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Results (1-50 of 608057 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
8.4.15243125.1	$x^{8} - x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - 6 x^{3} - 2 x^{2} + 3 x + 1$	$8$	[4,2]	$5^{4}\cdot 29^{3}$	$2$	$7.90467923584$	$27.943673649584856$	?	$C_4\wr C_2$ (as 8T17)	trivial	$2$	$5$	$2.29779629129$
8.4.15297613.1	$x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 2 x^{4} - 6 x^{3} + 3 x^{2} + 2 x - 1$	$8$	[4,2]	$37\cdot 643^{2}$	$2$	$7.90820572796$	$154.2433142797444$	✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.30435678407$
8.4.15908237.1	$x^{8} - x^{6} - x^{5} - 3 x^{4} + 4 x^{2} - 1$	$8$	[4,2]	$43\cdot 369959$	$2$	$7.94699164741$	$3988.513131481455$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.3628354116$
8.4.16324589.1	$x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 2 x^{2} - 4 x - 1$	$8$	[4,2]	$149\cdot 331^{2}$	$2$	$7.97269741897$	$222.07881483833617$	✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.40223672764$
8.4.16374773.1	$x^{8} - x^{7} - x^{6} - 2 x^{4} + 2 x^{3} + 4 x^{2} - x - 1$	$8$	[4,2]	$1753\cdot 9341$	$2$	$7.97575695057$	$4046.5754657487855$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4093209353$
8.4.16526789.1	$x^{8} - 3 x^{6} - x^{3} + 3 x^{2} - 1$	$8$	[4,2]	$19\cdot 607\cdot 1433$	$3$	$7.98497499174$	$4065.3153629208155$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4220975910452807$
8.4.16623109.1	$x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 3 x^{4} - 2 x^{3} + 3 x^{2} - x - 1$	$8$	[4,2]	$16623109$	$1$	$7.990777380370964$	$4077.1447116824293$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4296621448382574$
8.4.16643125.1	$x^{8} - x^{7} - 2 x^{6} + 2 x^{5} - x^{3} + x + 1$	$8$	[4,2]	$5^{4}\cdot 31\cdot 859$	$3$	$7.99197946602$	$364.89039450223953$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.43215022883$
8.4.16706269.1	$x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 1$	$8$	[4,2]	$73\cdot 228853$	$2$	$7.995763384931862$	$4087.3303022877903$	?	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4390110595294625$
8.4.16877741.1	$x^{8} - 3 x^{7} + 2 x^{6} + x^{5} + x^{3} - 4 x^{2} + 1$	$8$	[4,2]	$16877741$	$1$	$8.005976108729776$	$4108.252791637827$	?	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4525063645502785$
8.4.16981229.1	$x^{8} - 3 x^{7} + 4 x^{6} - x^{5} - 4 x^{4} + 5 x^{3} - 2 x^{2} - 2 x + 1$	$8$	[4,2]	$3329\cdot 5101$	$2$	$8.012095917303123$	$4120.828678797506$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.462471617197491$
8.4.17025973.1	$x^{8} - 3 x^{7} + 2 x^{6} + 4 x^{5} - 8 x^{4} + 3 x^{3} + 3 x^{2} - 4 x + 1$	$8$	[4,2]	$67\cdot 254119$	$2$	$8.01473177362$	$4126.254112388136$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.4665460579731495$
8.4.17129069.1	$x^{8} - 2 x^{7} + x^{5} - x^{3} + x^{2} + 2 x - 1$	$8$	[4,2]	$17129069$	$1$	$8.020782133197997$	$4138.727944670923$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.477759313535453$
8.4.17238125.1	$x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} - 3 x^{3} - 3 x^{2} + 2 x + 1$	$8$	[4,2]	$5^{4}\cdot 27581$	$2$	$8.0271476835$	$371.35562470494506$	?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.48717621365$
8.4.17318125.1	$x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 7 x^{4} + 4 x^{3} - 4 x^{2} + 4 x - 1$	$8$	[4,2]	$5^{4}\cdot 11^{2}\cdot 229$	$3$	$8.03179488069$	$112.22744762311936$	?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$5$	$2.49677825404$
8.4.17383253.1	$x^{8} - x^{6} - x^{5} - 2 x^{4} + x^{2} + 2 x + 1$	$8$	[4,2]	$17383253$	$1$	$8.03556431378$	$4169.32284669825$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.510646602137753$
