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Results (1-50 of 77956 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
8.8.282300416.1	$x^{8} - 4 x^{7} + 14 x^{5} - 8 x^{4} - 12 x^{3} + 7 x^{2} + 2 x - 1$	$8$	[8,0]	$2^{12}\cdot 41^{3}$	$2$	$11.3851547954$	$45.82820910616052$		✓	$C_4\wr C_2$ (as 8T17)	trivial	$2$	$7$	$22.4468700736$
8.8.309593125.1	$x^{8} - 4 x^{7} - x^{6} + 17 x^{5} - 5 x^{4} - 23 x^{3} + 6 x^{2} + 9 x - 1$	$8$	[8,0]	$5^{4}\cdot 19\cdot 29^{2}\cdot 31$	$4$	$11.5172531693$	$292.24133862272123$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$23.6967890277$
8.8.324000000.1	$x^{8} - 7 x^{6} + 14 x^{4} - 8 x^{2} + 1$	$8$	[8,0]	$2^{8}\cdot 3^{4}\cdot 5^{6}$	$3$	$11.5829218529$	$11.582921852882691$	✓	✓	$C_4\times C_2$ (as 8T2)	trivial	$2$	$7$	$24.3884064258$
8.8.410338673.1	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} + 15 x^{4} - 10 x^{3} - 10 x^{2} + 4 x + 1$	$8$	[8,0]	$17^{7}$	$1$	$11.9300648987$	$11.93006489865314$	✓	✓	$C_8$ (as 8T1)	trivial	$2$	$7$	$28.437595417$
8.8.432640000.1	$x^{8} - 2 x^{7} - 7 x^{6} + 16 x^{5} + 4 x^{4} - 18 x^{3} + 2 x^{2} + 4 x - 1$	$8$	[8,0]	$2^{12}\cdot 5^{4}\cdot 13^{2}$	$3$	$12.0092485618$	$22.80350850198276$		✓	$Q_8:C_2$ (as 8T11)	trivial	$2$	$7$	$28.9890220694$
8.8.442050625.1	$x^{8} - 2 x^{7} - 12 x^{6} + 26 x^{5} + 17 x^{4} - 36 x^{3} - 5 x^{2} + 11 x - 1$	$8$	[8,0]	$5^{4}\cdot 29^{4}$	$2$	$12.0415945788$	$12.041594578792296$	✓	?	$D_4$ (as 8T4)	trivial	$2$	$7$	$29.6385151004$
8.8.456768125.1	$x^{8} - 2 x^{7} - 7 x^{6} + 11 x^{5} + 14 x^{4} - 18 x^{3} - 8 x^{2} + 9 x - 1$	$8$	[8,0]	$5^{4}\cdot 11\cdot 29^{2}\cdot 79$	$4$	$12.0909931103$	$354.97182986823054$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$30.3398226576$
8.8.483345053.1	$x^{8} - x^{7} - 7 x^{6} + 4 x^{5} + 15 x^{4} - 3 x^{3} - 9 x^{2} + 1$	$8$	[8,0]	$483345053$	$1$	$12.1767715918$	$21985.109801863626$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$31.4056495019$
8.8.494613125.1	$x^{8} - x^{7} - 7 x^{6} + 4 x^{5} + 13 x^{4} - 4 x^{3} - 7 x^{2} + x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 941$	$3$	$12.2118990229$	$369.3846233940985$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$31.4375526025$
8.8.582918125.1	$x^{8} - 2 x^{7} - 6 x^{6} + 9 x^{5} + 11 x^{4} - 9 x^{3} - 6 x^{2} + 2 x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1109$	$3$	$12.4652486189$	$401.00498750015566$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$35.7205035025$
8.8.656505625.1	$x^{8} - 3 x^{7} - 4 x^{6} + 13 x^{5} + 5 x^{4} - 13 x^{3} - 4 x^{2} + 3 x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1249$	$3$	$12.6518724942$	$425.5643312120977$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$37.2825779024$
8.8.661518125.1	$x^{8} - x^{7} - 7 x^{6} + 5 x^{5} + 15 x^{4} - 7 x^{3} - 10 x^{2} + 2 x + 1$	$8$	[8,0]	$5^{4}\cdot 439\cdot 2411$	$3$	$12.6639071738$	$2300.4662570878972$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$37.8654262114$
