Number field search results

Results (14 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	Unit group torsion	Unit group rank	Regulator
16.0.934...456.3	$x^{16} + 22 x^{12} - 60 x^{10} + 243 x^{8} - 204 x^{6} + 70 x^{4} - 12 x^{2} + 1$	$16$	[0,8]	$2^{44}\cdot 3^{12}$	$2$	$15.3346345019$	$18.23605645563822$			?	$C_4^2:C_2$ (as 16T30)	trivial	$12$	$7$	$5432.88069635$
16.0.136...000.1	$x^{16} - 2 x^{15} - 8 x^{14} + 10 x^{13} + 63 x^{12} - 98 x^{11} - 86 x^{10} + 48 x^{9} + 757 x^{8} - 1896 x^{7} + 2378 x^{6} - 1668 x^{5} + 404 x^{4} + 296 x^{3} - 184 x^{2} + 16$	$16$	[0,8]	$2^{20}\cdot 3^{12}\cdot 5^{12}$	$3$	$18.1282523841$	$21.558246717785053$			?	$C_4^2:C_2$ (as 16T30)	$[2]$	$6$	$7$	$5165.64894396$
16.4.149...296.3	$x^{16} - 32 x^{12} - 120 x^{10} - 222 x^{8} - 192 x^{6} - 80 x^{4} - 24 x^{2} + 1$	$16$	[4,6]	$2^{48}\cdot 3^{12}$	$2$	$18.2360564556$	$18.23605645563822$			?	$C_4^2:C_2$ (as 16T30)	trivial	$2$	$9$	$10977.0741836$
16.4.217...000.2	$x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 19 x^{12} - 18 x^{11} + 140 x^{10} - 132 x^{9} + 142 x^{8} - 336 x^{7} + 310 x^{6} - 56 x^{5} - 84 x^{4} + 70 x^{3} - 14 x^{2} - 2 x + 1$	$16$	[4,6]	$2^{24}\cdot 3^{12}\cdot 5^{12}$	$3$	$21.5582467178$	$21.558246717785053$			?	$C_4^2:C_2$ (as 16T30)	$[2]$	$2$	$9$	$14037.4430501$
16.0.239...736.1	$x^{16} + 4 x^{12} - 96 x^{10} + 150 x^{8} + 96 x^{6} + 4 x^{4} + 1$	$16$	[0,8]	$2^{52}\cdot 3^{12}$	$2$	$21.6864480866$	$21.686448086636275$			?	$C_4^2:C_2$ (as 16T30)	$[2]$	$4$	$7$	$46193.7886141$
16.4.239...736.1	$x^{16} - 20 x^{12} - 48 x^{10} - 138 x^{8} + 384 x^{6} + 172 x^{4} + 48 x^{2} + 1$	$16$	[4,6]	$2^{52}\cdot 3^{12}$	$2$	$21.6864480866$	$21.686448086636275$			?	$C_4^2:C_2$ (as 16T30)	trivial	$2$	$9$	$53618.6042833$
16.0.239...736.51	$x^{16} - 4 x^{14} - 8 x^{13} + 32 x^{12} - 24 x^{11} + 20 x^{10} - 48 x^{9} - 56 x^{8} + 336 x^{7} - 356 x^{6} - 136 x^{5} + 588 x^{4} - 472 x^{3} + 148 x^{2} - 64 x + 79$	$16$	[0,8]	$2^{52}\cdot 3^{12}$	$2$	$21.686448086636275$	$23.64923933252054$			?	$C_4^2:C_2$ (as 16T30)	trivial	$6$	$7$	$69240.5471694659$
16.4.957...944.16	$x^{16} - 20 x^{12} - 120 x^{10} - 192 x^{8} - 48 x^{6} - 104 x^{4} + 240 x^{2} + 4$	$16$	[4,6]	$2^{54}\cdot 3^{12}$	$2$	$23.64923933252054$	$23.64923933252054$			?	$C_4^2:C_2$ (as 16T30)	trivial	$2$	$9$	$104519.85194942706$
