Number field search results

Results (1-50 of 238 matches)

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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
8.4.1627389952.1	$x^{8} - 4 x^{6} - 8 x^{5} + 12 x^{4} + 16 x^{3} - 8 x^{2} - 8 x - 2$	$8$	[4,2]	$2^{24}\cdot 97$	$2$	$14.172173282$	$89.72613864016142$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$63.3494974377$
8.6.6157238272.2	$x^{8} - 8 x^{6} + 18 x^{4} - 16 x^{2} - 8 x - 1$	$8$	[6,1]	$-\,2^{24}\cdot 367$	$2$	$16.7368315455$	$174.52841447639096$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$6$	$191.844957904$
8.2.6157238272.3	$x^{8} + 4 x^{6} - 8 x^{5} + 8 x^{4} - 16 x^{3} + 16 x^{2} - 8 x + 2$	$8$	[2,3]	$-\,2^{24}\cdot 367$	$2$	$16.7368315455$	$174.52841447639096$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$106.251396843$
8.2.6157238272.4	$x^{8} - 4 x^{6} - 16 x^{5} - 16 x^{4} - 8 x^{3} + 8 x^{2} + 8 x + 2$	$8$	[2,3]	$-\,2^{24}\cdot 367$	$2$	$16.7368315455$	$174.52841447639096$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$94.839663567$
8.2.6157238272.5	$x^{8} - 4 x^{6} - 8 x^{5} - 16 x^{4} - 24 x^{3} - 8 x^{2} - 8 x - 14$	$8$	[2,3]	$-\,2^{24}\cdot 367$	$2$	$16.7368315455$	$174.52841447639096$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$102.156321215$
8.4.6190792704.1	$x^{8} - 4 x^{6} + 4 x^{4} - 8 x^{2} - 8 x - 2$	$8$	[4,2]	$2^{24}\cdot 3^{2}\cdot 41$	$3$	$16.7482055667$	$101.03821541482583$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$160.469525081$
8.4.8338276352.1	$x^{8} - 8 x^{6} - 8 x^{5} + 18 x^{4} + 32 x^{3} - 16 x - 1$	$8$	[4,2]	$2^{24}\cdot 7\cdot 71$	$3$	$17.3833924744$	$203.1006463661288$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$165.901527719$
8.4.8338276352.2	$x^{8} - 8 x^{5} - 2 x^{4} + 8 x^{2} - 1$	$8$	[4,2]	$2^{24}\cdot 7\cdot 71$	$3$	$17.3833924744$	$203.1006463661288$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$170.965042939$
8.4.8338276352.5	$x^{8} + 4 x^{6} - 16 x^{2} - 8 x + 2$	$8$	[4,2]	$2^{24}\cdot 7\cdot 71$	$3$	$17.3833924744$	$203.1006463661288$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$177.050836339$
8.4.12901679104.1	$x^{8} + 4 x^{6} - 16 x^{5} + 12 x^{4} - 8 x^{3} + 8 x - 2$	$8$	[4,2]	$2^{24}\cdot 769$	$2$	$18.3582288536$	$252.6366076436748$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$162.054891788$
8.4.12901679104.2	$x^{8} - 8 x^{6} + 14 x^{4} - 8 x - 1$	$8$	[4,2]	$2^{24}\cdot 769$	$2$	$18.3582288536$	$252.6366076436748$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$223.234961115$
8.4.12901679104.3	$x^{8} - 4 x^{6} + 6 x^{4} - 16 x^{3} - 36 x^{2} + 16 x + 41$	$8$	[4,2]	$2^{24}\cdot 769$	$2$	$18.3582288536$	$252.6366076436748$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$176.619402632$
8.2.13404995584.1	$x^{8} - 4 x^{6} - 16 x^{5} - 20 x^{4} - 24 x^{3} - 16 x^{2} - 8 x - 2$	$8$	[2,3]	$-\,2^{24}\cdot 17\cdot 47$	$3$	$18.4462603687$	$257.5173537193834$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$160.558729138$