8.8.707295133.1	$x^{8} - 8 x^{6} - 2 x^{5} + 19 x^{4} + 7 x^{3} - 13 x^{2} - 4 x + 1$	$8$	[8,0]	$9973\cdot 70921$	$2$	$12.7702701211$	$26595.02083097511$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$39.2596652535$
8.8.733968125.1	$x^{8} - 2 x^{7} - 6 x^{6} + 10 x^{5} + 11 x^{4} - 11 x^{3} - 7 x^{2} + 2 x + 1$	$8$	[8,0]	$5^{4}\cdot 11\cdot 106759$	$3$	$12.8294976034$	$2423.1683804473846$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$40.3475819574$
8.8.740605625.1	$x^{8} - x^{7} - 9 x^{6} + 8 x^{5} + 21 x^{4} - 12 x^{3} - 14 x^{2} + 4 x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1409$	$3$	$12.8439431844$	$452.0011061933367$		?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$40.3991503507$
8.8.803680625.1	$x^{8} - 2 x^{7} - 9 x^{6} + 12 x^{5} + 22 x^{4} - 24 x^{3} - 14 x^{2} + 14 x - 1$	$8$	[8,0]	$5^{4}\cdot 11\cdot 29^{2}\cdot 139$	$4$	$12.9758386715$	$470.8556041930477$		?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$42.7587953365$
8.8.852038125.1	$x^{8} - 10 x^{6} - 5 x^{5} + 17 x^{4} + 5 x^{3} - 10 x^{2} + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1621$	$3$	$13.0709567759$	$484.81439747598256$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$44.7501704817$
8.8.877268125.1	$x^{8} - 3 x^{7} - 6 x^{6} + 20 x^{5} + 5 x^{4} - 25 x^{3} - x^{2} + 7 x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1669$	$3$	$13.1187224452$	$491.9400369963803$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$45.8191285307$
8.8.898293125.1	$x^{8} - x^{7} - 9 x^{6} + 10 x^{5} + 15 x^{4} - 10 x^{3} - 9 x^{2} + x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 1709$	$3$	$13.1576175741$	$497.80016070708535$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$46.6119375927$
8.8.1000118125.1	$x^{8} - 3 x^{7} - 4 x^{6} + 14 x^{5} + 5 x^{4} - 19 x^{3} - x^{2} + 7 x - 1$	$8$	[8,0]	$5^{4}\cdot 31\cdot 41\cdot 1259$	$4$	$13.3354112142$	$2828.594173790224$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$49.7759598432$
8.8.1024000000.1	$x^{8} - 8 x^{6} + 19 x^{4} - 12 x^{2} + 1$	$8$	[8,0]	$2^{16}\cdot 5^{6}$	$2$	$13.3748060995$	$13.37480609952844$	✓	✓	$C_4\times C_2$ (as 8T2)	trivial	$2$	$7$	$55.5791824785$
8.8.1032588125.1	$x^{8} - 9 x^{6} - 2 x^{5} + 23 x^{4} + 9 x^{3} - 17 x^{2} - 9 x - 1$	$8$	[8,0]	$5^{4}\cdot 1652141$	$2$	$13.3887764654$	$2874.14422045937$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$54.3817514238$
8.8.1064390625.1	$x^{8} - 13 x^{6} + 44 x^{4} - 17 x^{2} + 1$	$8$	[8,0]	$3^{4}\cdot 5^{6}\cdot 29^{2}$	$3$	$13.4396398271$	$31.187971562966524$		?	$C_2^2:C_4$ (as 8T10)	trivial	$2$	$7$	$49.355192321$
8.8.1077044573.1	$x^{8} - x^{7} - 8 x^{6} + 8 x^{5} + 16 x^{4} - 17 x^{3} - 2 x^{2} + 5 x - 1$	$8$	[8,0]	$11\cdot 97913143$	$2$	$13.459508764$	$32818.357256267416$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$54.1448931786$
8.8.1095205625.1	$x^{8} - 3 x^{7} - 5 x^{6} + 18 x^{5} + 2 x^{4} - 23 x^{3} + 2 x^{2} + 8 x - 1$	$8$	[8,0]	$5^{4}\cdot 349\cdot 5021$	$3$	$13.4876708258$	$2960.007601341591$		?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$59.084256483$
