Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Results (1-50 of 94 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
7.7.13841287201.1	x^7 - 21x^5 - 21x^4 + 91x^3 + 112x^2 - 84x - 97	$7$	[7,0]	$7^{12}$	$1$	$28.1021467385$		✓		$C_7$ (as 7T1)	trivial	$2$	$6$	$550.88577714$
7.3.3543369523456.3	x^7 - 21x^5 - 28x^4 - 7x^3 - 112x^2 + 259x + 244	$7$	[3,2]	$2^{8}\cdot 7^{12}$	$2$	$62.0545710514$				$\GL(3,2)$ (as 7T5)	$[7]$	$2$	$4$	$12405.1123243$
7.3.3543369523456.4	x^7 - 21x^5 - 70x^4 + 238x^3 + 1092x^2 - 2240x + 736	$7$	[3,2]	$2^{8}\cdot 7^{12}$	$2$	$62.0545710514$				$\GL(3,2)$ (as 7T5)	$[14]$	$2$	$4$	$6202.55616215$
7.3.645779095649856.3	x^7 - 21x^5 - 70x^4 - 105x^3 - 84x^2 - 35x + 40818	$7$	[3,2]	$2^{6}\cdot 3^{6}\cdot 7^{12}$	$3$	$130.53479252$			not computed	$A_7$ (as 7T6)	$[7]$	$2$	$4$	$58386.9611144$
7.3.1148051725599744.1	x^7 - 42x^5 - 28x^4 + 609x^3 + 756x^2 - 3024x + 864	$7$	[3,2]	$2^{10}\cdot 3^{4}\cdot 7^{12}$	$3$	$141.717363809$			not computed	$A_7$ (as 7T6)	$[7]$	$2$	$4$	$105789.61343$
7.3.13841287201000000.2	x^7 - 2744x^2 + 27440	$7$	[3,2]	$2^{6}\cdot 5^{6}\cdot 7^{12}$	$3$	$202.247123883$			not computed	$A_7$ (as 7T6)	$[7]$	$2$	$4$	$63284.5358524$
7.3.52308106747638336.4	x^7 - 84x^5 - 420x^4 + 5376x^3 - 3780x^2 - 16156x + 27900	$7$	[3,2]	$2^{6}\cdot 3^{10}\cdot 7^{12}$	$3$	$244.549624435$			not computed	$\GL(3,2)$ (as 7T5)	$[7]$	$2$	$4$	$539181.587994$
7.3.52308106747638336.6	x^7 - 84x^5 - 364x^4 - 1680x^3 + 6720x^2 + 77728x + 391638	$7$	[3,2]	$2^{6}\cdot 3^{10}\cdot 7^{12}$	$3$	$244.549624435$			not computed	$\GL(3,2)$ (as 7T5)	$[7]$	$2$	$4$	$539181.587994$
7.1.247979172729544704.1	x^7 - 882x^4 + 882x^3 - 15876	$7$	[1,3]	$-\,2^{13}\cdot 3^{7}\cdot 7^{12}$	$3$	$305.433351812$			not computed	$S_7$ (as 7T7)	$[7]$	$2$	$3$	$1346046.93683$
7.1.1313840933532421875.2	x^7 - 35x^5 - 70x^4 + 280x^3 + 1232x^2 + 1680x - 117325	$7$	[1,3]	$-\,3^{5}\cdot 5^{8}\cdot 7^{12}$	$3$	$387.581693052$			not computed	$S_7$ (as 7T7)	$[7]$	$2$	$3$	$620527.310781$
7.7.874...849.1	x^7 - 903x^5 - 11739x^4 - 4515x^3 + 484008x^2 + 1555568x - 609267	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$80239711.6814$
7.7.874...849.2	x^7 - 903x^5 - 3311x^4 + 256753x^3 + 1655500x^2 - 20129676x - 154845881	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$3504328.2978067407$
7.7.874...849.3	x^7 - 903x^5 - 1204x^4 + 218827x^3 + 753704x^2 - 16141125x - 86614900	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$2429511482.583454$