8.2.13404995584.2	$x^{8} + 2 x^{4} - 8 x^{2} - 8 x - 1$	$8$	[2,3]	$-\,2^{24}\cdot 17\cdot 47$	$3$	$18.4462603687$	$257.5173537193834$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$132.163567291$
8.6.13404995584.2	$x^{8} - 4 x^{6} - 8 x^{5} - 16 x^{4} + 16 x^{3} + 48 x^{2} + 24 x + 2$	$8$	[6,1]	$-\,2^{24}\cdot 17\cdot 47$	$3$	$18.4462603687$	$257.5173537193834$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$6$	$304.767203518$
8.2.13404995584.7	$x^{8} - 16 x^{5} - 8 x^{4} - 16 x^{3} + 48 x^{2} + 32 x + 56$	$8$	[2,3]	$-\,2^{24}\cdot 17\cdot 47$	$3$	$18.4462603687$	$257.5173537193834$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$155.311160793$
8.4.13975420928.1	$x^{8} + 4 x^{6} - 8 x^{5} + 12 x^{4} + 24 x^{3} - 8 x - 2$	$8$	[4,2]	$2^{24}\cdot 7^{2}\cdot 17$	$3$	$18.5425992457$	$137.4536463433003$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$226.919029285$
8.6.15284043776.2	$x^{8} - 8 x^{6} - 8 x^{5} + 30 x^{4} + 8 x^{3} - 16 x^{2} - 8 x - 1$	$8$	[6,1]	$-\,2^{24}\cdot 911$	$2$	$18.7512310046$	$274.9744231639962$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$6$	$349.696449051$
8.2.15284043776.2	$x^{8} - 4 x^{6} + 4 x^{4} - 8 x^{2} - 24 x - 18$	$8$	[2,3]	$-\,2^{24}\cdot 911$	$2$	$18.7512310046$	$274.9744231639962$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$125.764165088$
8.2.15284043776.5	$x^{8} - 10 x^{4} - 8 x^{3} - 8 x^{2} - 16 x + 7$	$8$	[2,3]	$-\,2^{24}\cdot 911$	$2$	$18.7512310046$	$274.9744231639962$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$179.657413883$
8.2.15284043776.6	$x^{8} - 8 x^{6} - 8 x^{5} - 6 x^{4} + 16 x^{2} - 16 x + 7$	$8$	[2,3]	$-\,2^{24}\cdot 911$	$2$	$18.7512310046$	$274.9744231639962$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$187.700450681$
8.2.17431527424.2	$x^{8} - 8 x^{5} + 2 x^{4} + 8 x^{2} - 16 x - 1$	$8$	[2,3]	$-\,2^{24}\cdot 1039$	$2$	$19.061932636$	$293.6573564991579$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$229.692332043$
8.2.17431527424.3	$x^{8} - 8 x^{5} + 18 x^{4} - 24 x^{3} + 24 x^{2} - 8 x - 1$	$8$	[2,3]	$-\,2^{24}\cdot 1039$	$2$	$19.061932636$	$293.6573564991579$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$186.65049879$
8.0.40282095616.11	$x^{8} + 4 x^{6} - 8 x^{5} + 18 x^{4} + 32 x^{3} + 44 x^{2} + 24 x + 9$	$8$	[0,4]	$2^{24}\cdot 7^{4}$	$2$	$21.1660104885$	$33.33740602939541$			?	$C_2^4:C_6$ (as 8T33)	trivial	trivial	$2$	$3$	$229.466079075$
8.4.82426462208.3	$x^{8} - 12 x^{6} - 16 x^{5} + 44 x^{4} + 120 x^{3} - 216 x - 162$	$8$	[4,2]	$2^{24}\cdot 17^{3}$	$2$	$23.1477259754$	$96.58445028064001$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$5$	$597.544801075$