8.4.17592581.1	$x^{8} - 2 x^{7} + 3 x^{5} - 4 x^{4} - x^{3} + 4 x^{2} + x - 1$	$8$	[4,2]	$137\cdot 128413$	$2$	$8.047596533882775$	$4194.351082110318$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.520773451379552$
8.4.17712197.1	$x^{8} - 2 x^{7} + 2 x^{5} - 2 x^{3} - 3 x^{2} + 2 x + 1$	$8$	[4,2]	$17712197$	$1$	$8.054415956387006$	$4208.586104619935$	?	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.532802833830868$
8.4.17919197.1	$x^{8} - x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$	$8$	[4,2]	$17919197$	$1$	$8.066122586617999$	$4233.1072511808625$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.5502372761598693$
8.4.17949581.1	$x^{8} - 2 x^{7} + x^{6} + x^{5} - 4 x^{4} + 3 x^{3} - 2 x + 1$	$8$	[4,2]	$13\cdot 71\cdot 19447$	$3$	$8.067830946181994$	$4236.69458422483$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.562767769989586$
8.4.18031373.1	$x^{8} - x^{7} - 3 x^{6} + 5 x^{5} + x^{4} - 7 x^{3} + 2 x^{2} + 2 x - 1$	$8$	[4,2]	$17\cdot 71\cdot 14939$	$3$	$8.072417210819594$	$4246.33642096337$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.5626865024968524$
8.4.18340381.1	$x^{8} - 4 x^{6} - x^{5} + 5 x^{4} + x^{3} - 4 x^{2} + 1$	$8$	[4,2]	$229\cdot 283^{2}$	$2$	$8.08958130305$	$254.57219015438432$	✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.592566302$
8.4.18416197.1	$x^{8} - x^{7} - x^{6} + x^{3} - x^{2} + x + 1$	$8$	[4,2]	$18416197$	$1$	$8.09375388086088$	$4291.409675153375$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.597965839480305$
8.4.18441341.1	$x^{8} - x^{7} - 2 x^{6} + 3 x^{4} + x^{3} - 3 x^{2} + x + 1$	$8$	[4,2]	$18441341$	$1$	$8.09513437685505$	$4294.3382493697445$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.595652330923824$
8.4.18553789.1	$x^{8} - x^{7} - x^{6} + 4 x^{5} - 4 x^{4} - 4 x^{3} + 4 x^{2} + x - 1$	$8$	[4,2]	$59\cdot 157\cdot 2003$	$3$	$8.101288095044568$	$4307.410939299848$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.606967521220819$
8.4.18660737.1	$x^{8} - 3 x^{6} - 4 x^{5} + 5 x^{4} + 4 x^{3} - 3 x^{2} + 1$	$8$	[4,2]	$233\cdot 283^{2}$	$2$	$8.10711062159$	$256.78590303986704$	?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.62356876075$
8.4.19009909.1	$x^{8} - x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - 3 x^{3} + 3 x^{2} - 1$	$8$	[4,2]	$197\cdot 96497$	$2$	$8.125919295990252$	$4360.035435635816$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.656488059392775$
8.4.19129013.1	$x^{8} - 2 x^{7} + 4 x^{5} - 5 x^{4} + x^{3} + 3 x^{2} - 4 x + 1$	$8$	[4,2]	$131\cdot 146023$	$2$	$8.13226590001272$	$4373.672712949609$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.662640398894129$
8.4.19268125.1	$x^{8} - 2 x^{7} + x^{6} + x^{5} - 5 x^{4} + 4 x^{3} + 4 x^{2} - 2 x - 1$	$8$	[4,2]	$5^{4}\cdot 30829$	$2$	$8.13963502486$	$392.6130410467793$	?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.69038254871$
8.4.19360000.1	$x^{8} - 3 x^{6} + 3 x^{4} - 3 x^{2} + 1$	$8$	[4,2]	$2^{8}\cdot 5^{4}\cdot 11^{2}$	$3$	$8.14447639858$	$20.97617696340303$	✓	$C_2^2 \wr C_2$ (as 8T18)	trivial	$2$	$5$	$2.67883629025$
8.4.19824653.1	$x^{8} - x^{7} - 3 x^{6} + 4 x^{5} + x^{4} - 4 x^{3} + 3 x^{2} + x - 1$	$8$	[4,2]	$19824653$	$1$	$8.168657729441854$	$4452.488405375134$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.7383524146405285$
8.4.19885949.1	$x^{8} - 3 x^{7} + 3 x^{6} + 3 x^{5} - 7 x^{4} + 3 x^{3} + 4 x^{2} - 2 x - 1$	$8$	[4,2]	$19885949$	$1$	$8.171810559154888$	$4459.3664348200855$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.7333382543791127$
8.4.20013373.1	$x^{8} - x^{7} - 2 x^{6} + 2 x^{4} + x^{3} + x - 1$	$8$	[4,2]	$20013373$	$1$	$8.178337638287886$	$4473.630852003773$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.747899469563084$
8.4.20030653.1	$x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 2 x^{4} - 6 x^{3} + 4 x^{2} + 3 x - 1$	$8$	[4,2]	$37\cdot 541369$	$2$	$8.17921997530875$	$4475.561752450747$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.747199056940384$
