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	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
20.0.133...125.4	$x^{20} - 99 x^{15} - 238249 x^{10} - 15944049 x^{5} + 25937424601$	$20$	(0, 10)	$5^{35}\cdot 11^{16}$	$2$	$113.844395586$	$113.8443955857766$	✓	✓	?	$C_{20}$ (as 20T1)	$[5, 2305]$	$[5, 2305]$	$10$	$9$	$864758391.9354854$	$0$	$11$
20.20.161...125.4	$x^{20} - 110 x^{18} + 4730 x^{16} - 594 x^{15} - 102850 x^{14} + 38830 x^{13} + 1213025 x^{12} - 900240 x^{11} - 7561554 x^{10} + 9114325 x^{9} + 20793245 x^{8} - 38665550 x^{7} - 7173485 x^{6} + 49271926 x^{5} - 24091100 x^{4} - 13196865 x^{3} + 15838900 x^{2} - 5164280 x + 560351$	$20$	(20, 0)	$5^{35}\cdot 11^{18}$	$2$	$144.694133784$	$144.69413378423255$		✓	?	$C_{20}$ (as 20T1)	$[5]$	$[2, 10]$	$2$	$19$	$236881395276923.9$	$18$	$11$
20.20.140...000.1	$x^{20} - 220 x^{18} + 20570 x^{16} - 1064800 x^{14} + 33308275 x^{12} - 644361905 x^{10} + 7546503800 x^{8} - 49386655175 x^{6} + 144482878375 x^{4} - 57797177625 x^{2} + 717482205$	$20$	(20, 0)	$2^{20}\cdot 5^{35}\cdot 11^{16}$	$3$	$227.688791172$	$227.6887911715532$		✓	?	$C_{20}$ (as 20T1)	$[5]$	$[10]$	$2$	$19$	$30525554138997190$	$19$	$11$
20.0.169...000.3	$x^{20} + 220 x^{18} + 20570 x^{16} + 1064800 x^{14} + 33308275 x^{12} + 644515355 x^{10} + 7563383300 x^{8} + 50036515925 x^{6} + 154694975875 x^{4} + 113963713875 x^{2} + 22064060205$	$20$	(0, 10)	$2^{20}\cdot 5^{35}\cdot 11^{18}$	$3$	$289.388267568$	$289.3882675684651$	✓	✓	?	$C_{20}$ (as 20T1)	$[2, 2, 4838410]$	$[4838410, 2, 2]$	$2$	$9$	$864758391.9354854$	$0$	$11$
20.0.185...125.2	$x^{20} - 17999 x^{15} + 160654851 x^{10} - 2085295761799 x^{5} + 13422659310152401$	$20$	(0, 10)	$5^{35}\cdot 41^{16}$	$2$	$326.155414748$	$326.15541474844105$	✓	✓	?	$C_{20}$ (as 20T1)	not computed	not computed	$10$	$9$			$41$
20.0.311...125.3	$x^{20} + 6150 x^{16} - 17999 x^{15} + 1013725 x^{13} + 5673375 x^{12} - 86991750 x^{11} + 156586626 x^{10} + 2061956625 x^{9} - 10451281300 x^{8} - 48365311750 x^{7} + 786214122200 x^{6} + 743005229201 x^{5} + 2568056765875 x^{4} + 86646635194725 x^{3} + 416474629912750 x^{2} + 480605665211400 x + 1491532134197851$	$20$	(0, 10)	$5^{35}\cdot 41^{18}$	$2$	$472.827773419$	$472.82777341945393$	✓	✓	?	$C_{20}$ (as 20T1)	not computed	not computed	$2$	$9$			$41$
20.20.194...000.1	$x^{20} - 820 x^{18} + 285770 x^{16} - 55136800 x^{14} + 6428606275 x^{12} - 463885574505 x^{10} + 20376858931300 x^{8} - 513995117364175 x^{6} + 6578416466955875 x^{4} - 32550683074482625 x^{2} + 3819107560285205$	$20$	(20, 0)	$2^{20}\cdot 5^{35}\cdot 41^{16}$	$3$	$652.310829497$	$652.3108294968821$		✓	?	$C_{20}$ (as 20T1)	$[5]$	$[10]$	$2$	$19$	$831339581441176400000$	$19$	$41$
20.20.327...000.4	$x^{20} - 820 x^{18} + 285770 x^{16} - 55136800 x^{14} + 6428606275 x^{12} - 464313380805 x^{10} + 20552259514300 x^{8} - 539165101024675 x^{6} + 8052658367070875 x^{4} - 62772642026840125 x^{2} + 197033028036814205$	$20$	(20, 0)	$2^{20}\cdot 5^{35}\cdot 41^{18}$	$3$	$945.655546839$	$945.6555468389079$		✓	?	$C_{20}$ (as 20T1)	$[2, 10]$	$[20, 2, 2]$	$2$	$19$	$7676273450964827000000$	$18$	$41$