7.7.874...849.4	x^7 - 903x^5 - 15953x^4 - 97223x^3 - 177590x^2 + 46956x + 94471	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$8351632.841147239$
7.7.874...849.5	x^7 - 903x^5 - 3311x^4 + 206185x^3 + 1491154x^2 - 1773492x + 461089	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$4703614.757954623$
7.7.874...849.6	x^7 - 903x^5 - 7525x^4 + 105049x^3 + 905408x^2 - 1520652x + 545369	$7$	[7,0]	$7^{12}\cdot 43^{6}$	$2$	$706.082286107$		✓		$C_7$ (as 7T1)	$[7]$	$2$	$6$	$12027627.652134134$
8.4.3543369523456.1	x^8 - 7x^6 - 14x^5 + 7x^4 + 28x^2 + 48x + 14	$8$	[4,2]	$2^{8}\cdot 7^{12}$	$2$	$37.0405183549$				$C_2^3:\GL(3,2)$ (as 8T48)	trivial	$2$	$5$	$7262.24637552$
8.0.14173478093824.1	x^8 + 7x^6 + 21x^4 - 14x^3 + 42x^2 - 48x + 28	$8$	[0,4]	$2^{10}\cdot 7^{12}$	$2$	$44.048847971$				$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$3$	$1447.05229669$
8.0.226775649501184.4	x^8 - 2x^7 + 14x^6 - 14x^5 - 126x^4 + 630x^3 + 658x^2 - 5130x + 10267	$8$	[0,4]	$2^{14}\cdot 7^{12}$	$2$	$62.2944782076$			not computed	$C_2^3:C_7$ (as 8T25)	trivial	$2$	$3$	$24239.5513308$
8.0.226775649501184.5	x^8 - 2x^7 + 14x^6 + 84x^4 - 112x^3 + 28x^2 + 188x + 310	$8$	[0,4]	$2^{14}\cdot 7^{12}$	$2$	$62.2944782076$			not computed	$C_2^3:C_7$ (as 8T25)	trivial	$2$	$3$	$26620.3609911$
8.0.907102598004736.3	x^8 - 56x^5 + 7x^4 - 84x^3 + 770x^2 - 116x + 2394	$8$	[0,4]	$2^{16}\cdot 7^{12}$	$2$	$74.0810367098$			not computed	$\PSL(2,7)$ (as 8T37)	$[2, 6]$	$2$	$3$	$10627.578275$
8.0.907102598004736.6	x^8 - 56x^5 - 70x^4 + 224x^3 + 672x^2 + 264x + 329	$8$	[0,4]	$2^{16}\cdot 7^{12}$	$2$	$74.0810367098$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$3$	$25714.4903521$
8.4.907102598004736.7	x^8 - 28x^6 - 84x^5 + 133x^4 + 1204x^3 + 2310x^2 + 1224x + 189	$8$	[4,2]	$2^{16}\cdot 7^{12}$	$2$	$74.0810367098$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$5$	$44501.4858602$
8.0.907102598004736.7	x^8 - 4x^7 + 14x^6 - 28x^5 + 70x^4 - 84x^3 + 378x^2 - 124x + 517	$8$	[0,4]	$2^{16}\cdot 7^{12}$	$2$	$74.0810367098$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$3$	$8070.98128542$
8.0.1803810389321521.1	x^8 - 2x^7 - 28x^6 + 154x^5 + 189x^4 - 2016x^3 + 5278x^2 + 2701x + 2949	$8$	[0,4]	$7^{12}\cdot 19^{4}$	$2$	$80.7279381627$			not computed	$C_2^3:C_7$ (as 8T25)	$[2, 4]$	$2$	$3$	$7631.3442133$
8.0.1803810389321521.2	x^8 - 4x^7 + 35x^6 - 42x^5 + 329x^4 - 14x^3 + 2611x^2 - 6607x + 3692	$8$	[0,4]	$7^{12}\cdot 19^{4}$	$2$	$80.7279381627$			not computed	$C_2^3:C_7$ (as 8T25)	$[2, 4]$	$2$	$3$	$7306.25989421$