8.8.1098290293.1	$x^{8} - 3 x^{7} - 4 x^{6} + 16 x^{5} + x^{4} - 23 x^{3} + 7 x^{2} + 5 x - 1$	$8$	[8,0]	$7523\cdot 145991$	$2$	$13.4924135208$	$33140.46307763366$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$63.9120234189$
8.8.1104338125.1	$x^{8} - 2 x^{7} - 8 x^{6} + 15 x^{5} + 17 x^{4} - 31 x^{3} - 9 x^{2} + 17 x - 1$	$8$	[8,0]	$5^{4}\cdot 11\cdot 29^{2}\cdot 191$	$4$	$13.5016783686$	$551.9465553837617$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$51.3049671711$
8.8.1114390153.1	$x^{8} - 8 x^{6} - 2 x^{5} + 16 x^{4} + 3 x^{3} - 10 x^{2} + 1$	$8$	[8,0]	$347\cdot 3211499$	$2$	$13.5169795965$	$33382.48272672361$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$52.8950121075$
8.8.1121463125.1	$x^{8} - 3 x^{7} - 4 x^{6} + 15 x^{5} + 2 x^{4} - 18 x^{3} + 5 x + 1$	$8$	[8,0]	$5^{4}\cdot 19\cdot 94439$	$3$	$13.5276738752$	$2995.280454314754$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$57.2610108044$
8.8.1136700613.1	$x^{8} - x^{7} - 7 x^{6} + 4 x^{5} + 14 x^{4} - 4 x^{3} - 8 x^{2} + x + 1$	$8$	[8,0]	$89\cdot 1301\cdot 9817$	$3$	$13.550513767$	$33714.99092391988$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$51.2625172436$
8.8.1142440000.1	$x^{8} - 3 x^{7} - 5 x^{6} + 15 x^{5} + 8 x^{4} - 15 x^{3} - 5 x^{2} + 4 x + 1$	$8$	[8,0]	$2^{6}\cdot 5^{4}\cdot 13^{4}$	$3$	$13.5590472788$	$22.80350850198276$		✓	$Q_8:C_2$ (as 8T11)	trivial	$2$	$7$	$59.9995786491$
8.8.1152784549.1	$x^{8} - 4 x^{7} - x^{6} + 15 x^{5} - 3 x^{4} - 16 x^{3} + 4 x^{2} + 4 x - 1$	$8$	[8,0]	$7\cdot 19^{2}\cdot 43\cdot 103^{2}$	$4$	$13.5743336077$	$767.500488599193$		✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$7$	$56.0040678259$
8.8.1153988125.1	$x^{8} - 2 x^{7} - 7 x^{6} + 11 x^{5} + 12 x^{4} - 16 x^{3} - 5 x^{2} + 6 x - 1$	$8$	[8,0]	$5^{4}\cdot 101^{2}\cdot 181$	$3$	$13.576104351$	$302.33259830855155$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$53.31986114$
8.8.1166547493.1	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} + 14 x^{4} - 9 x^{3} - 9 x^{2} + 3 x + 1$	$8$	[8,0]	$1166547493$	$1$	$13.5944863533$	$34154.757984796204$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$57.6779331487$
8.8.1183423341.1	$x^{8} - x^{7} - 8 x^{6} + 9 x^{5} + 17 x^{4} - 20 x^{3} - 8 x^{2} + 10 x - 1$	$8$	[8,0]	$3\cdot 19^{2}\cdot 103^{3}$	$3$	$13.6189152203$	$244.09863248010305$		✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$7$	$66.8194726815$
8.8.1202043125.1	$x^{8} - 3 x^{7} - 4 x^{6} + 16 x^{5} - 21 x^{3} + 9 x^{2} + 2 x - 1$	$8$	[8,0]	$5^{4}\cdot 41\cdot 61\cdot 769$	$4$	$13.6455173546$	$3101.023218229751$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$55.7182141133$
8.8.1225026133.1	$x^{8} - 3 x^{7} - 4 x^{6} + 18 x^{5} - 6 x^{4} - 17 x^{3} + 9 x^{2} + 2 x - 1$	$8$	[8,0]	$83\cdot 14759351$	$2$	$13.6778604721$	$35000.37332658039$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$56.1212063278$
