LMFDB - Global number field search results

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Results (displaying all 27 matches)

Label	Polynomial	Discriminant	Galois group	Class group
38.2.1086466936935771765474507582942119612061614764913786264052821.1	x³⁸ - x - 1	$ 624808693\cdot 1738879354765590249997542180390437704844184626147297 $	$S_{38}$ (as 38T76)	Trivial (GRH)
38.2.2901373404155647104441523981239181159929184708380460029220825235930489.1	x³⁸ - 4x - 1	$ 11149\cdot 365159\cdot 14342233\cdot 49689992079559593586453718567433043366296684203166163 $	$S_{38}$ (as 38T76)	n/a
38.2.2901373405231558906417603818965707338993499524889151117093324667748352.1	x³⁸ - 2x - 1	$ 2^{39}\cdot 199\cdot 28308359\cdot 2683125188231\cdot 180622253751001441\cdot 1933097818431428689 $	$S_{38}$ (as 38T76)	n/a
38.0.7892746960221820898131562172323886834213973461541107170325061114527744.1	x³⁸ - 4x + 4	$ -\,2^{38}\cdot 3\cdot 1061\cdot 24469\cdot 188414113\cdot 393131311\cdot 4977192294056925650789352450614791 $	$S_{38}$ (as 38T76)	n/a
38.2.76837469450307682292059279224725537680200512645417292029451367237025792.1	x³⁸ - 4x - 4	$ 2^{38}\cdot 727\cdot 5261563\cdot 73077559047116249833260249644378329868669917729193 $	$S_{38}$ (as 38T76)	n/a
38.0.144970818688148423270805728938735241101988898053513592814114008664637440.1	x³⁸ - 2x + 2	$ -\,2^{38}\cdot 5\cdot 41\cdot 367\cdot 263591\cdot 73599203\cdot 4905513061473881\cdot 73660168063921443246200957 $	$S_{38}$ (as 38T76)	n/a
38.0.147872192092293515240287560992226440858040277966341129166293547068332971.1	x³⁸ - x + 2	$ -\,27991188787\cdot 5282812145548104521106046048555288208740138420986354414469033 $	$S_{38}$ (as 38T76)	n/a
38.2.150773565496459717479680948612545797274263649545060920310639825870913536.1	x³⁸ - 2x - 2	$ 2^{38}\cdot 3\cdot 182837011981924924814764318838019240834623693499526077249223 $	$S_{38}$ (as 38T76)	n/a
38.2.14258422185282661194839449228784338024756499615792788929321629765271215858317.1	x³⁸ - 3x - 1	$ 487\cdot 521\cdot 4519\cdot 26317\cdot 11892563\cdot 39732930972782132460495746364538247928675306727948539379 $	$S_{38}$ (as 38T76)	n/a
38.0.470207346404490340384495199475209233402018357248959736621334835182883335380339.1	x³⁸ - 3x + 3	$ -\,3^{37}\cdot 11\cdot 71\cdot 7880009\cdot 21435017\cdot 7915920170803969017816295491376945943528821 $	$S_{38}$ (as 38T76)	n/a
38.0.484465765688399596347775742286389752461067517871253000661505347854829883490304.1	x³⁸ - 2x + 3	$ -\,2^{39}\cdot 523\cdot 599\cdot 213961453\cdot 35576001825507809\cdot 369549036309479457672944372639639227 $	$S_{38}$ (as 38T76)	n/a
38.2.498724190775055660622350493972789945330672850768297756249003357052593637876365.1	x³⁸ - 3x - 3	$ 3^{37}\cdot 5\cdot 221515441369465466460532848622822255590773911416105332587571 $	$S_{38}$ (as 38T76)	n/a
38.2.948879803050989584620936728952856178707584223842026603837566232766082191458304.1	x³⁸ - 4x - 3	$ 2^{38}\cdot 40980168689701\cdot 203965927976641\cdot 412990441418705007555356829064473217351 $	$S_{38}$ (as 38T76)	n/a
38.2.31900937949806586390320337463114855419174100233410480755209811568901372071903232.1	x³⁸ - 4x - 2	$ 2^{75}\cdot 3\cdot 23\cdot 277\cdot 1513583473\cdot 5473293451459721\cdot 5332978185985420820488513531 $	$S_{38}$ (as 38T76)	n/a
