LMFDB - Global number field search results

Further refine search

Results (displaying all 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
27.1.437270368662830612637452956330749689027.1	x²⁷ - x - 1	$ -\,23\cdot 3539\cdot 535391\cdot 10033918834509020645502251401 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.449582607823244927259046304907550096579.1	x²⁷ + x - 1	$ -\,151\cdot 144512650291622071\cdot 20602820982951053299 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.826260826778206666631489441194722724701633731.1	x²⁷ + 2x - 1	$ -\,229351\cdot 3602603985935124183594095692605319901381 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.28105327126796183803132932513380581740627623936.1	x²⁷ - 4x - 4	$ -\,2^{26}\cdot 263\cdot 1592403079552126010285410393405129573 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.28931587510147902226726652006325673846179364864.1	x²⁷ - 2x - 2	$ -\,2^{26}\cdot 239\cdot 911\cdot 1492637\cdot 10924843\cdot 125481509\cdot 967669291801 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.29757847887343501070113214188474091663330902016.1	x²⁷ - x - 2	$ -\,2^{27}\cdot 47\cdot 4717303065439408933563627808093088051 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.29757847893499620558587041306002149293331489783.1	x²⁷ - x - 4	$ -\,167\cdot 359\cdot 10245289151\cdot 48446943180119740684317685671961 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.30584108276851339073914090992215858057282846720.1	x²⁷ + 2x - 2	$ -\,2^{26}\cdot 5\cdot 7\cdot 11\cdot 80071\cdot 14783591491235038142928766927013 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.31410368660203057497507810485160950162834587648.1	x²⁷ + 4x - 4	$ -\,2^{26}\cdot 1831\cdot 255625869232040633091991440618651397 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.43207461914112074238522908041698612863100209996211.1	x²⁷ - 3x - 3	$ -\,3^{27}\cdot 71\cdot 337\cdot 14619373\cdot 78563389\cdot 206180539890995287 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.46944089987663498525424751985000152191384750818109.1	x²⁷ - 3x - 1	$ 3^{27}\cdot 11\cdot 29\cdot 318911\cdot 7780103222533\cdot 7777884788734331 $	$S_{27}$ (as 27T2392)	$[2]$ (GRH)
27.1.46944089988550351501910827524896651452623050603715.1	x²⁷ + 3x - 1	$ -\,3^{27}\cdot 5\cdot 29573\cdot 718375177076041\cdot 57954924238599673 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.46973847836000424634318110126447672587955631816704.1	x²⁷ + 3x - 2	$ -\,2^{27}\cdot 3^{27}\cdot 1592729\cdot 28815787221263522142841 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127129811580525429258316897077920778307403598875259.1	x²⁷ - 2x - 3	$ -\,2833\cdot 233083\cdot 3093889\cdot 426423967391\cdot 1293809775098462396398319 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127130637840902624857160283640102926725220750412411.1	x²⁷ - x - 3	$ -\,5388993289\cdot 58684642644166161743\cdot 3564036539687671224493 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127130637840914937096320697954724520073797550819963.1	x²⁷ + x - 3	$ -\,991\cdot 43499487821953\cdot 240698508804661\cdot 108628318596533067121 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1174074727829015705990408280552362125221513051327099.1	x²⁷ + 3x - 3	$ -\,3^{27}\cdot 11083579402853\cdot 13891265934804536061236909 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.110898761632028778210869975092030791887124902069665792.1	x²⁷ - 4x - 2	$ 2^{26}\cdot 555937897\cdot 70012520507\cdot 42456561322999590418419407 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.110898791389876228284002382374632342908260234650878781.1	x²⁷ - 4x - 1	$ 241\cdot 3119\cdot 12228551\cdot 12064779711493270243744089382808808946789 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.110898791389877115136978868450172239407521472950664387.1	x²⁷ + 4x - 1	$ -\,937\cdot 1655257\cdot 4229767\cdot 92058643\cdot 183628791318117083204427628903 $	$S_{27}$ (as 27T2392)	$[2]$ (GRH)