8.0.2296103451199488.1	x^8 - 3x^7 + 28x^6 - 161x^5 + 392x^4 + 371x^3 + 672x^2 + 353x + 187	$8$	[0,4]	$2^{11}\cdot 3^{4}\cdot 7^{12}$	$3$	$83.2001159276$			not computed	$\PGL(2,7)$ (as 8T43)	$[2]$	$2$	$3$	$91728.6569631$
8.0.3628410392018944.1	x^8 - 4x^7 - 56x^5 + 196x^4 - 224x^3 + 1792x^2 + 1408x + 1088	$8$	[0,4]	$2^{18}\cdot 7^{12}$	$2$	$88.0976959421$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$3$	$131688.580848$
8.4.3628410392018944.1	x^8 - 4x^7 + 28x^6 - 196x^4 - 784x^2 + 2016x - 1008	$8$	[4,2]	$2^{18}\cdot 7^{12}$	$2$	$88.0976959421$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	trivial	$2$	$5$	$118573.087895$
8.0.3628410392018944.3	x^8 - 4x^7 + 28x^6 - 56x^5 + 301x^4 - 280x^3 + 2128x^2 + 320x + 6672	$8$	[0,4]	$2^{18}\cdot 7^{12}$	$2$	$88.0976959421$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$3$	$181346.72701$
8.4.3628410392018944.3	x^8 - 4x^7 - 28x^6 - 28x^5 + 70x^4 + 588x^3 + 1764x^2 + 1940x + 661	$8$	[4,2]	$2^{18}\cdot 7^{12}$	$2$	$88.0976959421$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	trivial	$2$	$5$	$146393.854072$
8.4.3628410392018944.4	x^8 - 4x^7 - 14x^6 + 56x^5 + 84x^4 - 28x^3 - 112x^2 - 16x + 50	$8$	[4,2]	$2^{18}\cdot 7^{12}$	$2$	$88.0976959421$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$5$	$51933.9162826$
8.0.12782719397154721.1	x^8 - 3x^7 - 56x^6 + 28x^5 + 1043x^4 - 567x^3 + 4704x^2 + 46853x + 57555	$8$	[0,4]	$7^{12}\cdot 31^{4}$	$2$	$103.116439039$			not computed	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$	$2$	$3$	$20731.5393723$
8.8.12782719397154721.1	x^8 - x^7 - 42x^6 + 77x^5 + 420x^4 - 854x^3 - 987x^2 + 1577x + 733	$8$	[8,0]	$7^{12}\cdot 31^{4}$	$2$	$103.116439039$			not computed	$C_2^3:C_7$ (as 8T25)	trivial	$2$	$7$	$942691.948946$
8.4.14513641568075776.1	x^8 - 4x^7 + 14x^6 - 28x^5 - 273x^4 - 84x^3 + 2534x^2 + 4384x - 9381	$8$	[4,2]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$5$	$208750.585146$
8.0.14513641568075776.2	x^8 - 4x^7 + 28x^6 - 56x^5 + 252x^4 - 280x^3 + 952x^2 - 464x + 1380	$8$	[0,4]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 12]$	$2$	$3$	$15171.4047761$
8.0.14513641568075776.3	x^8 - 56x^5 + 126x^4 + 224x^3 - 112x^2 + 1048x + 1505	$8$	[0,4]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$3$	$32642.9044999$
