Number field search results

Results (31 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
43.1.171...443.1	x^43 - x - 1	$43$	[1,21]	$-\,109\cdot 809\cdot 397519523\cdot 49\!\cdots\!61$	$4$	$42.9913070099$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.174...571.1	x^43 + x - 1	$43$	[1,21]	$-\,59\cdot 397\cdot 877\cdot 935899\cdot 2402649604770175349\cdot 37\!\cdots\!51$	$6$	$43.0086198004$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.736...104.1	x^43 - 4x - 4	$43$	[1,21]	$-\,2^{42}\cdot 13\cdot 10239413\cdot 21464295562499\cdot 7440631653201968227\cdot 787580389820760746433715250923$	$6$	$84.5554977562$			not computed	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.749...416.1	x^43 - 2x - 2	$43$	[1,21]	$-\,2^{42}\cdot 5577217\cdot 417006008813\cdot 34910848872522797\cdot 201068225194855523\cdot 1043987668577822729$	$6$	$84.5904566931$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.762...664.1	x^43 - x - 2	$43$	[1,21]	$-\,2^{43}\cdot 20380951\cdot 61480213\cdot 69\!\cdots\!91$	$4$	$84.6248191691$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.762...487.1	x^43 - x - 4	$43$	[1,21]	$-\,229\cdot 293\cdot 4986887\cdot 566527637659\cdot 4239521573605607851\cdot 94\!\cdots\!37$	$6$	$84.6248191691$			not computed	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.762...728.1	x^43 - 2	$43$	[1,21]	$-\,2^{42}\cdot 43^{43}$	$2$	$84.6248191691$			✓	$F_{43}$ (as 43T8)	not computed	$2$	$21$	$$
43.1.775...040.1	x^43 + 2x - 2	$43$	[1,21]	$-\,2^{42}\cdot 5\cdot 19\cdot 4987\cdot 11154877\cdot 914818621983827673311\cdot 36\!\cdots\!97$	$7$	$84.6586054265$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.789...352.1	x^43 + 4x - 4	$43$	[1,21]	$-\,2^{42}\cdot 90073\cdot 2923961\cdot 68\!\cdots\!71$	$4$	$84.691834691$			not computed	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.3.492...621.1	x^43 - 3x - 1	$43$	[3,20]	$193\cdot 25\!\cdots\!97$	$2$	$115.510260058$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$22$	$$
43.1.492...856.1	x^43 + 3x - 2	$43$	[1,21]	$-\,2^{43}\cdot 83\cdot 67\!\cdots\!29$	$3$	$115.510264216$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.189...651.1	x^43 - 2x - 3	$43$	[1,21]	$-\,3^{42}\cdot 139\cdot 12\!\cdots\!01$	$3$	$125.745909717$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.189...899.1	x^43 - x - 3	$43$	[1,21]	$-\,3^{43}\cdot 3929\cdot 27164077\cdot 1696291894163\cdot 4471934430678427\cdot 71\!\cdots\!89$	$6$	$125.74590972$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.189...963.1	x^43 - 3	$43$	[1,21]	$-\,3^{42}\cdot 43^{43}$	$2$	$125.74590972$			✓	$F_{43}$ (as 43T8)	not computed	$2$	$21$	$$