27.1.110898821147724565210111275732773790428656805531877376.1	x²⁷ + 4x - 2	$ -\,2^{26}\cdot 7\cdot 211\cdot 277\cdot 9820621\cdot 411289693845079379557406117008951 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.112025922027717580491467365903199704881290362951387771.1	x²⁷ + 4x - 3	$ -\,11854057\cdot 9450428830207040550882062225886015638467940803 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.499253841597823035730555735945079609621365309403299840.1	x²⁷ - 2x - 4	$ -\,2^{50}\cdot 5\cdot 139\cdot 42307\cdot 361717434139\cdot 41692232937963286631 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.499253842010953227406414947741939356093911362179170304.1	x²⁷ + 2x - 4	$ -\,2^{50}\cdot 61379\cdot 35649361663\cdot 202651613609462963242873 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1996968423127564419348927699584282983028731339264229376.1	x²⁷ - 3x - 4	$ -\,2^{26}\cdot 3^{27}\cdot 41\cdot 1531018773258677\cdot 62166019490421251 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1997015367217552532430060947581195242227227631565144064.1	x²⁷ + x - 4	$ -\,2^{26}\cdot 97\cdot 739\cdot 7753\cdot 53544585743558317501712559568164689899 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.11466666281598039055674857163705092874817691487932776448.1	x²⁷ + 5x - 2	$ -\,2^{27}\cdot 102533\cdot 472897035109621\cdot 1761964015755790324648349537 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45865537965996467420418831264009202586276600490849383813.1	x²⁷ - 5x - 3	$ 17\cdot 359\cdot 5984861568115119773\cdot 1255709015602496871819754676848927 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45866665066876460435700187354179628500729234048268894208.1	x²⁷ - 5x - 2	$ 2^{27}\cdot 7\cdot 12805208083\cdot 398913576491\cdot 9557048364382464605843591 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45866665096634307885773319761462230051750369380850107197.1	x²⁷ - 5x - 1	$ 191\cdot 180797\cdot 135031817\cdot 9836406442864970501664393432790394942983 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.45866665096634308772626296247537769948249630619149892803.1	x²⁷ + 5x - 1	$ -\,83\cdot 563\cdot 796853\cdot 1231778062127328031049100178271442365420402719 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.45867792227272149237980784744990797413723399509150616187.1	x²⁷ + 5x - 3	$ -\,26784394391927\cdot 906908513152058455369\cdot 1888263188591623325749 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.47863680463851860855473749371874037931430553343164940288.1	x²⁷ + 5x - 4	$ -\,2^{26}\cdot 23\cdot 4591\cdot 1054203587\cdot 40409162693929\cdot 158557479410628355703 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.73417444981913314280334795949102827452496728781547778643.1	x²⁷ + 3x - 5	$ -\,3^{25}\cdot 41\cdot 181\cdot 3917\cdot 23593\cdot 985450601\cdot 128213533389611086945001 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.614890292796495532086888341869635692124068737030029296875.1	x²⁷ - 5x - 5	$ -\,5^{26}\cdot 7\cdot 769\cdot 76657233947984763773781582607681381 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660646059101739963744377659248723289832910846176228525291.1	x²⁷ - 4x - 5	$ -\,75879359\cdot 6952540213\cdot 1353159565227731\cdot 925449390832864291185083 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756910949039852309163136206345937175666915026128585963.1	x²⁷ - 3x - 5	$ -\,3^{27}\cdot 7\cdot 139\cdot 373\cdot 857\cdot 14813\cdot 4501099\cdot 23278727\cdot 179491764750951217 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957892303580032736431450541972631123644924477555947.1	x²⁷ - 2x - 5	$ -\,433\cdot 1525997593284765773747659195035893701226613498670848859 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957893129840409932030293928534813272062741629093099.1	x²⁷ - x - 5	$ -\,11\cdot 2677\cdot 1349003\cdot 16633658205572341285537878058065875365475538839 $	$S_{27}$ (as 27T2392)	n/a
27.1.660756957893129840422244269454342849434865411318429500651.1	x²⁷ + x - 5	$ -\,7\cdot 547\cdot 2521\cdot 1416868547115429907\cdot 48311883957459219861654301784077 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957893956100799439868297729411617013829135581037803.1	x²⁷ + 2x - 5	$ -\,7\cdot 227\cdot 577841778572143\cdot 719629418837446831792679984277590823889 $	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.706623622989764148745287957878635692124068737030029296875.1	x²⁷ + 5x - 5	$ -\,5^{26}\cdot 17\cdot 181\cdot 159437\cdot 34030554306031\cdot 28404189802114157 $	$S_{27}$ (as 27T2392)	Trivial (GRH)