8.8.1243893125.1	$x^{8} - x^{7} - 8 x^{6} + 3 x^{5} + 18 x^{4} - x^{3} - 12 x^{2} - 2 x + 1$	$8$	[8,0]	$5^{4}\cdot 1990229$	$2$	$13.7040168337$	$3154.5435485978$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$54.6552881572$
8.8.1255718125.1	$x^{8} - 2 x^{7} - 8 x^{6} + 19 x^{5} + 10 x^{4} - 41 x^{3} + 13 x^{2} + 10 x - 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 2389$	$3$	$13.7202340629$	$588.5618064400713$		✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$54.2354730586$
8.8.1261609229.1	$x^{8} - 2 x^{7} - 6 x^{6} + 12 x^{5} + 9 x^{4} - 19 x^{3} - x^{2} + 6 x - 1$	$8$	[8,0]	$397\cdot 3177857$	$2$	$13.7282635234$	$35519.138911296825$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$61.0590696819$
8.8.1292203125.1	$x^{8} - 4 x^{7} - x^{6} + 17 x^{5} - 6 x^{4} - 21 x^{3} + 6 x^{2} + 8 x + 1$	$8$	[8,0]	$3^{4}\cdot 5^{6}\cdot 1021$	$3$	$13.7694422325$	$185.05507578936948$		✓	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$7$	$53.9529294588$
8.8.1299600812.1	$x^{8} - 2 x^{7} - 6 x^{6} + 10 x^{5} + 12 x^{4} - 13 x^{3} - 8 x^{2} + 3 x + 1$	$8$	[8,0]	$2^{2}\cdot 324900203$	$2$	$13.7792711639$	$36049.97658806452$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$91.1201780925$
8.8.1317743125.1	$x^{8} - x^{7} - 8 x^{6} + 7 x^{5} + 19 x^{4} - 14 x^{3} - 12 x^{2} + 8 x - 1$	$8$	[8,0]	$5^{4}\cdot 2108389$	$2$	$13.8031702571$	$3246.83615231813$		✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$7$	$58.4588266704$
8.8.1318279381.1	$x^{8} - x^{7} - 7 x^{6} + 5 x^{5} + 14 x^{4} - 6 x^{3} - 9 x^{2} + x + 1$	$8$	[8,0]	$1318279381$	$1$	$13.8038722827$	$36308.117288011505$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$58.5595232418$
8.8.1326417388.1	$x^{8} - 2 x^{7} - 6 x^{6} + 10 x^{5} + 12 x^{4} - 13 x^{3} - 9 x^{2} + 4 x + 2$	$8$	[8,0]	$2^{2}\cdot 43\cdot 2777^{2}$	$3$	$13.8144953894$	$691.1179349430892$		✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$7$	$92.233039402$
8.8.1348097653.1	$x^{8} - 2 x^{7} - 6 x^{6} + 11 x^{5} + 11 x^{4} - 17 x^{3} - 6 x^{2} + 6 x + 1$	$8$	[8,0]	$7^{2}\cdot 27512197$	$2$	$13.8425203$	$13877.513430006113$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$72.5535341153$
8.8.1358954496.1	$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 1$	$8$	[8,0]	$2^{24}\cdot 3^{4}$	$2$	$13.8564064606$	$13.856406460551018$	✓	✓	$C_4\times C_2$ (as 8T2)	trivial	$2$	$7$	$93.4711768963$
8.8.1359341129.1	$x^{8} - 8 x^{6} - x^{5} + 18 x^{4} + 2 x^{3} - 12 x^{2} - x + 2$	$8$	[8,0]	$1359341129$	$1$	$13.856899181$	$36869.24367274165$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$93.7187751003$
8.8.1377663125.1	$x^{8} - 12 x^{6} + 33 x^{4} - 5 x^{3} - 22 x^{2} + 5 x + 1$	$8$	[8,0]	$5^{4}\cdot 29^{2}\cdot 2621$	$3$	$13.880109084$	$616.4778990361293$		?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$7$	$56.5417886705$
8.8.1381875749.1	$x^{8} - 3 x^{7} - 4 x^{6} + 14 x^{5} + 4 x^{4} - 18 x^{3} + x^{2} + 5 x - 1$	$8$	[8,0]	$1381875749$	$1$	$13.885407332$	$37173.58940161684$		✓	$S_8$ (as 8T50)	trivial	$2$	$7$	$74.1276222327$

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