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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
40.0.11976663048684220554521970551011110940069807894780803482990048041.1	x^40 - x + 1	\( 89\cdot 2963\cdot 2969\cdot 36703533640127\cdot 206798756592464370511\cdot 2015339302026829599091 \)	$S_{40}$ (as 40T315842)	Trivial (GRH)
40.2.12201853343608362939601549448988889059930192105219196517009951959.1	x^40 - x - 1	\( -\,25788481\cdot 473151301296433975293137639591447400873676588598576105239 \)	$S_{40}$ (as 40T315842)	Trivial (GRH)
40.2.123799673865700652129832399822361287621723938537943027700441950831650013184.1	x^40 - 4x - 1	\( -\,2^{40}\cdot 65581\cdot 130948229477800849\cdot 13111186908622089242206486448360790839011 \)	$S_{40}$ (as 40T315842)	n/a
40.2.123799673877789910325967696453145287621723938537943027700441950831650013184.1	x^40 - 2x - 1	\( -\,2^{40}\cdot 299179\cdot 176896234253\cdot 2127502014851899658221712726961346777625280857 \)	$S_{40}$ (as 40T315842)	n/a
40.0.3199270315596589030129696245994777912378276061462056972299558049168349986816.1	x^40 - 4x + 4	\( 2^{40}\cdot 168323\cdot 1917232819781\cdot 9016392149180870791777884329882006637603974407 \)	$S_{40}$ (as 40T315842)	n/a
40.2.3446869663327990334389339055406944967621723938537943027700441950831650013184.1	x^40 - 4x - 4	\( -\,2^{40}\cdot 195992147998081969\cdot 15995078009601298847824572226328581653291688711 \)	$S_{40}$ (as 40T315842)	n/a
40.0.6522340305058878712389213896695639352378276061462056972299558049168349986816.1	x^40 - 2x + 2	\( 2^{40}\cdot 7\cdot 709\cdot 3469\cdot 45247\cdot 9564613\cdot 796155428932457198813694339611851235726797373 \)	$S_{40}$ (as 40T315842)	n/a
40.0.6646139978924466769371573230209183090551011110940069807894780803482990048041.1	x^40 - x + 2	\( 59\cdot 1459\cdot 3833\cdot 1738871593\cdot 3542704547\cdot 3269797924202183308143643467236069456997219997027 \)	$S_{40}$ (as 40T315842)	n/a
40.2.6769939652790280016648856706107806407621723938537943027700441950831650013184.1	x^40 - 2x - 2	\( -\,2^{40}\cdot 41\cdot 285346141\cdot 454772160964243\cdot 1157271450150352380488274641452541109673 \)	$S_{40}$ (as 40T315842)	n/a
40.2.1368894135157044344794112376926497609757905625361762098834793591080436851093471159.1	x^40 - 3x + 1	\( -\,67\cdot 20431255748612602161106154879499964324744860080026299982608859568364729120798077 \)	$S_{40}$ (as 40T315842)	n/a
40.2.1368894135157044368972628769219081103881425625361762098834793591080436851093471159.1	x^40 - 3x - 1	\( -\,317\cdot 126493\cdot 709237\cdot 5225047\cdot 5648197\cdot 991002953\cdot 30082576347511\cdot 54709495555999135006716598974751 \)	$S_{40}$ (as 40T315842)	n/a
40.0.47623491463812503995875147927428631066430254374638237901165206408919563148906528841.1	x^40 - 3x + 3	\( 3^{39}\cdot 6893916847\cdot 1704614809630888222612527785401257947637299618322827509 \)	$S_{40}$ (as 40T315842)	n/a
40.0.48992385475169874487057866370680015717166392378276061462056972299558049168349986816.1	x^40 - 2x + 3	\( 2^{40}\cdot 3^{40}\cdot 61\cdot 17393\cdot 49999\cdot 118358164571\cdot 314964076619\cdot 1853333925864801067 \)	$S_{40}$ (as 40T315842)	n/a