16.16.228...000.2	$x^{16} - 4 x^{15} - 36 x^{14} + 184 x^{13} + 276 x^{12} - 2532 x^{11} + 1576 x^{10} + 10204 x^{9} - 12939 x^{8} - 15196 x^{7} + 25960 x^{6} + 6876 x^{5} - 16638 x^{4} + 32 x^{3} + 1620 x^{2} + 196 x + 1$	$16$	[16,0]	$2^{44}\cdot 3^{12}\cdot 5^{12}$	$3$	$51.2744407675$	$60.97592977855377$			?	$C_4^2:C_2$ (as 16T30)	$[2]$	$2$	$15$	$279059448.286$
16.0.228...000.3	$x^{16} - 4 x^{15} + 4 x^{14} - 16 x^{13} + 156 x^{12} - 652 x^{11} + 1516 x^{10} - 2436 x^{9} + 7441 x^{8} - 30156 x^{7} + 82820 x^{6} - 142404 x^{5} + 136322 x^{4} - 54488 x^{3} + 75320 x^{2} - 199044 x + 167101$	$16$	[0,8]	$2^{44}\cdot 3^{12}\cdot 5^{12}$	$3$	$51.2744407675$	$60.97592977855377$	✓		?	$C_4^2:C_2$ (as 16T30)	$[2, 2, 80]$	$2$	$7$	$55877.3346526$
16.16.221...144.1	$x^{16} - 8 x^{15} - 32 x^{14} + 352 x^{13} + 184 x^{12} - 5432 x^{11} + 2236 x^{10} + 38968 x^{9} - 32168 x^{8} - 135384 x^{7} + 149568 x^{6} + 195744 x^{5} - 285732 x^{4} - 31752 x^{3} + 158652 x^{2} - 67104 x + 8433$	$16$	[16,0]	$2^{48}\cdot 3^{12}\cdot 23^{6}$	$3$	$59.0988277479$	$87.45705441086021$			?	$C_4^2:C_2$ (as 16T30)	trivial	$2$	$15$	$1875974037.6$
16.0.221...144.1	$x^{16} + 24 x^{14} - 24 x^{13} + 388 x^{12} - 552 x^{11} + 4236 x^{10} - 7104 x^{9} + 32370 x^{8} - 73872 x^{7} + 166488 x^{6} - 409752 x^{5} + 576784 x^{4} - 963552 x^{3} + 989808 x^{2} + 1020648 x + 855742$	$16$	[0,8]	$2^{48}\cdot 3^{12}\cdot 23^{6}$	$3$	$59.0988277479$	$87.45705441086021$	✓		?	$C_4^2:C_2$ (as 16T30)	$[2, 4, 4, 8]$	$2$	$7$	$204141.742403$
16.0.221...144.2	$x^{16} - 32 x^{14} - 24 x^{13} + 528 x^{12} + 696 x^{11} - 4340 x^{10} - 8976 x^{9} + 20776 x^{8} + 65760 x^{7} - 11160 x^{6} - 191712 x^{5} + 39996 x^{4} + 850104 x^{3} + 1807452 x^{2} + 1890576 x + 1377009$	$16$	[0,8]	$2^{48}\cdot 3^{12}\cdot 23^{6}$	$3$	$59.0988277479$	$87.45705441086021$	✓		?	$C_4^2:C_2$ (as 16T30)	$[2, 2, 4, 8]$	$2$	$7$	$475824.014517$
16.0.354...304.1	$x^{16} - 8 x^{15} + 48 x^{14} - 88 x^{13} + 240 x^{12} + 1968 x^{11} - 5588 x^{10} + 16184 x^{9} + 11832 x^{8} - 83624 x^{7} + 415672 x^{6} - 951840 x^{5} + 2031636 x^{4} - 2871392 x^{3} + 3696324 x^{2} - 3324304 x + 1977337$	$16$	[0,8]	$2^{52}\cdot 3^{12}\cdot 23^{6}$	$3$	$70.2807464461$	$104.00455136257506$	✓		?	$C_4^2:C_2$ (as 16T30)	$[2, 4, 4, 16]$	$2$	$7$	$431260.406848$

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