43.1.194...091.1	x^43 + 3x - 3	$43$	[1,21]	$-\,3^{42}\cdot 11\cdot 4458821\cdot 2188196233\cdot 250952988948637\cdot 66\!\cdots\!49$	$6$	$125.820903255$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.335...704.1	x^43 - 2x - 4	$43$	[1,21]	$-\,2^{82}\cdot 17\cdot 911\cdot 1321\cdot 196825567\cdot 17\!\cdots\!89$	$6$	$149.628879545$			not computed	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.43.995...529.1	x^43 - x^42 - 84x^41 + 79x^40 + 3160x^39 - 2786x^38 - 70521x^37 + 58076x^36 + 1042773x^35 - 798942x^34 - 10810701x^33 + 7671648x^32 + 81126975x^31 - 53056499x^30 - 448758019x^29 + 268953093x^28 + 1846875875x^27 - 1007873658x^26 - 5671315301x^25 + 2797394685x^24 + 12962901258x^23 - 5730420663x^22 - 21895326590x^21 + 8590544711x^20 + 27001558938x^19 - 9297003415x^18 - 23896748020x^17 + 7121607714x^16 + 14834334408x^15 - 3755010451x^14 - 6269987218x^13 + 1310830451x^12 + 1732796449x^11 - 287529242x^10 - 294221159x^9 + 37041429x^8 + 27505221x^7 - 2599666x^6 - 1134285x^5 + 90620x^4 + 12893x^3 - 370x^2 - 54x - 1	$43$	[43,0]	$173^{42}$	$1$	$153.461175075$		✓		$C_{43}$ (as 43T1)	trivial	$2$	$42$	$2657880348049265700000000000000000$
43.1.116...403.1	x^43 + 4x - 1	$43$	[1,21]	$-\,181\cdot 155556871099633\cdot 21154104412279303\cdot 19\!\cdots\!37$	$4$	$154.013680078$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.116...624.1	x^43 + 4x - 2	$43$	[1,21]	$-\,2^{42}\cdot 13\cdot 53\cdot 359\cdot 379\cdot 397\cdot 15583\cdot 15667\cdot 16763\cdot 1652591\cdot 7443949\cdot 81974567114861\cdot 17\!\cdots\!91$	$13$	$154.013680078$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.116...859.1	x^43 + 4x - 3	$43$	[1,21]	$-\,3^{42}\cdot 17\cdot 251\cdot 24\!\cdots\!53$	$4$	$154.014265194$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.335...584.1	x^43 - 3x - 4	$43$	[1,21]	$-\,2^{42}\cdot 5736251\cdot 13\!\cdots\!71$	$3$	$166.543255696$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.426...432.1	x^43 + 5x - 2	$43$	[1,21]	$-\,2^{43}\cdot 48\!\cdots\!29$	$2$	$186.409446144$			not computed	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.3.170...493.1	x^43 - 5x - 1	$43$	[3,20]	$67\cdot 25\!\cdots\!79$	$2$	$192.517100097$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$22$	$$
43.1.377...875.1	x^43 - 5x - 5	$43$	[1,21]	$-\,5^{42}\cdot 1201\cdot 3109\cdot 627374521\cdot 70\!\cdots\!83$	$5$	$206.888556661$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.394...811.1	x^43 - x - 5	$43$	[1,21]	$-\,4378013\cdot 253946916604529\cdot 37511360891773121\cdot 94\!\cdots\!83$	$4$	$207.101547263$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.394...875.1	x^43 - 5	$43$	[1,21]	$-\,5^{42}\cdot 43^{43}$	$2$	$207.101547263$			✓	$F_{43}$ (as 43T8)	not computed	$2$	$21$	$$
43.1.394...003.1	x^43 + 3x - 5	$43$	[1,21]	$-\,4787\cdot 56783432887\cdot 65016935311\cdot 22\!\cdots\!17$	$4$	$207.101547263$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.1.411...875.1	x^43 + 5x - 5	$43$	[1,21]	$-\,5^{42}\cdot 68281\cdot 26\!\cdots\!67$	$3$	$207.305717468$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$	$$