40.0.48992385598969548352645923353039349230710130551011110940069807894780803482990048041.1	x^40 - x + 3	\( 3^{40}\cdot 677\cdot 5952367403321660141326428487365658014394958115455011167043733 \)	$S_{40}$ (as 40T315842)	n/a
40.2.48992385598969548352871113647963491615789709448988889059930192105219196517009951959.1	x^40 - x - 3	\( -\,3^{39}\cdot 47\cdot 31247\cdot 1492676502904837324513\cdot 5514774660213950753706902645463792581 \)	$S_{40}$ (as 40T315842)	n/a
40.2.50361279734126592709641889073574209780069585625361762098834793591080436851093471159.1	x^40 - 3x - 3	\( -\,3^{39}\cdot 19\cdot 29\cdot 22553618218752278266208944368360557495082715636402158894791027 \)	$S_{40}$ (as 40T315842)	n/a
40.2.136119180930214450437992564702356620013434883881159515925662787473504462935871700598784.1	x^40 - 4x + 1	\( -\,2^{80}\cdot 5317370417\cdot 21174967819074018167987909988947655427216799295477127 \)	$S_{40}$ (as 40T315842)	n/a
40.2.136119180936860590416929233325071801606583668521159515925662787473504462935871700598784.1	x^40 - 4x - 2	\( -\,2^{80}\cdot 41\cdot 47\cdot 75109\cdot 91086967\cdot 8540626670650203198360722999925267617168459339 \)	$S_{40}$ (as 40T315842)	n/a
40.2.136168173315813419986357412479053267725605195561159515925662787473504462935871700598784.1	x^40 - 4x - 3	\( -\,2^{80}\cdot 3^{39}\cdot 22898527\cdot 1219719433\cdot 995129348796489940662957347 \)	$S_{40}$ (as 40T315842)	n/a
40.0.913438523331783373958836595284644431933781318478094569015365514243074889512292087496704.1	x^40 - 2x + 4	\( 2^{38}\cdot 7\cdot 23\cdot 643\cdot 1621\cdot 19802481879023096430651036170353377414078397518352976208297537134327 \)	$S_{40}$ (as 40T315842)	n/a
40.2.913438523331845273795769445610709342636134360241905430984634485756925110487707912503296.1	x^40 - 2x - 4	\( -\,2^{38}\cdot 127\cdot 4663\cdot 27761297\cdot 202129917885388785314297446219230581863638472574083092701289647 \)	$S_{40}$ (as 40T315842)	n/a
40.0.3653752724433122138464855198420134476350474537774374638237901165206408919563148906528841.1	x^40 - 3x + 4	\( 20611\cdot 84491007767770337133473\cdot 2098116497816396572885715162595405369382361532980887707054947 \)	$S_{40}$ (as 40T315842)	n/a
40.0.3653754093327257295509211969195560087068638817650551011110940069807894780803482990048041.1	x^40 - x + 4	\( 487\cdot 503\cdot 47143\cdot 205427\cdot 1540166343925677624072393302991232358238541202032450757174530380307948021 \)	$S_{40}$ (as 40T315842)	n/a
40.2.3653754093327257295509212194385855011211023897229448988889059930192105219196517009951959.1	x^40 - x - 4	\( -\,1607\cdot 934111\cdot 1438075378526603\cdot 8959474307278141\cdot 1679138406187605606151\cdot 112505635596093083651652679 \)	$S_{40}$ (as 40T315842)	n/a
40.2.113782983514285285698196744032513830356987213682796689968476703143096528947353363037109375.1	x^40 - 5x + 3	\( -\,3^{39}\cdot 5^{40}\cdot 61\cdot 12041\cdot 136952659\cdot 30689184606850102963971847171 \)	$S_{40}$ (as 40T315842)	n/a
40.2.448780256235102043342850487055115349588191932777214849422937521182510769396774506768367616.1	x^40 - 2x - 5	\( -\,2^{40}\cdot 11\cdot 17\cdot 41737\cdot 116269\cdot 170049501036703\cdot 25343270439968515087037\cdot 104368423294285319545974931771 \)	$S_{40}$ (as 40T315842)	n/a