38.2.797523448449420275573400295827384707928071467459009471281670776097780467262029824.1	x³⁸ - 4x + 2	$ 2^{75}\cdot 7\cdot 47\cdot 64164954126569673234813332462561408162487876014661903017 $	$S_{38}$ (as 38T76)	n/a
38.2.797523448597292467664628454400648052721651557394279621301842545291326968465195008.1	x³⁸ - 4x + 1	$ 2^{38}\cdot 3\cdot 811\cdot 2302291\cdot 517966057255956009554954225246160624258380010402927414479869 $	$S_{38}$ (as 38T76)	n/a
38.0.5080849832193481021043781792889688288464476220368709136423318533586081437892739072.1	x³⁸ - 2x + 4	$ -\,2^{36}\cdot 3\cdot 7\cdot 269683\cdot 243410960929\cdot 53634411417457511001169668118600282980215765726407141 $	$S_{38}$ (as 38T76)	n/a
38.2.5080849832194931707745859616441907093382928859411777824296205365460212892194308096.1	x³⁸ - 2x - 4	$ 2^{36}\cdot 101\cdot 919\cdot 1949\cdot 3539\cdot 185240700233\cdot 17140715362231\cdot 36371555198831357772204065739472223 $	$S_{38}$ (as 38T76)	n/a
38.2.20323399328776825457579293373798146541478224237891059917271993925488672030373536853.1	x³⁸ - x - 4	$ 773\cdot 4813\cdot 6781\cdot 44087\cdot 282407\cdot 4622799406751\cdot 23120981570369\cdot 605354715250981541649232676485669447 $	$S_{38}$ (as 38T76)	n/a
38.2.3839935727511250084381873285947946387767292827812861625609590641933945885923046717821.1	x³⁸ - 5x + 1	$ 3\cdot 4921063777787\cdot 260102009166133812584985142358770156526818265636216301398179309035254861 $	$S_{38}$ (as 38T76)	n/a
38.2.3839935727511250084381875437771550347755256948671367337857148872908683546755175938429.1	x³⁸ - 5x - 1	$ 163\cdot 315952440047\cdot 735114279983971219\cdot 101428447464121945448827044448280047869601556164829131 $	$S_{38}$ (as 38T76)	n/a
38.2.9124758045063636213395680721976151947343770081895790497970374417491257190704345703125.1	x³⁸ - 5x - 5	$ 5^{37}\cdot 131\cdot 181\cdot 2011\cdot 898776624172831\cdot 2926290836145496407027696425922931571 $	$S_{38}$ (as 38T76)	n/a
38.0.19570721669515368233701461995069628680180704735885478465656063556584062934272849215488.1	x³⁸ - 2x + 5	$ -\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357 $	$S_{38}$ (as 38T76)	n/a
38.0.74442950950550225751797377774065870790571380960577885518266630242578685283660888671875.1	x³⁸ - 5x + 5	$ -\,5^{37}\cdot 23\cdot 139\cdot 299699\cdot 9433691167\cdot 85263102703\cdot 14613295519063\cdot 90847825344374471 $	$S_{38}$ (as 38T76)	n/a
38.0.78282886663803053650896592016997971909542299884492753240330990186165739065144848751987.1	x³⁸ - 3x + 5	$ -\,313\cdot 1019481121\cdot 8471154741571\cdot 28960142293866467628247950531735628005572712542426606634900089 $	$S_{38}$ (as 38T76)	n/a
38.2.78282886678061475836179252146480754114110439262898330085995832946127396083370199442517.1	x³⁸ - x - 5	$ 3\cdot 4441\cdot 68315627\cdot 8533124051989\cdot 10079446546039780216505179050024688541395414940881977168831593 $	$S_{38}$ (as 38T76)	n/a
38.2.78282886678061478737552656291572723595942492754098086137375745773663748262908603138048.1	x³⁸ - 2x - 5	$ 2^{39}\cdot 3\cdot 17\cdot 929\cdot 26261\cdot 1587413\cdot 12103709\cdot 158015743\cdot 1243193510457304691\cdot 30321616657803787127474779 $	$S_{38}$ (as 38T76)	n/a

