LMFDB - Global number field search results

Further refine search

Results (displaying all 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
30.0.203323445941487788865438171785268983873516531.1	x³⁰ - x + 1	$ -\,7\cdot 4547\cdot 625861750823\cdot 40306090892659\cdot 253230129277627 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.208458818247810211134561828214731016126483469.1	x³⁰ - x - 1	$ 4421\cdot 22659339443160463\cdot 2080906233684319160584903 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2757032013554862401424586100944031593515138235298081.1	x³⁰ - 4x - 1	$ 1657\cdot 56091358577718162989\cdot 29663564839667553243668426797 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2757032219445994304322526868059944925023774709907456.1	x³⁰ - 2x - 1	$ 2^{31}\cdot 309259\cdot 14808181703558627\cdot 280341823437737461079 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.52511447916628477265270473131940055074976225290092544.1	x³⁰ - 4x + 4	$ -\,2^{30}\cdot 23\cdot 2126308559587001689801659642837781907544197 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.58025511943738201684617526868059944925023774709907456.1	x³⁰ - 4x - 4	$ 2^{30}\cdot 11\cdot 19\cdot 163\cdot 1523\cdot 192007\cdot 2905267\cdot 16453379\cdot 331846583\cdot 341971373 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.107779927846811816740214473131940055074976225290092544.1	x³⁰ - 2x + 2	$ -\,2^{30}\cdot 4261\cdot 1538746509977\cdot 15309443470070730473327119823 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.110536959857798992796726788865438171785268983873516531.1	x³⁰ - x + 2	$ -\,16069\cdot 6878894757470844034894939875875174048495176045399 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.113293991873921541159561526868059944925023774709907456.1	x³⁰ - 2x - 2	$ 2^{30}\cdot 31\cdot 1493\cdot 294391\cdot 7743922161827546044216740165330673 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528663808937910174564399958795650464488012557052441857381.1	x³⁰ - 3x + 1	$ 3^{30}\cdot 7\cdot 83\cdot 547\cdot 8079388286476418501045691928532147267 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528663808938321956828589256795650464488012557052441857381.1	x³⁰ - 3x - 1	$ 3^{31}\cdot 2579\cdot 3847572842487629\cdot 86254644893658285239753 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528774345897976432375444495795650464488012557052441857381.1	x³⁰ - 3x - 2	$ 3^{30}\cdot 31\cdot 1769381441963\cdot 46821958249121311829160660473 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.13601722282800618439068316459204349535511987442947558142619.1	x³⁰ - 3x + 3	$ -\,3^{30}\cdot 13\cdot 5081745477824752989649090137328383374885887 $	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.0.14130383334706720949902601393473131940055074976225290092544.1	x³⁰ - 2x + 3	$ -\,2^{31}\cdot 4447\cdot 21434117\cdot 86927089867957\cdot 794138426549944803348421 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.14130386091738731937078657905788865438171785268983873516531.1	x³⁰ - x + 3	$ -\,13\cdot 179\cdot 560893979\cdot 1599364314633798641\cdot 6769077172765732520137982927 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14130386091738737072450964228211134561828214731016126483469.1	x³⁰ - x - 3	$ 277\cdot 400264301\cdot 5331180702097\cdot 132214342318352251\cdot 180811241978611351 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14659049900676850570461305674795650464488012557052441857381.1	x³⁰ - 3x - 3	$ 3^{30}\cdot 883\cdot 468509\cdot 30594564677969\cdot 5625294473757709912283 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.490446929338367368469464950504274472186461390204388563028789.1	x³⁰ - x - 4	$ 313\cdot 1553\cdot 2467\cdot 408984714634382156915687128942520668312227370530703 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340472523830612716844233935692605134571100381102676639744.1	x³⁰ - 4x + 2	$ 2^{59}\cdot 1847\cdot 15727\cdot 398407\cdot 551671\cdot 2918921\cdot 275568568450197721 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340583060790267192391089174692605134571100381102676639744.1	x³⁰ - 4x + 1	$ 2^{30}\cdot 7\cdot 149\cdot 8329\cdot 14869697\cdot 24084784266299\cdot 886175540693210057361991 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340693597750333450202133711692605134571100381102676639744.1	x³⁰ - 4x - 2	$ 2^{59}\cdot 31\cdot 101\cdot 36470152085223887711\cdot 