LMFDB - Global number field search results

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Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
43.1.17193642429484970947547009316647777700494014568443353175841873665979443.1	x⁴³ - x - 1	$ -\,109\cdot 809\cdot 397519523\cdot 490494801020731074863763714627948664201245545640512874061 $	$S_{43}$ (as 43T10)	n/a
43.1.17493904304575564092260553260976286616122110509580830730313660732011571.1	x⁴³ + x - 1	$ -\,59\cdot 397\cdot 877\cdot 935899\cdot 2402649604770175349\cdot 378726079619435938610415929241631681351 $	$S_{43}$ (as 43T10)	n/a
43.1.73637590561926486479405912723338063733861614147899437889774600865607334016376111104.1	x⁴³ - 4x - 4	$ -\,2^{42}\cdot 13\cdot 10239413\cdot 21464295562499\cdot 7440631653201968227\cdot 787580389820760746433715250923 $	$S_{43}$ (as 43T10)	n/a
43.1.74958156254086214703443254449187449178282319802617704397438354084969927035548860416.1	x⁴³ - 2x - 2	$ -\,2^{42}\cdot 5577217\cdot 417006008813\cdot 34910848872522797\cdot 201068225194855523\cdot 1043987668577822729 $	$S_{43}$ (as 43T10)	n/a
43.1.76278721946245792796543050878464477850730861202878156857131538565555284161188593664.1	x⁴³ - x - 2	$ -\,2^{43}\cdot 20380951\cdot 61480213\cdot 6920759952665299941538917396384169453478934159485941391 $	$S_{43}$ (as 43T10)	n/a
43.1.76278721946245942927480596140901011555290620195994458453535643977522773548439024487.1	x⁴³ - x - 4	$ -\,229\cdot 293\cdot 4986887\cdot 566527637659\cdot 4239521573605607851\cdot 94914557329966604524084292149520799491137 $	$S_{43}$ (as 43T10)	n/a
43.1.77599287638405671151517937900886220067123731112054237412765860523695113073894359040.1	x⁴³ + 2x - 2	$ -\,2^{42}\cdot 5\cdot 19\cdot 4987\cdot 11154877\cdot 914818621983827673311\cdot 3649515064680458585719692338597379997 $	$S_{43}$ (as 43T10)	n/a
43.1.78919853330565399375555279626735605511544436766772503920429613743057706093067108352.1	x⁴³ + 4x - 4	$ -\,2^{42}\cdot 90073\cdot 2923961\cdot 68133429255140007202167625043712385709578872658361664978371 $	$S_{43}$ (as 43T10)	n/a
43.3.49281526270717699300509198722877092539271399739749264767815294437558226291076362607004621.1	x⁴³ - 3x - 1	$ 193\cdot 255344695703200514510410356077083381032494299169685309677799453044343141404540738896397 $	$S_{43}$ (as 43T10)	n/a
43.1.49281602549439645563795899570503535096009803731586754262094262078677622576674184527609856.1	x⁴³ + 3x - 2	$ -\,2^{43}\cdot 83\cdot 67502042791558118041804533258686204716076628322729472986933623501167834329 $	$S_{43}$ (as 43T10)	n/a
43.1.1897738148225932665352052841514539485919791655231439979873933030555398665105804881388324651.1	x⁴³ - 2x - 3	$ -\,3^{42}\cdot 139\cdot 124775347877419985548920353165571925958504525515910258911325684164601 $	$S_{43}$ (as 43T10)	n/a
43.1.1897738149546498357511630934614335915196820327679981380134385490248583145691162007028057899.1	x⁴³ - x - 3	$ -\,3^{43}\cdot 3929\cdot 27164077\cdot 1696291894163\cdot 4471934430678427\cdot 7140840614667743763301231198589 $	$S_{43}$ (as 43T10)	n/a
43.1.1947019675817216056829634037641788571828352280680706931518322895195722202712552030367074091.1	x⁴³ + 3x - 3	$ -\,3^{42}\cdot 11\cdot 4458821\cdot 2188196233\cdot 250952988948637\cdot 660672576607742254821201853013034985249 $	$S_{43}$ (as 43T10)	n/a
43.1.3354773669271577653568285803640546404693410239170973401358900578361902104169371242332059336704.1	x⁴³ - 2x - 4	$ -\,2^{82}\cdot 17\cdot 911\cdot 1321\cdot 196825567\cdot 172286779949557395632536883985559201167052023742651489 $	$S_{43}$ (as 43T10)	n/a
43.1.11615818670173463204840555036546350439901529918004080992211006956821939425490704861593631716403.1	x⁴³ + 4x - 1	$ -\,181\cdot 155556871099633\cdot 21154104412279303\cdot 19502370656284022684705331520651631010500317670728311348739537 $	$S_{43}$ (as 43T10)	n/a
43.1.11615818670249741926786783635700464005809046848845495205636184619664502520703084303881154330624.1	x⁴³ + 4x - 2	$ -\,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 17195311805158423964285480495891 $	$S_{43}$ (as 43T10)	n/a
