Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
42.0.148800059914663860358058572923291111558062081238577126241568395062423.1	x^42 - x + 1	\( -\,250460976091\cdot 2191665374655671317777039\cdot 271074578334716402754124978170427 \)	$S_{42}$ (as 42T9491)	n/a
42.2.151461815175929284355485371405217804070033859898900428230218670969705.1	x^42 - x - 1	\( 5\cdot 3355730803775717\cdot 9027053958291963044489986637364046584886518936629873 \)	$S_{42}$ (as 42T9491)	Trivial (GRH)
42.2.5853261720260687939540400640891858773248095902186156682496904257250187676745728.1	x^42 - 2x - 1	\( 2^{43}\cdot 151\cdot 4132611804876851\cdot 111869437509421489132043\cdot 9532243245509920520310487 \)	$S_{42}$ (as 42T9491)	n/a
42.0.6368697991994218840106904466505523750060174615816448189841639477612393330114560.1	x^42 - 4x + 4	\( -\,2^{42}\cdot 5\cdot 14815048403\cdot 223886382998191\cdot 87315245161684521362070855931280070146911 \)	$S_{42}$ (as 42T9491)	n/a
42.2.170923973240076585006662819799708267353672048284155422169897317900338421540323328.1	x^42 - 4x - 4	\( 2^{42}\cdot 37\cdot 479\cdot 22037\cdot 3375017\cdot 4905809483\cdot 799858695525167\cdot 7513694603813636232170428411 \)	$S_{42}$ (as 42T9491)	n/a
42.0.324288161319821499007340327393811274304092572235194518204010139360633960649457664.1	x^42 - 2x + 2	\( -\,2^{42}\cdot 19\cdot 11483\cdot 457151\cdot 739269240650992830782068773491929591684851555740229248233 \)	$S_{42}$ (as 42T9491)	n/a
42.2.335994684760042613011330535530881447906260255123938735627866470320662548936916992.1	x^42 - 2x - 2	\( 2^{42}\cdot 13\cdot 43\cdot 7237697\cdot 7281116753\cdot 16009936396480001782447\cdot 161984247228508288433890361 \)	$S_{42}$ (as 42T9491)	n/a
42.2.145623285001573634100250550474921067849138776627782144579392805206367874810820848413905.1	x^42 - 3x + 1	\( 3^{42}\cdot 5\cdot 277\cdot 9883\cdot 24851\cdot 5267491\cdot 28880594132963764921\cdot 25718507492700353234963282659 \)	$S_{42}$ (as 42T9491)	n/a
42.0.5330101856189281845511059855302822366369109365492551944953598888288262041748188930347823.1	x^42 - 3x + 3	\( -\,3^{42}\cdot 17\cdot 2865456953988204634522191655713027824433143187808898514763100375591 \)	$S_{42}$ (as 42T9491)	n/a
42.2.5621348426192429114011822831343257646780930863076625149740480439838475345841617693207761.1	x^42 - 3x - 3	\( 3^{42}\cdot 733\cdot 68553343\cdot 351501200862401\cdot 10459852944644953\cdot 278075548230630365691581947 \)	$S_{42}$ (as 42T9491)	n/a
42.2.25742917286380691552742753359900798778254242549105496402743504951132097494038819618557001728.1	x^42 - 4x + 2	\( 2^{83}\cdot 13\cdot 12436342330109\cdot 16463876538231681806130383128159764631891692537995873 \)	$S_{42}$ (as 42T9491)	n/a
42.2.25742917286710832975782535284972588913144232138238508561965257530077467060102231979817172992.1	x^42 - 4x + 1	\( 2^{42}\cdot 349\cdot 16771523553325378229212234764217820597932894277534834227692947479277329115027 \)	$S_{42}$ (as 42T9491)	n/a
42.0.725988666885841450302533604467433832469413627175525270297831784561573195675770992164014091415.1	x^42 - x + 4	\( -\,5\cdot 145197733377168290060506720893486766493882725435105054059566356912314639135154198432802818283 \)	$S_{42}$ (as 42T9491)	n/a
42.2.302606538442139605362186891689008382608944369517013180955902083904215368794193387901702482203297.1	x^42 - 5x + 2	\( 19\cdot 103\cdot 12613\cdot 12259396352512970244632341383064531792896532951399397720777987489941835112339925374125417 \)	$S_{42}$ (as 42T9491)	n/a
42.2.302606538442139935503609931771195329489672404220146258296570221284890255301237005785850808406689.1	x^42 - 5x - 1	\( 14087\cdot 14537\cdot 2332805104561\cdot 633441547854075390686353614294706494604521824972593793196858282759647977871 \)	$S_{42}$ (as 42T9491)	n/a
42.0.1706791153370620261603760192550683915841711308180357561779039638906972822017958629996426464067584.1	x^42 - 2x + 5	\( -\,2^{42}\cdot 47\cdot 29989\cdot 133117577\cdot 2068356136392292742885048864559553903077433124109604781071241999887231 \)	$S_{42}$ (as 42T9491)	n/a
42.0.6524558075040341116764692558692228273417573469393142762067684236529157715267501771450042724609375.1	x^42 - 5x + 5	\( -\,5^{41}\cdot 143476549392133012363204975959437726534118523917930522264267843247859 \)	$S_{42}$ (as 42T9491)	n/a
42.0.6827138870565194341435326707627876755227739584667606837527183576928421951964201120532126649810944.1	x^42 - 4x + 5	\( -\,2^{42}\cdot 257\cdot 3481561\cdot 654827729\cdot 761992291147\cdot 1236911477052699683\cdot 2810965583895622035799170714070354517 \)	$S_{42}$ (as 42T9491)	n/a
42.0.6827164613482481052268302490311961787731316589257803648959036653744014110669838349005674862046359.1	x^42 - x + 5	\( -\,2897\cdot 16037383\cdot 15911394874499255951\cdot 9235281219070225126384628429046289956396011098793278160408720753359 \)	$S_{42}$ (as 42T9491)	n/a
42.2.6827164613482481058121564210423849667357053369791603849283841444372108711928165480014294143729664.1	x^42 - 2x - 5	\( 2^{43}\cdot 753458691670301\cdot 3525521090014396699\cdot 292191647246322726371560515917614279121677398687917 \)	$S_{42}$ (as 42T9491)	n/a
42.2.6827164613628104337269876124563674153382166941462427796992036602393440775775106652046714381429969.1	x^42 - 3x - 5	\( 3^{42}\cdot 10431018730019\cdot 17617983839831\cdot 339519516498825242123808246117475938341866528706869 \)	$S_{42}$ (as 42T9491)	n/a
42.2.7129771151924620987771912421934357057306325133119891334332315763470842284732498228549957275390625.1	x^42 - 5x - 5	\( 5^{41}\cdot 11\cdot 88163104517\cdot 308782183121\cdot 54247978409543239\cdot 9651394343916620260340096573 \)	$S_{42}$ (as 42T9491)	n/a