44972943052468912543 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2974470969152529207588287994890692605134571100381102676639744.1	x³⁰ - 4x - 3	$ 2^{30}\cdot 47\cdot 113\cdot 70468441\cdot 118739592888857\cdot 62336633454993137535840733 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.14836019611796354892170677662045618282985013768744056322523136.1	x³⁰ - 2x + 4	$ -\,2^{28}\cdot 4899563\cdot 468731357\cdot 5400051347\cdot 4456544800255361855961256703 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14836019613174870898948108766882381717014986231255943677476864.1	x³⁰ - 2x - 4	$ 2^{28}\cdot 11\cdot 2579\cdot 1948199793180973091335796507968621672062145867901 $	$S_{30}$ (as 30T5712)	n/a
30.0.59343549786133513466171876363248204349535511987442947558142619.1	x³⁰ - 3x + 4	$ -\,3^{30}\cdot 4329008673689392661\cdot 66580556933815696116855581671 $	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.0.59344078449942451579669886704694788865438171785268983873516531.1	x³⁰ - x + 4	$ -\,288817\cdot 111899407981\cdot 6492534437104925213\cdot 282821607796117415613307931 $	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.2.2391329948580521314201606080705383820940983481705188751220703125.1	x³⁰ - 5x + 3	$ 5^{30}\cdot 21713739362807\cdot 118250980997440906149013156123 $	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078856076093075744166566562820940983481705188751220703125.1	x³⁰ - 5x + 2	$ 5^{30}\cdot 167\cdot 2357\cdot 6094873\cdot 26805343\cdot 39928211377608794948777 $	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078966613052730219713421801820940983481705188751220703125.1	x³⁰ - 5x + 1	$ 5^{30}\cdot 7\cdot 5801\cdot 3546119\cdot 17831493849226271130635818385621 $	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078966613053142001977611099820940983481705188751220703125.1	x³⁰ - 5x - 1	$ 5^{31}\cdot 10309974007\cdot 49809750275177607143367885979807 $	$S_{30}$ (as 30T5712)	n/a
30.2.2391344079077150012796477524466338820940983481705188751220703125.1	x³⁰ - 5x - 2	$ 5^{30}\cdot 31\cdot 43441\cdot 1906691503180731813087022084752319811 $	$S_{30}$ (as 30T5712)	n/a
30.2.2391358209352704791670615610327517820940983481705188751220703125.1	x³⁰ - 5x - 3	$ 5^{30}\cdot 13\cdot 5801281\cdot 34046874574873365201475419661436609 $	$S_{30}$ (as 30T5712)	n/a
30.2.2450688157416555504518348418374306820940983481705188751220703125.1	x³⁰ - 5x - 4	$ 5^{30}\cdot 11\cdot 839\cdot 1871\cdot 2027569\cdot 75159493718018483766865870303 $	$S_{30}$ (as 30T5712)	n/a
30.0.4261134590879223155064689667620390800483281723554160327506460291.1	x³⁰ - 3x + 5	$ -\,3^{29}\cdot 71\cdot 467\cdot 51628578737\cdot 9899468832468151\cdot 3663798440144491003 $	$S_{30}$ (as 30T5712)	n/a
30.0.9587552961643515075421179460717112868282985013768744056322523136.1	x³⁰ - 2x + 5	$ -\,2^{31}\cdot 27697516504717\cdot 161189623390592288097213202537300077892721 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.35958867767610204280762161859561674179059016518294811248779296875.1	x³⁰ - 5x + 5	$ -\,5^{30}\cdot 22824228476857\cdot 1691647115472857190280342038283 $	$S_{30}$ (as 30T5712)	n/a
30.0.38347251505993756543225189181894301307394865428899618897323360256.1	x³⁰ - 4x + 5	$ -\,2^{30}\cdot 71\cdot 109\cdot 128047\cdot 65725731723640882837\cdot 548333383871954330575047389 $	$S_{30}$ (as 30T5712)	n/a
30.0.38350211846576817333695705018924963788865438171785268983873516531.1	x³⁰ - x + 5	$ -\,17\cdot 47\cdot 16981\cdot 2826556858296592645707884592131201321956420421866275558649 $	$S_{30}$ (as 30T5712)	n/a
30.2.38350211846576817333700840391231286211134561828214731016126483469.1	x³⁰ - x - 5	$ 23\cdot 107\cdot 352188553406401\cdot 44246703173900112184165555414284317559667420529 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.38350211846579574365711827567287798526868059944925023774709907456.1	x³⁰ - 2x - 5	$ 2^{31}\cdot 49823\cdot 4049666919614429899\cdot 88509262710421943273744704806461 $	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.38350212375240626271814338401572732795650464488012557052441857381.1	x³⁰ - 3x - 5	$ 3^{30}\cdot 2477\cdot 75197625147671318646027910602272190040781641697 $	$S_{30}$ (as 30T5712)	n/a
30.2.40741555925543430386634383550594575820940983481705188751220703125.1	x³⁰ - 5x - 5	$ 5^{30}\cdot 5217677\cdot 8384174139581850531292341058047674497 $	$S_{30}$ (as 30T5712)	$[2]$ (GRH)

