Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (10 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
20.0.295...000.1	$x^{20} - 2 x^{19} + 13 x^{18} - 50 x^{17} + 145 x^{16} - 452 x^{15} + 1268 x^{14} - 2956 x^{13} + 6269 x^{12} - 12602 x^{11} + 22489 x^{10} - 32942 x^{9} + 38015 x^{8} - 33892 x^{7} + 23006 x^{6} - 11744 x^{5} + 4561 x^{4} - 1586 x^{3} + 727 x^{2} - 326 x + 67$	$20$	(0, 10)	$2^{46}\cdot 3^{16}\cdot 5^{10}$	$3$	$26.518624632134397$					$C_5^4.C_4^3.C_2^2$ (as 20T837)	trivial	trivial	$6$	$9$	$17131938.164651237$
20.12.106...000.1	$x^{20} - 20 x^{18} - 2 x^{17} + 78 x^{16} + 154 x^{15} + 259 x^{14} - 184 x^{13} - 4383 x^{12} - 6452 x^{11} + 20315 x^{10} + 34510 x^{9} - 40000 x^{8} - 70486 x^{7} + 27069 x^{6} + 55412 x^{5} + 192 x^{4} + 208 x^{3} + 8481 x^{2} - 9576 x - 6904$	$20$	(12, 4)	$2^{40}\cdot 5^{10}\cdot 17^{13}$	$3$	$56.40749224887394$				?	$C_5^2:F_5^2.\OD_{16}$ (as 20T820)	trivial	$[2]$	$2$	$15$	$99281672353.20975$
20.12.339...000.1	$x^{20} - 4 x^{19} - 30 x^{18} + 196 x^{17} + 65 x^{16} - 1944 x^{15} - 1976 x^{14} + 9176 x^{13} + 45474 x^{12} - 12496 x^{11} - 227012 x^{10} - 268368 x^{9} + 203330 x^{8} + 1343752 x^{7} + 530280 x^{6} - 2266888 x^{5} - 557807 x^{4} + 1698132 x^{3} - 71142 x^{2} - 453492 x + 117297$	$20$	(12, 4)	$2^{58}\cdot 3^{16}\cdot 5^{10}\cdot 23^{4}$	$4$	$75.25139592544727$				?	$C_5^2:F_5^2.D_4$ (as 20T742)	trivial	$[2]$	$2$	$15$	$1862239265668.0706$
20.4.455...000.1	$x^{20} - 8 x^{19} + 28 x^{18} + 24 x^{17} - 1186 x^{16} + 8336 x^{15} - 32728 x^{14} + 79056 x^{13} - 82978 x^{12} - 185088 x^{11} + 1000144 x^{10} - 2017920 x^{9} + 1447400 x^{8} + 3143280 x^{7} - 10251080 x^{6} + 10913840 x^{5} + 771225 x^{4} - 13239800 x^{3} + 12568500 x^{2} - 4968600 x + 1002050$	$20$	(4, 8)	$2^{73}\cdot 5^{12}\cdot 7^{11}$	$3$	$96.1491410429941$				?	$C_5^4:(\OD_{16}:D_4)$ (as 20T719)	trivial	$[2]$	$2$	$11$	$4146180099468.085$
20.4.966...625.1	$x^{20} - 2 x^{19} - 3 x^{18} + 105 x^{17} - 360 x^{16} - 138 x^{15} + 3725 x^{14} - 11515 x^{13} + 13818 x^{12} + 8359 x^{11} - 64571 x^{10} + 114258 x^{9} - 108933 x^{8} + 51038 x^{7} + 40714 x^{6} - 189947 x^{5} + 319619 x^{4} - 299574 x^{3} + 183081 x^{2} - 92242 x + 25492$	$20$	(4, 8)	$5^{10}\cdot 31^{4}\cdot 41^{18}$	$3$	$125.67902764281172$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$18974861689545.34$
20.4.390...625.1	$x^{20} - 36 x^{18} - 253 x^{17} - 1137 x^{16} + 4856 x^{15} + 64319 x^{14} + 204393 x^{13} - 207178 x^{12} - 3522058 x^{11} - 9662372 x^{10} - 8469856 x^{9} + 9738652 x^{8} + 5703059 x^{7} + 18025370 x^{6} + 348679071 x^{5} - 558765822 x^{4} - 9034252597 x^{3} - 33109646405 x^{2} - 56256805302 x - 25939547828$	$20$	(4, 8)	$5^{10}\cdot 41^{18}\cdot 139^{4}$	$3$	$169.66545779506598$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$336685945963379.5$
20.4.892...625.1	$x^{20} - 4 x^{19} - 48 x^{18} - 163 x^{17} + 170 x^{16} + 1270 x^{15} - 75609 x^{14} - 1136164 x^{13} - 8452535 x^{12} - 45319270 x^{11} - 169650989 x^{10} - 390441788 x^{9} - 8231764 x^{8} + 4770093808 x^{7} + 25062892560 x^{6} + 78578701312 x^{5} + 171567828224 x^{4} + 268666136960 x^{3} + 288134625792 x^{2} + 186034923520 x + 50500934656$	$20$	(4, 8)	$5^{10}\cdot 31^{8}\cdot 41^{18}$	$3$	$249.76705364116071$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$22653658134436830$
20.4.892...625.2	$x^{20} - 4 x^{19} - 48 x^{18} - 40 x^{17} + 1359 x^{16} + 12053 x^{15} - 50927 x^{14} - 208621 x^{13} - 206820 x^{12} + 6881520 x^{11} + 6939947 x^{10} - 67336532 x^{9} - 279723924 x^{8} + 706570360 x^{7} + 4438227632 x^{6} - 9443462656 x^{5} - 18706952896 x^{4} + 43163586432 x^{3} + 38609260800 x^{2} - 126841600000 x + 70336233472$	$20$	(4, 8)	$5^{10}\cdot 31^{8}\cdot 41^{18}$	$3$	$249.76705364116071$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$20595696945593150$
20.4.145...625.1	$x^{20} - 4 x^{19} - 172 x^{18} + 1313 x^{17} + 891 x^{16} - 47918 x^{15} + 143660 x^{14} + 825186 x^{13} - 6961932 x^{12} + 3476418 x^{11} + 137509917 x^{10} - 305777766 x^{9} - 1460468485 x^{8} + 4681240481 x^{7} + 6316446658 x^{6} - 25513585137 x^{5} - 17423433044 x^{4} + 72541270441 x^{3} + 7874661257 x^{2} - 39689075310 x - 32202555239$	$20$	(4, 8)	$5^{10}\cdot 41^{18}\cdot 139^{8}$	$3$	$455.1938578872197$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$8528206623169880000$
20.4.145...625.2	$x^{20} - 6 x^{19} - 112 x^{18} + 1696 x^{17} + 21532 x^{16} - 267473 x^{15} - 950162 x^{14} + 25868382 x^{13} - 42842892 x^{12} - 1208882449 x^{11} + 6310121120 x^{10} + 31481258951 x^{9} - 266107611596 x^{8} + 63404974091 x^{7} + 4767142146962 x^{6} - 5598377726243 x^{5} - 65206016809695 x^{4} + 67358139202889 x^{3} + 720499096134239 x^{2} - 1918736438852372 x + 1349574335680469$	$20$	(4, 8)	$5^{10}\cdot 41^{18}\cdot 139^{8}$	$3$	$455.1938578872197$					$C_5^4:C_8.C_8$ (as 20T597)	trivial	trivial	$2$	$11$	$9358194902209102000$

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