8.4.14513641568075776.5	x^8 - 28x^6 - 84x^5 + 210x^4 + 5096x^3 + 13552x^2 + 6008x - 2002	$8$	[4,2]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$5$	$144495.61499$
8.0.14513641568075776.7	x^8 - 4x^7 - 56x^5 + 490x^4 - 1008x^3 + 1400x^2 - 3296x + 4616	$8$	[0,4]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$3$	$44578.5697838$
8.4.14513641568075776.11	x^8 - 4x^7 - 28x^6 + 56x^5 + 686x^4 - 4256x^3 + 14112x^2 - 16672x + 4080	$8$	[4,2]	$2^{20}\cdot 7^{12}$	$2$	$104.76640683$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$2$	$5$	$896141.00032$
8.0.470772960728745024.2	x^8 - 2x^7 + 28x^6 - 13608x + 27216	$8$	[0,4]	$2^{6}\cdot 3^{12}\cdot 7^{12}$	$3$	$161.84580193$			not computed	$\PSL(2,7)$ (as 8T37)	$[4]$	$2$	$3$	$747394.855325$
8.0.928873060356849664.4	x^8 + 56x^6 + 952x^4 - 896x^3 + 7392x^2 + 2304x + 15120	$8$	[0,4]	$2^{26}\cdot 7^{12}$	$2$	$176.195391884$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 4]$	$2$	$3$	$258306.421026$
8.4.928873060356849664.7	x^8 - 56x^6 - 112x^5 + 350x^4 + 3528x^3 + 11592x^2 + 16120x + 6727	$8$	[4,2]	$2^{26}\cdot 7^{12}$	$2$	$176.195391884$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[4]$	$2$	$5$	$719098.828771$
8.4.928873060356849664.8	x^8 - 28x^6 - 224x^5 - 1176x^4 - 1064x^3 - 6104x^2 - 7920x + 8442	$8$	[4,2]	$2^{26}\cdot 7^{12}$	$2$	$176.195391884$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 2]$	$2$	$5$	$1034710.48001$
8.0.928873060356849664.12	x^8 - 28x^6 - 112x^5 + 1386x^4 + 6272x^3 + 18060x^2 - 49520x + 426209	$8$	[0,4]	$2^{26}\cdot 7^{12}$	$2$	$176.195391884$			not computed	$C_2^3:\GL(3,2)$ (as 8T48)	$[2, 4]$	$2$	$3$	$121607.01614$
8.0.3715492241427398656.1	x^8 - 896x + 1568	$8$	[0,4]	$2^{28}\cdot 7^{12}$	$2$	$209.532813659$			not computed	$A_8$ (as 8T49)	$[2, 2]$	$2$	$3$	$468980.925517$
8.2.650...376.1	x^8 - 3528x^2 - 6048x - 2646	$8$	[2,3]	$-\,2^{31}\cdot 3^{7}\cdot 7^{12}$	$3$	$710.590490282$			not computed	$S_8$ (as 8T50)	trivial	$2$	$4$	$683277868.793$
8.2.131...864.1	x^8 - 56x^5 - 1050x^4 - 8400x^3 - 35000x^2 - 75000x - 65625	$8$	[2,3]	$-\,2^{29}\cdot 3^{11}\cdot 7^{12}$	$3$	$1034.95750826$			not computed	$S_8$ (as 8T50)	$[2]$	$2$	$4$	$1754817880.49$
8.2.186...216.1	x^8 - 5824x - 5096	$8$	[2,3]	$-\,2^{31}\cdot 7^{12}\cdot 13^{7}$	$3$	$2563.53190246$			not computed	$S_8$ (as 8T50)	$[2, 2]$	$2$	$4$	$16760064929.9$
9.3.203...368.1	x^9 - 3x^8 + 756x^2 - 2268x + 1764	$9$	[3,3]	$-\,2^{10}\cdot 3^{15}\cdot 7^{12}$	$3$	$180.500018538$			not computed	$S_9$ (as 9T34)	trivial	$2$	$5$	$38577167.6361$