$2$	$3$	$3.68434504411$
8.0.155356461.1	$x^{8} - 2 x^{7} - 7 x^{6} + 16 x^{5} + 22 x^{4} - 43 x^{3} - 37 x^{2} + 44 x + 37$	$8$	[0,4]	$3^{6}\cdot 13^{3}\cdot 97$	$3$	$10.5661352364$	$153.70370011141938$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$9.76935975144$