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Results (displaying all 42 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
27.1.437270368662830612637452956330749689027.1	x²⁷ - x - 1	\( -\,23\cdot 3539\cdot 535391\cdot 10033918834509020645502251401 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.449582607823244927259046304907550096579.1	x²⁷ + x - 1	\( -\,151\cdot 144512650291622071\cdot 20602820982951053299 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.826260826778206666631489441194722724701633731.1	x²⁷ + 2x - 1	\( -\,229351\cdot 3602603985935124183594095692605319901381 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.28105327126796183803132932513380581740627623936.1	x²⁷ - 4x - 4	\( -\,2^{26}\cdot 263\cdot 1592403079552126010285410393405129573 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.28931587510147902226726652006325673846179364864.1	x²⁷ - 2x - 2	\( -\,2^{26}\cdot 239\cdot 911\cdot 1492637\cdot 10924843\cdot 125481509\cdot 967669291801 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.29757847887343501070113214188474091663330902016.1	x²⁷ - x - 2	\( -\,2^{27}\cdot 47\cdot 4717303065439408933563627808093088051 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.29757847893499620558587041306002149293331489783.1	x²⁷ - x - 4	\( -\,167\cdot 359\cdot 10245289151\cdot 48446943180119740684317685671961 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.30584108276851339073914090992215858057282846720.1	x²⁷ + 2x - 2	\( -\,2^{26}\cdot 5\cdot 7\cdot 11\cdot 80071\cdot 14783591491235038142928766927013 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.31410368660203057497507810485160950162834587648.1	x²⁷ + 4x - 4	\( -\,2^{26}\cdot 1831\cdot 255625869232040633091991440618651397 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.43207461914112074238522908041698612863100209996211.1	x²⁷ - 3x - 3	\( -\,3^{27}\cdot 71\cdot 337\cdot 14619373\cdot 78563389\cdot 206180539890995287 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.46944089987663498525424751985000152191384750818109.1	x²⁷ - 3x - 1	\( 3^{27}\cdot 11\cdot 29\cdot 318911\cdot 7780103222533\cdot 7777884788734331 \)	$S_{27}$ (as 27T2392)	$[2]$ (GRH)
27.1.46944089988550351501910827524896651452623050603715.1	x²⁷ + 3x - 1	\( -\,3^{27}\cdot 5\cdot 29573\cdot 718375177076041\cdot 57954924238599673 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.46973847836000424634318110126447672587955631816704.1	x²⁷ + 3x - 2	\( -\,2^{27}\cdot 3^{27}\cdot 1592729\cdot 28815787221263522142841 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127129811580525429258316897077920778307403598875259.1	x²⁷ - 2x - 3	\( -\,2833\cdot 233083\cdot 3093889\cdot 426423967391\cdot 1293809775098462396398319 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127130637840902624857160283640102926725220750412411.1	x²⁷ - x - 3	\( -\,5388993289\cdot 58684642644166161743\cdot 3564036539687671224493 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1127130637840914937096320697954724520073797550819963.1	x²⁷ + x - 3	\( -\,991\cdot 43499487821953\cdot 240698508804661\cdot 108628318596533067121 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1174074727829015705990408280552362125221513051327099.1	x²⁷ + 3x - 3	\( -\,3^{27}\cdot 11083579402853\cdot 13891265934804536061236909 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.110898761632028778210869975092030791887124902069665792.1	x²⁷ - 4x - 2	\( 2^{26}\cdot 555937897\cdot 70012520507\cdot 42456561322999590418419407 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.110898791389876228284002382374632342908260234650878781.1	x²⁷ - 4x - 1	\( 241\cdot 3119\cdot 12228551\cdot 12064779711493270243744089382808808946789 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.110898791389877115136978868450172239407521472950664387.1	x²⁷ + 4x - 1	\( -\,937\cdot 1655257\cdot 4229767\cdot 92058643\cdot 183628791318117083204427628903 \)	$S_{27}$ (as 27T2392)	$[2]$ (GRH)