43.1.11617716408323009703198049473838535290845779191322444325813440848297619565283220181726993794859.1	x⁴³ + 4x - 3	$ -\,3^{42}\cdot 17\cdot 251\cdot 24883154146172620815006293556540010583439231599502655506743920009280153 $	$S_{43}$ (as 43T10)	n/a
43.1.335477317645632815204821422239306587903706814127360732280247849979340897599838242672095300419584.1	x⁴³ - 3x - 4	$ -\,2^{42}\cdot 5736251\cdot 13297659175117020385300439521039825046372945434356686517822982914329253832871 $	$S_{43}$ (as 43T10)	n/a
43.1.42669778834265525646357377125943811028661226892061887227006364333992726275526826083130013680402432.1	x⁴³ + 5x - 2	$ -\,2^{43}\cdot 4850992221948391221116864599701308523965647838401979155037948241214590584096052462329 $	$S_{43}$ (as 43T10)	n/a
43.3.170679115337062026306707562240488543267018465011509144916187967841691937460987908046922232801004493.1	x⁴³ - 5x - 1	$ 67\cdot 2547449482642716810547874063290873780104753209127002162928178624502864738223700120103316907477679 $	$S_{43}$ (as 43T10)	n/a
43.1.3772838381179050124528639896195900262054652258977602756862847748815326440308126620948314666748046875.1	x⁴³ - 5x - 5	$ -\,5^{42}\cdot 1201\cdot 3109\cdot 627374521\cdot 7083328981731612358415823717337673911296516278980882783 $	$S_{43}$ (as 43T10)	n/a
43.1.3943517496516112150835347458453582447751155694936658911095683494357512392337557882171078773215030811.1	x⁴³ - x - 5	$ -\,4378013\cdot 253946916604529\cdot 37511360891773121\cdot 94558584147022639554815783215214951921556301363567987461405383 $	$S_{43}$ (as 43T10)	n/a
43.1.3943517496565393677106065157771585550778608351568190864096409045741449797284696939192468796554047003.1	x⁴³ + 3x - 5	$ -\,4787\cdot 56783432887\cdot 65016935311\cdot 223137316352143056032093232478629204773290672599490333442273344596696250817 $	$S_{43}$ (as 43T10)	n/a
43.1.4114196611853174177142055020711564895322749724040428609272847748815326440308126620948314666748046875.1	x⁴³ + 5x - 5	$ -\,5^{42}\cdot 68281\cdot 264999458923518261034367410401624235839813453110759740473297621067 $	$S_{43}$ (as 43T10)	n/a

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Results (displaying all 24 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
43.1.17193642429484970947547009316647777700494014568443353175841873665979443.1	x⁴³ - x - 1	\( -\,109\cdot 809\cdot 397519523\cdot 490494801020731074863763714627948664201245545640512874061 \)	$S_{43}$ (as 43T10)	n/a
43.1.17493904304575564092260553260976286616122110509580830730313660732011571.1	x⁴³ + x - 1	\( -\,59\cdot 397\cdot 877\cdot 935899\cdot 2402649604770175349\cdot 378726079619435938610415929241631681351 \)	$S_{43}$ (as 43T10)	n/a
43.1.73637590561926486479405912723338063733861614147899437889774600865607334016376111104.1	x⁴³ - 4x - 4	\( -\,2^{42}\cdot 13\cdot 10239413\cdot 21464295562499\cdot 7440631653201968227\cdot 787580389820760746433715250923 \)	$S_{43}$ (as 43T10)	n/a
43.1.74958156254086214703443254449187449178282319802617704397438354084969927035548860416.1	x⁴³ - 2x - 2	\( -\,2^{42}\cdot 5577217\cdot 417006008813\cdot 34910848872522797\cdot 201068225194855523\cdot 1043987668577822729 \)	$S_{43}$ (as 43T10)	n/a
43.1.76278721946245792796543050878464477850730861202878156857131538565555284161188593664.1	x⁴³ - x - 2	\( -\,2^{43}\cdot 20380951\cdot 61480213\cdot 6920759952665299941538917396384169453478934159485941391 \)	$S_{43}$ (as 43T10)	n/a
43.1.76278721946245942927480596140901011555290620195994458453535643977522773548439024487.1	x⁴³ - x - 4	\( -\,229\cdot 293\cdot 4986887\cdot 566527637659\cdot 4239521573605607851\cdot 94914557329966604524084292149520799491137 \)	$S_{43}$ (as 43T10)	n/a
43.1.77599287638405671151517937900886220067123731112054237412765860523695113073894359040.1	x⁴³ + 2x - 2	\( -\,2^{42}\cdot 5\cdot 19\cdot 4987\cdot 11154877\cdot 914818621983827673311\cdot 3649515064680458585719692338597379997 \)	$S_{43}$ (as 43T10)	n/a
43.1.78919853330565399375555279626735605511544436766772503920429613743057706093067108352.1	x⁴³ + 4x - 4	\( -\,2^{42}\cdot 90073\cdot 2923961\cdot 68133429255140007202167625043712385709578872658361664978371 \)	$S_{43}$ (as 43T10)	n/a