40.2.1024046949613338769222867401809661474215725769645010209716290328287868760526180267333984375.1	x^40 - 5x - 3	\( -\,3^{39}\cdot 5^{40}\cdot 7\cdot 238347710179\cdot 303974618220029\cdot 54782823889028869 \)	$S_{40}$ (as 40T315842)	n/a
40.2.1027700654714280427548828261132933681263445177752530209716290328287868760526180267333984375.1	x^40 - 5x - 4	\( -\,5^{40}\cdot 1409\cdot 277273\cdot 1576117\cdot 395080003450900487\cdot 464487876487482964927883111701 \)	$S_{40}$ (as 40T315842)	n/a
40.0.5497558138879999969050081533574836967544648823479118094569015365514243074889512292087496704.1	x^40 - 2x + 5	\( 2^{38}\cdot 14756617\cdot 125350691971\cdot 4593762876149\cdot 30747484746820755469\cdot 76548782187418446465742657723 \)	$S_{40}$ (as 40T315842)	n/a
40.0.20966185654899046829746680950948857026285694653604909790283709671712131239473819732666015625.1	x^40 - 5x + 5	\( 5^{40}\cdot 17\cdot 14336401\cdot 3525770155993\cdot 13466978569729\cdot 199207656273558550240761826609 \)	$S_{40}$ (as 40T315842)	n/a
40.0.21990096436339069785549561995346039447233694818054358840484074337212526495537064128299401216.1	x^40 - 4x + 5	\( 2^{80}\cdot 127\cdot 6163\cdot 316421509\cdot 14859902891161\cdot 112118849869317089\cdot 44082984501882421864081 \)	$S_{40}$ (as 40T315842)	n/a
40.2.21990232556888894135157044356883370573072789356819665625361762098834793591080436851093471159.1	x^40 - 3x - 5	\( -\,11\cdot 22181713\cdot 39596371\cdot 384916815739\cdot 5913162119878974881045527037115866612882317962669562981259702677 \)	$S_{40}$ (as 40T315842)	n/a
40.2.23014279456140953170253319049051142973714305346395090209716290328287868760526180267333984375.1	x^40 - 5x - 5	\( -\,5^{40}\cdot 7\cdot 11\cdot 23\cdot 139\cdot 263\cdot 49921\cdot 350641766719\cdot 1082515310287\cdot 28189512647977\cdot 73171096236097 \)	$S_{40}$ (as 40T315842)	n/a
40.4.818380493827663732613543259594667183634328825351814767249590812771172429611764531578535936000000000000000000000000.1	x^40 - 20x^39 + 198x^38 + 1024x^37 - 36068x^36 + 259680x^35 + 1497696x^34 - 33104520x^33 + 160318881x^32 + 2610452884x^31 - 6879123998x^30 + 176849382312x^29 + 4086792360022x^28 + 22821387509152x^27 + 183136305521712x^26 + 3461079483509184x^25 + 36791832526211640x^24 + 243226399927467600x^23 + 1630838116240157304x^22 + 15684628915838324736x^21 + 148676542850261879424x^20 + 1094555702225628334944x^19 + 6175860294063058627536x^18 + 27500637919324676682528x^17 + 99275620461555285598644x^16 + 296069266727479829997360x^15 + 737510649338519637350040x^14 + 1538660650564897293864096x^13 + 2665957190465280126142008x^12 + 3726694189110949405579584x^11 + 3860744775405859251848736x^10 + 2003714444328444974615040x^9 - 2364665119699343002683120x^8 - 8369166482885528217875520x^7 - 13648935640574809132025760x^6 - 15631766178885580005797760x^5 - 13468976980779782363580000x^4 - 8765166219033111033484800x^3 - 4168397528000957970432000x^2 - 1320687936380639564236800x - 212265281716190997033600	\( 2^{111}\cdot 3^{56}\cdot 5^{24}\cdot 7^{29}\cdot 11^{12} \)	$S_{40}$ (as 40T315842)	n/a