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Further refine search

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
30.0.203323445941487788865438171785268983873516531.1	x³⁰ - x + 1	\( -\,7\cdot 4547\cdot 625861750823\cdot 40306090892659\cdot 253230129277627 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.208458818247810211134561828214731016126483469.1	x³⁰ - x - 1	\( 4421\cdot 22659339443160463\cdot 2080906233684319160584903 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2757032013554862401424586100944031593515138235298081.1	x³⁰ - 4x - 1	\( 1657\cdot 56091358577718162989\cdot 29663564839667553243668426797 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2757032219445994304322526868059944925023774709907456.1	x³⁰ - 2x - 1	\( 2^{31}\cdot 309259\cdot 14808181703558627\cdot 280341823437737461079 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.52511447916628477265270473131940055074976225290092544.1	x³⁰ - 4x + 4	\( -\,2^{30}\cdot 23\cdot 2126308559587001689801659642837781907544197 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.58025511943738201684617526868059944925023774709907456.1	x³⁰ - 4x - 4	\( 2^{30}\cdot 11\cdot 19\cdot 163\cdot 1523\cdot 192007\cdot 2905267\cdot 16453379\cdot 331846583\cdot 341971373 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.107779927846811816740214473131940055074976225290092544.1	x³⁰ - 2x + 2	\( -\,2^{30}\cdot 4261\cdot 1538746509977\cdot 15309443470070730473327119823 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.110536959857798992796726788865438171785268983873516531.1	x³⁰ - x + 2	\( -\,16069\cdot 6878894757470844034894939875875174048495176045399 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.113293991873921541159561526868059944925023774709907456.1	x³⁰ - 2x - 2	\( 2^{30}\cdot 31\cdot 1493\cdot 294391\cdot 7743922161827546044216740165330673 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528663808937910174564399958795650464488012557052441857381.1	x³⁰ - 3x + 1	\( 3^{30}\cdot 7\cdot 83\cdot 547\cdot 8079388286476418501045691928532147267 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528663808938321956828589256795650464488012557052441857381.1	x³⁰ - 3x - 1	\( 3^{31}\cdot 2579\cdot 3847572842487629\cdot 86254644893658285239753 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.528774345897976432375444495795650464488012557052441857381.1	x³⁰ - 3x - 2	\( 3^{30}\cdot 31\cdot 1769381441963\cdot 46821958249121311829160660473 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.13601722282800618439068316459204349535511987442947558142619.1	x³⁰ - 3x + 3	\( -\,3^{30}\cdot 13\cdot 5081745477824752989649090137328383374885887 \)	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.0.14130383334706720949902601393473131940055074976225290092544.1	x³⁰ - 2x + 3	\( -\,2^{31}\cdot 4447\cdot 21434117\cdot 86927089867957\cdot 794138426549944803348421 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.14130386091738731937078657905788865438171785268983873516531.1	x³⁰ - x + 3	\( -\,13\cdot 179\cdot 560893979\cdot 1599364314633798641\cdot 6769077172765732520137982927 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14130386091738737072450964228211134561828214731016126483469.1	x³⁰ - x - 3	\( 277\cdot 400264301\cdot 5331180702097\cdot 132214342318352251\cdot 180811241978611351 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14659049900676850570461305674795650464488012557052441857381.1	x³⁰ - 3x - 3	\( 3^{30}\cdot 883\cdot 468509\cdot 30594564677969\cdot 5625294473757709912283 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.490446929338367368469464950504274472186461390204388563028789.1	x³⁰ - x - 4	\( 313\cdot 1553\cdot 2467\cdot 408984714634382156915687128942520668312227370530703 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340472523830612716844233935692605134571100381102676639744.1	x³⁰ - 4x + 2	\( 2^{59}\cdot 1847\cdot 15727\cdot 398407\cdot 551671\cdot 2918921\cdot 275568568450197721 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340583060790267192391089174692605134571100381102676639744.1	x³⁰ - 4x + 1	\( 2^{30}\cdot 7\cdot 149\cdot 8329\cdot 14869697\cdot 24084784266299\cdot 886175540693210057361991 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2960340693597750333450202133711692605134571100381102676639744.1	x³⁰ - 4x - 2	\( 2^{59}\cdot 31\cdot 101\cdot 36470152085223887711\cdot 44972943052468912543 