27.1.110898821147724565210111275732773790428656805531877376.1	x²⁷ + 4x - 2	\( -\,2^{26}\cdot 7\cdot 211\cdot 277\cdot 9820621\cdot 411289693845079379557406117008951 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.112025922027717580491467365903199704881290362951387771.1	x²⁷ + 4x - 3	\( -\,11854057\cdot 9450428830207040550882062225886015638467940803 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.499253841597823035730555735945079609621365309403299840.1	x²⁷ - 2x - 4	\( -\,2^{50}\cdot 5\cdot 139\cdot 42307\cdot 361717434139\cdot 41692232937963286631 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.499253842010953227406414947741939356093911362179170304.1	x²⁷ + 2x - 4	\( -\,2^{50}\cdot 61379\cdot 35649361663\cdot 202651613609462963242873 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1996968423127564419348927699584282983028731339264229376.1	x²⁷ - 3x - 4	\( -\,2^{26}\cdot 3^{27}\cdot 41\cdot 1531018773258677\cdot 62166019490421251 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.1997015367217552532430060947581195242227227631565144064.1	x²⁷ + x - 4	\( -\,2^{26}\cdot 97\cdot 739\cdot 7753\cdot 53544585743558317501712559568164689899 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.11466666281598039055674857163705092874817691487932776448.1	x²⁷ + 5x - 2	\( -\,2^{27}\cdot 102533\cdot 472897035109621\cdot 1761964015755790324648349537 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45865537965996467420418831264009202586276600490849383813.1	x²⁷ - 5x - 3	\( 17\cdot 359\cdot 5984861568115119773\cdot 1255709015602496871819754676848927 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45866665066876460435700187354179628500729234048268894208.1	x²⁷ - 5x - 2	\( 2^{27}\cdot 7\cdot 12805208083\cdot 398913576491\cdot 9557048364382464605843591 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.3.45866665096634307885773319761462230051750369380850107197.1	x²⁷ - 5x - 1	\( 191\cdot 180797\cdot 135031817\cdot 9836406442864970501664393432790394942983 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.45866665096634308772626296247537769948249630619149892803.1	x²⁷ + 5x - 1	\( -\,83\cdot 563\cdot 796853\cdot 1231778062127328031049100178271442365420402719 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.45867792227272149237980784744990797413723399509150616187.1	x²⁷ + 5x - 3	\( -\,26784394391927\cdot 906908513152058455369\cdot 1888263188591623325749 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.47863680463851860855473749371874037931430553343164940288.1	x²⁷ + 5x - 4	\( -\,2^{26}\cdot 23\cdot 4591\cdot 1054203587\cdot 40409162693929\cdot 158557479410628355703 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.73417444981913314280334795949102827452496728781547778643.1	x²⁷ + 3x - 5	\( -\,3^{25}\cdot 41\cdot 181\cdot 3917\cdot 23593\cdot 985450601\cdot 128213533389611086945001 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.614890292796495532086888341869635692124068737030029296875.1	x²⁷ - 5x - 5	\( -\,5^{26}\cdot 7\cdot 769\cdot 76657233947984763773781582607681381 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660646059101739963744377659248723289832910846176228525291.1	x²⁷ - 4x - 5	\( -\,75879359\cdot 6952540213\cdot 1353159565227731\cdot 925449390832864291185083 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756910949039852309163136206345937175666915026128585963.1	x²⁷ - 3x - 5	\( -\,3^{27}\cdot 7\cdot 139\cdot 373\cdot 857\cdot 14813\cdot 4501099\cdot 23278727\cdot 179491764750951217 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957892303580032736431450541972631123644924477555947.1	x²⁷ - 2x - 5	\( -\,433\cdot 1525997593284765773747659195035893701226613498670848859 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957893129840409932030293928534813272062741629093099.1	x²⁷ - x - 5	\( -\,11\cdot 2677\cdot 1349003\cdot 16633658205572341285537878058065875365475538839 \)	$S_{27}$ (as 27T2392)	n/a
27.1.660756957893129840422244269454342849434865411318429500651.1	x²⁷ + x - 5	\( -\,7\cdot 547\cdot 2521\cdot 1416868547115429907\cdot 48311883957459219861654301784077 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.660756957893956100799439868297729411617013829135581037803.1	x²⁷ + 2x - 5	\( -\,7\cdot 227\cdot 577841778572143\cdot 719629418837446831792679984277590823889 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)
27.1.706623622989764148745287957878635692124068737030029296875.1	x²⁷ + 5x - 5	\( -\,5^{26}\cdot 17\cdot 181\cdot 159437\cdot 34030554306031\cdot 28404189802114157 \)	$S_{27}$ (as 27T2392)	Trivial (GRH)