8.4.20099501.1	$x^{8} - 3 x^{7} + 2 x^{6} + x^{5} - 2 x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$	$8$	[4,2]	$31\cdot 648371$	$2$	$8.182728834692947$	$4483.24670300442$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.753005701385745$
8.4.20182493.1	$x^{8} - x^{7} - 3 x^{6} + 5 x^{5} - x^{4} - 4 x^{3} + 3 x^{2} - 1$	$8$	[4,2]	$20182493$	$1$	$8.18694459493272$	$4492.49296048419$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.7754566353984966$
8.4.20262517.1	$x^{8} - 2 x^{6} - 3 x^{5} - x^{4} + 9 x^{3} + x^{2} - 5 x + 1$	$8$	[4,2]	$11\cdot 23\cdot 283^{2}$	$3$	$8.19099524896$	$267.5798946109367$	?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.77770211865$
8.4.20268125.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$	$8$	[4,2]	$5^{4}\cdot 32429$	$2$	$8.1912785895$	$402.67232335982567$	?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.77655261097$
8.4.20493125.1	$x^{8} - x^{7} + 3 x^{5} - 3 x^{4} + 2 x^{2} - 2 x - 1$	$8$	[4,2]	$5^{4}\cdot 32789$	$2$	$8.2025903666$	$404.90122252223443$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.79523269146$
8.4.20502784.1	$x^{8} - x^{6} + 4 x^{4} - 4 x^{2} + 1$	$8$	[4,2]	$2^{8}\cdot 283^{2}$	$2$	$8.20307353161$	$56.58426906139804$	✓	$C_2^3:S_4$ (as 8T39)	trivial	$2$	$5$	$2.7869643821$
8.4.20613077.1	$x^{8} - x^{7} - x^{6} + x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + x - 1$	$8$	[4,2]	$20613077$	$1$	$8.208576561202333$	$4540.162662284249$	✓	$S_8$ (as 8T50)	trivial	$2$	$5$	$2.797217454034451$
8.4.20993125.1	$x^{8} - x^{7} - 2 x^{5} + x^{3} + x^{2} + 2 x - 1$	$8$	[4,2]	$5^{4}\cdot 33589$	$2$	$8.22734362391$	$409.8109320162165$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.86231896498$
8.4.21543941.1	$x^{8} - x^{7} + 2 x^{6} - 7 x^{5} + 4 x^{4} - 5 x^{3} + 6 x^{2} + 2 x - 1$	$8$	[4,2]	$269\cdot 283^{2}$	$2$	$8.25402241402$	$275.9112176045041$	?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2.86814778847$
8.4.21550625.1	$x^{8} - x^{7} - x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{3} - 4 x^{2} - 2 x + 1$	$8$	[4,2]	$5^{4}\cdot 29^{2}\cdot 41$	$3$	$8.25434247152$	$77.10382610480494$	✓	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$5$	$2.87097626663$
8.4.22974464.1	$x^{8} - 2 x^{7} + x^{6} - 4 x^{4} + 6 x^{3} - 6 x^{2} + 4 x - 1$	$8$	[4,2]	$2^{12}\cdot 71\cdot 79$	$3$	$8.32061971494$	$211.83012061555362$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$2.99088852843$
8.4.23040000.1	$x^{8} - 2 x^{7} - x^{6} - 5 x^{4} - x^{2} - 2 x + 1$	$8$	[4,2]	$2^{12}\cdot 3^{2}\cdot 5^{4}$	$3$	$8.32358290058$	$10.954451150103322$	?	$Q_8:C_2$ (as 8T11)	trivial	$2$	$5$	$3.04219016894$
8.4.23643125.1	$x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 5 x^{4} + 3 x^{3} + x^{2} - 3 x + 1$	$8$	[4,2]	$5^{4}\cdot 11\cdot 19\cdot 181$	$4$	$8.35051210248$	$434.90803625594225$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$3.05802636676$
8.4.24212981.1	$x^{8} - x^{7} - 3 x^{6} + 4 x^{5} + 3 x^{4} - 4 x^{3} - 3 x^{2} + x + 1$	$8$	[4,2]	$13\cdot 17\cdot 331^{2}$	$3$	$8.37540916076$	$270.46441540431897$	✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$3.09605261817$
8.4.25338125.1	$x^{8} - 3 x^{7} + 3 x^{6} - x^{5} - 3 x^{4} + 6 x^{3} - 5 x^{2} + 4 x - 1$	$8$	[4,2]	$5^{4}\cdot 71\cdot 571$	$3$	$8.42309714067$	$450.22772015947663$	✓	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$3.19294999955$
8.4.25388213.1	$x^{8} - 3 x^{7} + 3 x^{6} + 4 x^{5} - 7 x^{4} - 4 x^{3} + 3 x^{2} + 3 x + 1$	$8$	[4,2]	$283^{2}\cdot 317$	$2$	$8.42517667332$	$299.51794603996603$	✓	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$3.20092850525$

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