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.2974470969152529207588287994890692605134571100381102676639744.1	x³⁰ - 4x - 3	\( 2^{30}\cdot 47\cdot 113\cdot 70468441\cdot 118739592888857\cdot 62336633454993137535840733 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.14836019611796354892170677662045618282985013768744056322523136.1	x³⁰ - 2x + 4	\( -\,2^{28}\cdot 4899563\cdot 468731357\cdot 5400051347\cdot 4456544800255361855961256703 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.14836019613174870898948108766882381717014986231255943677476864.1	x³⁰ - 2x - 4	\( 2^{28}\cdot 11\cdot 2579\cdot 1948199793180973091335796507968621672062145867901 \)	$S_{30}$ (as 30T5712)	n/a
30.0.59343549786133513466171876363248204349535511987442947558142619.1	x³⁰ - 3x + 4	\( -\,3^{30}\cdot 4329008673689392661\cdot 66580556933815696116855581671 \)	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.0.59344078449942451579669886704694788865438171785268983873516531.1	x³⁰ - x + 4	\( -\,288817\cdot 111899407981\cdot 6492534437104925213\cdot 282821607796117415613307931 \)	$S_{30}$ (as 30T5712)	$[2]$ (GRH)
30.2.2391329948580521314201606080705383820940983481705188751220703125.1	x³⁰ - 5x + 3	\( 5^{30}\cdot 21713739362807\cdot 118250980997440906149013156123 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078856076093075744166566562820940983481705188751220703125.1	x³⁰ - 5x + 2	\( 5^{30}\cdot 167\cdot 2357\cdot 6094873\cdot 26805343\cdot 39928211377608794948777 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078966613052730219713421801820940983481705188751220703125.1	x³⁰ - 5x + 1	\( 5^{30}\cdot 7\cdot 5801\cdot 3546119\cdot 17831493849226271130635818385621 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2391344078966613053142001977611099820940983481705188751220703125.1	x³⁰ - 5x - 1	\( 5^{31}\cdot 10309974007\cdot 49809750275177607143367885979807 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2391344079077150012796477524466338820940983481705188751220703125.1	x³⁰ - 5x - 2	\( 5^{30}\cdot 31\cdot 43441\cdot 1906691503180731813087022084752319811 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2391358209352704791670615610327517820940983481705188751220703125.1	x³⁰ - 5x - 3	\( 5^{30}\cdot 13\cdot 5801281\cdot 34046874574873365201475419661436609 \)	$S_{30}$ (as 30T5712)	n/a
30.2.2450688157416555504518348418374306820940983481705188751220703125.1	x³⁰ - 5x - 4	\( 5^{30}\cdot 11\cdot 839\cdot 1871\cdot 2027569\cdot 75159493718018483766865870303 \)	$S_{30}$ (as 30T5712)	n/a
30.0.4261134590879223155064689667620390800483281723554160327506460291.1	x³⁰ - 3x + 5	\( -\,3^{29}\cdot 71\cdot 467\cdot 51628578737\cdot 9899468832468151\cdot 3663798440144491003 \)	$S_{30}$ (as 30T5712)	n/a
30.0.9587552961643515075421179460717112868282985013768744056322523136.1	x³⁰ - 2x + 5	\( -\,2^{31}\cdot 27697516504717\cdot 161189623390592288097213202537300077892721 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.0.35958867767610204280762161859561674179059016518294811248779296875.1	x³⁰ - 5x + 5	\( -\,5^{30}\cdot 22824228476857\cdot 1691647115472857190280342038283 \)	$S_{30}$ (as 30T5712)	n/a
30.0.38347251505993756543225189181894301307394865428899618897323360256.1	x³⁰ - 4x + 5	\( -\,2^{30}\cdot 71\cdot 109\cdot 128047\cdot 65725731723640882837\cdot 548333383871954330575047389 \)	$S_{30}$ (as 30T5712)	n/a
30.0.38350211846576817333695705018924963788865438171785268983873516531.1	x³⁰ - x + 5	\( -\,17\cdot 47\cdot 16981\cdot 2826556858296592645707884592131201321956420421866275558649 \)	$S_{30}$ (as 30T5712)	n/a
30.2.38350211846576817333700840391231286211134561828214731016126483469.1	x³⁰ - x - 5	\( 23\cdot 107\cdot 352188553406401\cdot 44246703173900112184165555414284317559667420529 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.38350211846579574365711827567287798526868059944925023774709907456.1	x³⁰ - 2x - 5	\( 2^{31}\cdot 49823\cdot 4049666919614429899\cdot 88509262710421943273744704806461 \)	$S_{30}$ (as 30T5712)	Trivial (GRH)
30.2.38350212375240626271814338401572732795650464488012557052441857381.1	x³⁰ - 3x - 5	\( 3^{30}\cdot 2477\cdot 75197625147671318646027910602272190040781641697 \)	$S_{30}$ (as 30T5712)	n/a
30.2.40741555925543430386634383550594575820940983481705188751220703125.1	x³⁰ - 5x - 5	\( 5^{30}\cdot 5217677\cdot 8384174139581850531292341058047674497 \)	$S_{30}$ (as 30T5712)	$[2]$ (GRH)