8.6.85614133248.2	$x^{8} - 8 x^{6} - 8 x^{5} - 6 x^{4} - 8 x^{3} + 16 x^{2} + 24 x + 7$	$8$	[6,1]	$-\,2^{24}\cdot 3^{6}\cdot 7$	$3$	$23.2577759787$	$110.85378863264648$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$6$	$994.127657325$
8.2.85614133248.5	$x^{8} - 8 x^{6} + 30 x^{4} - 24 x^{3} - 32 x^{2} + 48 x - 17$	$8$	[2,3]	$-\,2^{24}\cdot 3^{6}\cdot 7$	$3$	$23.2577759787$	$110.85378863264648$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$439.586545086$
8.2.85614133248.6	$x^{8} - 16 x^{5} - 6 x^{4} - 8 x^{2} - 24 x - 9$	$8$	[2,3]	$-\,2^{24}\cdot 3^{6}\cdot 7$	$3$	$23.2577759787$	$110.85378863264648$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$450.022818112$
8.2.85614133248.7	$x^{8} - 8 x^{5} + 6 x^{4} + 8 x^{2} - 9$	$8$	[2,3]	$-\,2^{24}\cdot 3^{6}\cdot 7$	$3$	$23.2577759787$	$110.85378863264648$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$470.72753089$
8.0.104706605056.4	$x^{8} - 8 x^{6} + 42 x^{4} - 8 x^{3} - 32 x^{2} + 16 x + 23$	$8$	[0,4]	$2^{24}\cdot 79^{2}$	$2$	$23.8504600104$	$167.73273893688736$			?	$A_4\wr C_2$ (as 8T42)	trivial	trivial	$2$	$3$	$225.490108118$
8.0.104706605056.9	$x^{8} + 4 x^{6} - 16 x^{5} + 24 x^{4} - 32 x^{3} + 32 x^{2} + 8 x + 2$	$8$	[0,4]	$2^{24}\cdot 79^{2}$	$2$	$23.8504600104$	$167.73273893688736$			?	$A_4\wr C_2$ (as 8T42)	trivial	trivial	$2$	$3$	$245.017160666$
8.0.110075314176.4	$x^{8} - 8 x^{6} - 8 x^{5} + 42 x^{4} - 8 x^{3} - 16 x^{2} - 24 x + 23$	$8$	[0,4]	$2^{24}\cdot 3^{8}$	$2$	$24.0$	$39.41801805957117$			?	$C_2^4:C_6$ (as 8T33)	trivial	trivial	$2$	$3$	$264.866283422$
8.8.177989484544.1	$x^{8} - 16 x^{6} - 16 x^{5} + 30 x^{4} + 32 x^{3} - 8 x^{2} - 8 x - 1$	$8$	[8,0]	$2^{24}\cdot 103^{2}$	$2$	$25.4858600044$	$200.18180197449726$			?	$A_4\wr C_2$ (as 8T42)	trivial	$[2, 2]$	$2$	$7$	$1668.85351287$
8.0.177989484544.3	$x^{8} - 8 x^{6} + 46 x^{4} - 24 x^{3} - 32 x^{2} + 48 x + 31$	$8$	[0,4]	$2^{24}\cdot 103^{2}$	$2$	$25.4858600044$	$200.18180197449726$			?	$A_4\wr C_2$ (as 8T42)	$[2]$	$[2]$	$2$	$3$	$156.741043086$
8.0.177989484544.5	$x^{8} + 4 x^{6} - 16 x^{5} + 16 x^{4} - 8 x^{3} + 24 x^{2} + 8 x + 2$	$8$	[0,4]	$2^{24}\cdot 103^{2}$	$2$	$25.4858600044$	$200.18180197449726$				$A_4\wr C_2$ (as 8T42)	$[2]$	$[2]$	$2$	$3$	$222.257954149$
8.0.177989484544.7	$x^{8} - 24 x^{5} - 12 x^{4} - 16 x^{3} + 160 x^{2} + 176 x + 316$	$8$	[0,4]	$2^{24}\cdot 103^{2}$	$2$	$25.4858600044$	$200.18180197449726$			?	$A_4\wr C_2$ (as 8T42)	$[2]$	$[2]$	$2$	$3$	$192.299378072$
8.4.237582155776.1	$x^{8} - 8 x^{5} - 34 x^{4} + 32 x^{3} + 88 x^{2} - 32 x - 49$	$8$	[4,2]	$2^{24}\cdot 7^{2}\cdot 17^{2}$	$3$	$26.4226716162$	$159.36076728258584$			?	$(A_4\wr C_2):C_2$ (as 8T45)	trivial	trivial	$2$	$5$	$1492.31714238$
8.4.237582155776.2	$x^{8} - 4 x^{6} - 16 x^{5} - 28 x^{4} - 40 x^{3} - 48 x^{2} - 24 x - 2$	$8$	[4,2]	$2^{24}\cdot 7^{2}\cdot 17^{2}$	$3$	$26.4226716162$	$159.36076728258584$			?	$(A_4\wr C_2):C_2$ (as 8T45)	trivial	trivial	$2$	$5$	$1010.66880362$