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Results (displaying all 27 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
38.2.1086466936935771765474507582942119612061614764913786264052821.1	x³⁸ - x - 1	\( 624808693\cdot 1738879354765590249997542180390437704844184626147297 \)	$S_{38}$ (as 38T76)	Trivial (GRH)
38.2.2901373404155647104441523981239181159929184708380460029220825235930489.1	x³⁸ - 4x - 1	\( 11149\cdot 365159\cdot 14342233\cdot 49689992079559593586453718567433043366296684203166163 \)	$S_{38}$ (as 38T76)	n/a
38.2.2901373405231558906417603818965707338993499524889151117093324667748352.1	x³⁸ - 2x - 1	\( 2^{39}\cdot 199\cdot 28308359\cdot 2683125188231\cdot 180622253751001441\cdot 1933097818431428689 \)	$S_{38}$ (as 38T76)	n/a
38.0.7892746960221820898131562172323886834213973461541107170325061114527744.1	x³⁸ - 4x + 4	\( -\,2^{38}\cdot 3\cdot 1061\cdot 24469\cdot 188414113\cdot 393131311\cdot 4977192294056925650789352450614791 \)	$S_{38}$ (as 38T76)	n/a
38.2.76837469450307682292059279224725537680200512645417292029451367237025792.1	x³⁸ - 4x - 4	\( 2^{38}\cdot 727\cdot 5261563\cdot 73077559047116249833260249644378329868669917729193 \)	$S_{38}$ (as 38T76)	n/a
38.0.144970818688148423270805728938735241101988898053513592814114008664637440.1	x³⁸ - 2x + 2	\( -\,2^{38}\cdot 5\cdot 41\cdot 367\cdot 263591\cdot 73599203\cdot 4905513061473881\cdot 73660168063921443246200957 \)	$S_{38}$ (as 38T76)	n/a
38.0.147872192092293515240287560992226440858040277966341129166293547068332971.1	x³⁸ - x + 2	\( -\,27991188787\cdot 5282812145548104521106046048555288208740138420986354414469033 \)	$S_{38}$ (as 38T76)	n/a
38.2.150773565496459717479680948612545797274263649545060920310639825870913536.1	x³⁸ - 2x - 2	\( 2^{38}\cdot 3\cdot 182837011981924924814764318838019240834623693499526077249223 \)	$S_{38}$ (as 38T76)	n/a
38.2.14258422185282661194839449228784338024756499615792788929321629765271215858317.1	x³⁸ - 3x - 1	\( 487\cdot 521\cdot 4519\cdot 26317\cdot 11892563\cdot 39732930972782132460495746364538247928675306727948539379 \)	$S_{38}$ (as 38T76)	n/a
38.0.470207346404490340384495199475209233402018357248959736621334835182883335380339.1	x³⁸ - 3x + 3	\( -\,3^{37}\cdot 11\cdot 71\cdot 7880009\cdot 21435017\cdot 7915920170803969017816295491376945943528821 \)	$S_{38}$ (as 38T76)	n/a
38.0.484465765688399596347775742286389752461067517871253000661505347854829883490304.1	x³⁸ - 2x + 3	\( -\,2^{39}\cdot 523\cdot 599\cdot 213961453\cdot 35576001825507809\cdot 369549036309479457672944372639639227 \)	$S_{38}$ (as 38T76)	n/a
38.2.498724190775055660622350493972789945330672850768297756249003357052593637876365.1	x³⁸ - 3x - 3	\( 3^{37}\cdot 5\cdot 221515441369465466460532848622822255590773911416105332587571 \)	$S_{38}$ (as 38T76)	n/a
38.2.948879803050989584620936728952856178707584223842026603837566232766082191458304.1	x³⁸ - 4x - 3	\( 2^{38}\cdot 40980168689701\cdot 203965927976641\cdot 412990441418705007555356829064473217351 \)	$S_{38}$ (as 38T76)	n/a
38.2.31900937949806586390320337463114855419174100233410480755209811568901372071903232.1	x³⁸ - 4x - 2	\( 2^{75}\cdot 3\cdot 23\cdot 277\cdot 1513583473\cdot 5473293451459721\cdot 5332978185985420820488513531 \)	$S_{38}$ (as 38T76)	n/a