43.43.444...961.1	x^43 - x^42 - 210x^41 + 177x^40 + 19424x^39 - 12392x^38 - 1053196x^37 + 410572x^36 + 37567316x^35 - 4029555x^34 - 936601673x^33 - 185951871x^32 + 16894280750x^31 + 8734312688x^30 - 224649876009x^29 - 189102381409x^28 + 2218265633870x^27 + 2604819705111x^26 - 16218499586789x^25 - 24791417254787x^24 + 86521587673786x^23 + 168116844068603x^22 - 325504806681996x^21 - 819692515707425x^20 + 795734675389219x^19 + 2859558999201013x^18 - 937302717934781x^17 - 7011360351157045x^16 - 902655412698460x^15 + 11681897146129224x^14 + 5604720542659268x^13 - 12486138055465655x^12 - 9886946345787043x^11 + 7728522779787490x^10 + 9075115953805640x^9 - 2183897418754987x^8 - 4579013283800046x^7 - 40649514655288x^6 + 1249295360564226x^5 + 160575454035341x^4 - 166814479770181x^3 - 29312399288701x^2 + 7715035819499x + 1403424452501	$43$	[43,0]	$431^{42}$	$1$	$374.291838114$		✓		$C_{43}$ (as 43T1)	not computed	$2$	$42$	$$
43.43.101...009.1	x^43 - x^42 - 462x^41 + 301x^40 + 94630x^39 - 49892x^38 - 11463758x^37 + 6368083x^36 + 921810336x^35 - 636827636x^34 - 52222121579x^33 + 47086072273x^32 + 2155113502777x^31 - 2510570612339x^30 - 65969924993323x^29 + 96629348183472x^28 + 1509193690295722x^27 - 2705517116526302x^26 - 25775660913572833x^25 + 55430418074111539x^24 + 325598895562519548x^23 - 832294062829303477x^22 - 2983438147701667253x^21 + 9129779342869086290x^20 + 19125104314160845818x^19 - 72594260758345520281x^18 - 79441906767691419891x^17 + 413102772817597404709x^16 + 166866840849449475306x^15 - 1650628224018564426381x^14 + 139804498689687778120x^13 + 4502348802434562518439x^12 - 1981830512581480780535x^11 - 8037383143222291539220x^10 + 5701308150866478483031x^9 + 8799946070456643867879x^8 - 8188607772821299311768x^7 - 5304980067316890480275x^6 + 6100770874409784770241x^5 + 1408273844297690430983x^4 - 2063406363097082700573x^3 - 90731765675438007935x^2 + 193966087122261586736x + 18221685305593614631	$43$	[43,0]	$947^{42}$	$1$	$807.481419163$		✓		$C_{43}$ (as 43T1)	not computed	$2$	$42$	$$
43.43.162...801.1	x^43 - 903x^41 - 645x^40 + 358276x^39 + 487362x^38 - 82668446x^37 - 161379172x^36 + 12386889944x^35 + 31035129471x^34 - 1275092913940x^33 - 3868686195114x^32 + 93052767268909x^31 + 330473143424644x^30 - 4897798025442393x^29 - 19967338988758228x^28 + 187329847291648022x^27 + 869728040966016241x^26 - 5201925841676982029x^25 - 27621776964130665961x^24 + 103748981858304966660x^23 + 643326429466437698421x^22 - 1445787294046167541816x^21 - 10999588529245966977339x^20 + 13140703542377826450494x^19 + 137573117593988043652238x^18 - 60838518194479293931722x^17 - 1247516677692517201034941x^16 - 134666416459554320685647x^15 + 8070410654031859605939559x^14 + 4203376282667672263555078x^13 - 36228120784944419229616219x^12 - 30515963297503545387850753x^11 + 107534691527795878017440861x^10 + 119306453339061961678830425x^9 - 192818992256047972290970619x^8 - 263326021640166500214931210x^7 + 170563929616560831037152772x^6 + 294222510747058121054570076x^5 - 33622183448420036732904682x^4 - 118832831442545361067982885x^3 - 7933826886293481520543865x^2 + 14571491290875996179048369x + 2572343484535669027372727	$43$	[43,0]	$43^{84}$	$1$	$1552.24987718$		✓		$C_{43}$ (as 43T1)	not computed	$2$	$42$	$$