40.0.261...625.1	$x^{40} - 594 x^{35} + 240768 x^{30} - 39766650 x^{25} + 3580650876 x^{20} - 135500258850 x^{15} + 2678488623657 x^{10} - 454012109958 x^{5} + 25937424601$	$40$	(0, 20)	$5^{70}\cdot 11^{36}$	$2$	$144.694133784$	$144.69413378423255$	✓	✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$10$	$19$			$11$
40.0.196...000.4	$x^{40} + 486299 x^{30} + 105480513501 x^{20} + 12613343646041699 x^{10} + 672749994932560009201$	$40$	(0, 20)	$2^{40}\cdot 5^{70}\cdot 11^{32}$	$3$	$227.688791172$	$227.6887911715532$	✓	✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$20$	$19$			$11$
40.0.287...000.1	$x^{40} + 990 x^{36} + 341825 x^{32} - 128700 x^{30} + 45465750 x^{28} - 95559750 x^{26} - 187005500 x^{24} - 13476375000 x^{22} - 826202149740 x^{20} + 2063996673750 x^{18} - 40426833250925 x^{16} + 260603669081250 x^{14} + 3310939947063375 x^{12} + 8689693619326500 x^{10} + 363555244286551625 x^{8} - 62474494850460000 x^{6} + 9400451839944969375 x^{4} + 765165773393381250 x^{2} + 677576408158587025$	$40$	(0, 20)	$2^{40}\cdot 5^{70}\cdot 11^{36}$	$3$	$289.388267568$	$289.3882675684651$	✓	✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$2$	$19$			$11$
40.40.287...000.4	$x^{40} - 220 x^{38} + 21560 x^{36} - 1246300 x^{34} + 47425950 x^{32} - 1255559844 x^{30} + 23833782610 x^{28} - 329628239930 x^{26} + 3343947000625 x^{24} - 24884845843000 x^{22} + 135171033088256 x^{20} - 531205522579985 x^{18} + 1493017799608005 x^{16} - 2961680992680850 x^{14} + 4083648899360525 x^{12} - 3836151555520284 x^{10} + 2382576056031270 x^{8} - 930560639556185 x^{6} + 207689662459400 x^{4} - 21065809007100 x^{2} + 313993243201$	$40$	(40, 0)	$2^{40}\cdot 5^{70}\cdot 11^{36}$	$3$	$289.388267568$	$289.3882675684651$		✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$2$	$39$			$11$
40.0.287...000.5	$x^{40} - 332849 x^{30} + 77400539601 x^{20} - 8633245841018249 x^{10} + 672749994932560009201$	$40$	(0, 20)	$2^{40}\cdot 5^{70}\cdot 11^{36}$	$3$	$289.388267568$	$289.3882675684651$	✓	✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$10$	$19$			$11$
40.0.287...000.12	$x^{40} + 220 x^{38} + 21560 x^{36} + 1246300 x^{34} + 47425950 x^{32} + 1255302444 x^{30} + 23804597410 x^{28} + 328217658230 x^{26} + 3305815847125 x^{24} + 24248593237000 x^{22} + 128338213085456 x^{20} + 483286076421335 x^{18} + 1273698080760105 x^{16} + 2312222140127350 x^{14} + 2852935729075025 x^{12} + 2358268629391884 x^{10} + 1277554365650970 x^{8} + 436441588388135 x^{6} + 87567197293400 x^{4} + 8919101010600 x^{2} + 313993243201$	$40$	(0, 20)	$2^{40}\cdot 5^{70}\cdot 11^{36}$	$3$	$289.388267568$	$289.3882675684651$	✓	✓	?	$C_2\times C_{20}$ (as 40T2)	not computed	not computed	$4$	$19$			$11$

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