38.2.797523448449420275573400295827384707928071467459009471281670776097780467262029824.1	x³⁸ - 4x + 2	\( 2^{75}\cdot 7\cdot 47\cdot 64164954126569673234813332462561408162487876014661903017 \)	$S_{38}$ (as 38T76)	n/a
38.2.797523448597292467664628454400648052721651557394279621301842545291326968465195008.1	x³⁸ - 4x + 1	\( 2^{38}\cdot 3\cdot 811\cdot 2302291\cdot 517966057255956009554954225246160624258380010402927414479869 \)	$S_{38}$ (as 38T76)	n/a
38.0.5080849832193481021043781792889688288464476220368709136423318533586081437892739072.1	x³⁸ - 2x + 4	\( -\,2^{36}\cdot 3\cdot 7\cdot 269683\cdot 243410960929\cdot 53634411417457511001169668118600282980215765726407141 \)	$S_{38}$ (as 38T76)	n/a
38.2.5080849832194931707745859616441907093382928859411777824296205365460212892194308096.1	x³⁸ - 2x - 4	\( 2^{36}\cdot 101\cdot 919\cdot 1949\cdot 3539\cdot 185240700233\cdot 17140715362231\cdot 36371555198831357772204065739472223 \)	$S_{38}$ (as 38T76)	n/a
38.2.20323399328776825457579293373798146541478224237891059917271993925488672030373536853.1	x³⁸ - x - 4	\( 773\cdot 4813\cdot 6781\cdot 44087\cdot 282407\cdot 4622799406751\cdot 23120981570369\cdot 605354715250981541649232676485669447 \)	$S_{38}$ (as 38T76)	n/a
38.2.3839935727511250084381873285947946387767292827812861625609590641933945885923046717821.1	x³⁸ - 5x + 1	\( 3\cdot 4921063777787\cdot 260102009166133812584985142358770156526818265636216301398179309035254861 \)	$S_{38}$ (as 38T76)	n/a
38.2.3839935727511250084381875437771550347755256948671367337857148872908683546755175938429.1	x³⁸ - 5x - 1	\( 163\cdot 315952440047\cdot 735114279983971219\cdot 101428447464121945448827044448280047869601556164829131 \)	$S_{38}$ (as 38T76)	n/a
38.2.9124758045063636213395680721976151947343770081895790497970374417491257190704345703125.1	x³⁸ - 5x - 5	\( 5^{37}\cdot 131\cdot 181\cdot 2011\cdot 898776624172831\cdot 2926290836145496407027696425922931571 \)	$S_{38}$ (as 38T76)	n/a
38.0.19570721669515368233701461995069628680180704735885478465656063556584062934272849215488.1	x³⁸ - 2x + 5	\( -\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357 \)	$S_{38}$ (as 38T76)	n/a
38.0.74442950950550225751797377774065870790571380960577885518266630242578685283660888671875.1	x³⁸ - 5x + 5	\( -\,5^{37}\cdot 23\cdot 139\cdot 299699\cdot 9433691167\cdot 85263102703\cdot 14613295519063\cdot 90847825344374471 \)	$S_{38}$ (as 38T76)	n/a
38.0.78282886663803053650896592016997971909542299884492753240330990186165739065144848751987.1	x³⁸ - 3x + 5	\( -\,313\cdot 1019481121\cdot 8471154741571\cdot 28960142293866467628247950531735628005572712542426606634900089 \)	$S_{38}$ (as 38T76)	n/a
38.2.78282886678061475836179252146480754114110439262898330085995832946127396083370199442517.1	x³⁸ - x - 5	\( 3\cdot 4441\cdot 68315627\cdot 8533124051989\cdot 10079446546039780216505179050024688541395414940881977168831593 \)	$S_{38}$ (as 38T76)	n/a
38.2.78282886678061478737552656291572723595942492754098086137375745773663748262908603138048.1	x³⁸ - 2x - 5	\( 2^{39}\cdot 3\cdot 17\cdot 929\cdot 26261\cdot 1587413\cdot 12103709\cdot 158015743\cdot 1243193510457304691\cdot 30321616657803787127474779 \)	$S_{38}$ (as 38T76)	n/a