43.3.49281526270717699300509198722877092539271399739749264767815294437558226291076362607004621.1	x⁴³ - 3x - 1	\( 193\cdot 255344695703200514510410356077083381032494299169685309677799453044343141404540738896397 \)	$S_{43}$ (as 43T10)	n/a
43.1.49281602549439645563795899570503535096009803731586754262094262078677622576674184527609856.1	x⁴³ + 3x - 2	\( -\,2^{43}\cdot 83\cdot 67502042791558118041804533258686204716076628322729472986933623501167834329 \)	$S_{43}$ (as 43T10)	n/a
43.1.1897738148225932665352052841514539485919791655231439979873933030555398665105804881388324651.1	x⁴³ - 2x - 3	\( -\,3^{42}\cdot 139\cdot 124775347877419985548920353165571925958504525515910258911325684164601 \)	$S_{43}$ (as 43T10)	n/a
43.1.1897738149546498357511630934614335915196820327679981380134385490248583145691162007028057899.1	x⁴³ - x - 3	\( -\,3^{43}\cdot 3929\cdot 27164077\cdot 1696291894163\cdot 4471934430678427\cdot 7140840614667743763301231198589 \)	$S_{43}$ (as 43T10)	n/a
43.1.1947019675817216056829634037641788571828352280680706931518322895195722202712552030367074091.1	x⁴³ + 3x - 3	\( -\,3^{42}\cdot 11\cdot 4458821\cdot 2188196233\cdot 250952988948637\cdot 660672576607742254821201853013034985249 \)	$S_{43}$ (as 43T10)	n/a
43.1.3354773669271577653568285803640546404693410239170973401358900578361902104169371242332059336704.1	x⁴³ - 2x - 4	\( -\,2^{82}\cdot 17\cdot 911\cdot 1321\cdot 196825567\cdot 172286779949557395632536883985559201167052023742651489 \)	$S_{43}$ (as 43T10)	n/a
43.1.11615818670173463204840555036546350439901529918004080992211006956821939425490704861593631716403.1	x⁴³ + 4x - 1	\( -\,181\cdot 155556871099633\cdot 21154104412279303\cdot 19502370656284022684705331520651631010500317670728311348739537 \)	$S_{43}$ (as 43T10)	n/a
43.1.11615818670249741926786783635700464005809046848845495205636184619664502520703084303881154330624.1	x⁴³ + 4x - 2	\( -\,2^{42}\cdot 13\cdot 53\cdot 359\cdot 379\cdot 397\cdot 15583\cdot 15667\cdot 16763\cdot 1652591\cdot 7443949\cdot 81974567114861\cdot 17195311805158423964285480495891 \)	$S_{43}$ (as 43T10)	n/a
43.1.11617716408323009703198049473838535290845779191322444325813440848297619565283220181726993794859.1	x⁴³ + 4x - 3	\( -\,3^{42}\cdot 17\cdot 251\cdot 24883154146172620815006293556540010583439231599502655506743920009280153 \)	$S_{43}$ (as 43T10)	n/a
43.1.335477317645632815204821422239306587903706814127360732280247849979340897599838242672095300419584.1	x⁴³ - 3x - 4	\( -\,2^{42}\cdot 5736251\cdot 13297659175117020385300439521039825046372945434356686517822982914329253832871 \)	$S_{43}$ (as 43T10)	n/a
43.1.42669778834265525646357377125943811028661226892061887227006364333992726275526826083130013680402432.1	x⁴³ + 5x - 2	\( -\,2^{43}\cdot 4850992221948391221116864599701308523965647838401979155037948241214590584096052462329 \)	$S_{43}$ (as 43T10)	n/a
43.3.170679115337062026306707562240488543267018465011509144916187967841691937460987908046922232801004493.1	x⁴³ - 5x - 1	\( 67\cdot 2547449482642716810547874063290873780104753209127002162928178624502864738223700120103316907477679 \)	$S_{43}$ (as 43T10)	n/a
43.1.3772838381179050124528639896195900262054652258977602756862847748815326440308126620948314666748046875.1	x⁴³ - 5x - 5	\( -\,5^{42}\cdot 1201\cdot 3109\cdot 627374521\cdot 7083328981731612358415823717337673911296516278980882783 \)	$S_{43}$ (as 43T10)	n/a
43.1.3943517496516112150835347458453582447751155694936658911095683494357512392337557882171078773215030811.1	x⁴³ - x - 5	\( -\,4378013\cdot 253946916604529\cdot 37511360891773121\cdot 94558584147022639554815783215214951921556301363567987461405383 \)	$S_{43}$ (as 43T10)	n/a
43.1.3943517496565393677106065157771585550778608351568190864096409045741449797284696939192468796554047003.1	x⁴³ + 3x - 5	\( -\,4787\cdot 56783432887\cdot 65016935311\cdot 223137316352143056032093232478629204773290672599490333442273344596696250817 \)	$S_{43}$ (as 43T10)	n/a
43.1.4114196611853174177142055020711564895322749724040428609272847748815326440308126620948314666748046875.1	x⁴³ + 5x - 5	\( -\,5^{42}\cdot 68281\cdot 264999458923518261034367410401624235839813453110759740473297621067 \)	$S_{43}$ (as 43T10)	n/a