8.4.237582155776.5	$x^{8} - 8 x^{6} + 6 x^{4} - 56 x^{3} - 32 x^{2} + 112 x + 71$	$8$	[4,2]	$2^{24}\cdot 7^{2}\cdot 17^{2}$	$3$	$26.4226716162$	$159.36076728258584$			?	$(A_4\wr C_2):C_2$ (as 8T45)	trivial	trivial	$2$	$5$	$993.190022772$
8.4.305764761600.17	$x^{8} - 8 x^{6} - 16 x^{5} - 6 x^{4} + 8 x^{3} + 64 x^{2} + 48 x + 7$	$8$	[4,2]	$2^{24}\cdot 3^{6}\cdot 5^{2}$	$3$	$27.2692647952$	$93.68855111565685$			?	$(A_4\wr C_2):C_2$ (as 8T45)	trivial	trivial	$2$	$5$	$1521.45299669$
8.0.479174066176.13	$x^{8} - 8 x^{6} - 24 x^{5} + 6 x^{4} + 88 x^{3} + 192 x^{2} + 152 x + 119$	$8$	[0,4]	$2^{24}\cdot 13^{4}$	$2$	$28.8444102037$	$50.36884737557236$			?	$C_2^4:C_6$ (as 8T33)	trivial	trivial	$2$	$3$	$649.109843532$
8.4.501454209024.4	$x^{8} + 6 x^{4} - 72 x^{2} - 72 x - 9$	$8$	[4,2]	$2^{24}\cdot 3^{6}\cdot 41$	$3$	$29.0087429771$	$132.97376962254822$			?	$S_4\wr C_2$ (as 8T47)	trivial	$[2]$	$2$	$5$	$1671.20244242$
8.0.513802240000.19	$x^{8} + 4 x^{6} + 20 x^{4} + 24 x^{2} - 40 x + 14$	$8$	[0,4]	$2^{24}\cdot 5^{4}\cdot 7^{2}$	$3$	$29.0970861005$	$97.47916657595673$			?	$A_4\wr C_2$ (as 8T42)	trivial	trivial	$2$	$3$	$604.449310431$
8.0.513802240000.23	$x^{8} - 8 x^{6} + 54 x^{4} - 40 x^{3} - 32 x^{2} + 80 x + 71$	$8$	[0,4]	$2^{24}\cdot 5^{4}\cdot 7^{2}$	$3$	$29.0970861005$	$97.47916657595673$			?	$A_4\wr C_2$ (as 8T42)	trivial	trivial	$2$	$3$	$905.32451038$
8.4.1305955270656.1	$x^{8} - 20 x^{6} - 8 x^{5} + 164 x^{4} + 200 x^{3} - 384 x^{2} - 856 x - 434$	$8$	[4,2]	$2^{24}\cdot 3^{4}\cdot 31^{2}$	$3$	$32.6957299607$	$87.85663907345199$			?	$V_4^2:(S_3\times C_2)$ (as 8T41)	trivial	$[2]$	$2$	$5$	$2660.61605936$
8.4.1305955270656.3	$x^{8} - 16 x^{6} - 24 x^{5} + 38 x^{4} + 96 x^{3} + 136 x^{2} + 96 x - 89$	$8$	[4,2]	$2^{24}\cdot 3^{4}\cdot 31^{2}$	$3$	$32.6957299607$	$87.85663907345199$			?	$V_4^2:(S_3\times C_2)$ (as 8T41)	trivial	$[2]$	$2$	$5$	$2271.66461368$
8.4.1305955270656.6	$x^{8} - 32 x^{5} + 40 x^{4} - 48 x^{3} + 16 x^{2} + 32 x - 8$	$8$	[4,2]	$2^{24}\cdot 3^{4}\cdot 31^{2}$	$3$	$32.6957299607$	$87.85663907345199$			?	$V_4^2:(S_3\times C_2)$ (as 8T41)	trivial	$[2]$	$2$	$5$	$2286.32254726$
8.4.2066969788416.2	$x^{8} + 4 x^{6} - 40 x^{5} - 48 x^{4} + 200 x^{3} + 152 x^{2} - 216 x - 142$	$8$	[4,2]	$2^{24}\cdot 3^{6}\cdot 13^{2}$	$3$	$34.6271514233$	$151.06824943181383$			?	$(A_4\wr C_2):C_2$ (as 8T45)	trivial	trivial	$2$	$5$	$3724.5762581$
8.0.2186423566336.14	$x^{8} + 4 x^{6} - 24 x^{5} + 10 x^{4} - 64 x^{3} + 156 x^{2} - 24 x + 193$	$8$	[0,4]	$2^{24}\cdot 19^{4}$	$2$	$34.8711915483$	$64.86874738888089$			?	$C_2^4:C_6$ (as 8T33)	trivial	trivial	$2$	$3$	$1613.28243214$
8.4.2461033037824.5	$x^{8} - 8 x^{6} - 16 x^{5} - 22 x^{4} + 8 x^{3} + 48 x^{2} + 64 x + 55$	$8$	[4,2]	$2^{24}\cdot 383^{2}$	$2$	$35.3907430073$	$178.29226333076136$			?	$C_2^3:\GL(3,2)$ (as 8T48)	$[2]$	$[4]$	$2$	$5$	$3220.64826673$

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