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 31 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.7174552902718171733819392.1	x^21 - 7x^20 + 21x^19 - 42x^18 + 77x^17 - 126x^16 + 168x^15 - 213x^14 + 266x^13 - 280x^12 + 259x^11 - 217x^10 + 133x^9 - 42x^8 - 53x^7 + 126x^6 - 112x^5 + 7x^4 + 63x^3 - 49x^2 + 14x - 1	\( -\,2^{18}\cdot 7^{23} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.9284127557257563917891699.1	x^21 - 5x^20 + 11x^19 - 13x^18 + 7x^17 + 4x^16 - 16x^15 + 13x^14 - 6x^13 + 2x^12 - 2x^11 + 21x^10 - 28x^8 + 29x^7 - 16x^6 - 18x^5 + 17x^4 - 9x^3 - 2x^2 + 3x - 1	\( -\,11^{9}\cdot 13^{14} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.378818692265664781682717625943.3	x^21 - x^14 - 9x^7 + 1	\( -\,7^{35} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.21.94142881806955162927406195366237.1	x^21 - 31x^19 - 3x^18 + 362x^17 + 32x^16 - 2119x^15 - 158x^14 + 6826x^13 + 676x^12 - 12509x^11 - 2021x^10 + 12809x^9 + 3175x^8 - 6710x^7 - 2254x^6 + 1442x^5 + 571x^4 - 97x^3 - 44x^2 + 2x + 1	\( 7^{14}\cdot 173^{9} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.21.2406787169604002863343075235725312.1	x^21 - 2x^20 - 32x^19 + 51x^18 + 432x^17 - 473x^16 - 3214x^15 + 1767x^14 + 14108x^13 - 305x^12 - 35382x^11 - 15763x^10 + 43350x^9 + 37753x^8 - 14531x^7 - 24311x^6 - 2788x^5 + 4492x^4 + 1052x^3 - 276x^2 - 56x + 8	\( 2^{27}\cdot 7^{14}\cdot 31^{9} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.26160559119874379648562947375700703.2	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 32x^16 + 201x^15 - 718x^14 + 847x^13 + 988x^12 - 1701x^11 - 6256x^10 + 18797x^9 - 15492x^8 - 45562x^7 + 150977x^6 - 83972x^5 - 198072x^4 + 215936x^3 + 70896x^2 - 133952x + 19264	\( -\,7^{17}\cdot 13^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.48958786234221774012025092444897160075327.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 52x^16 - 373x^15 + 248x^14 - 3577x^13 + 42918x^12 - 170639x^11 + 225822x^10 + 43556x^9 + 105237x^8 - 3230632x^7 + 5161290x^6 + 1287601x^5 + 2320101x^4 - 14827477x^3 + 4310250x^2 + 1634962x + 569387	\( -\,7^{17}\cdot 29^{18} \)	$F_7$ (as 21T4)	$[7, 7]$ (GRH)
21.3.24933089799576296242287986136979936417017847.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 316x^17 - 375x^16 + 5x^15 - 1019x^14 + 20797x^13 + 115088x^12 + 265993x^11 + 283880x^10 + 220817x^9 + 3096540x^8 + 13444516x^7 + 20299735x^6 - 8975624x^5 - 86530794x^4 - 152378359x^3 - 129757565x^2 - 50056244x - 6446237	\( -\,7^{17}\cdot 41^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.58762312802028807390251370834685864006539343.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 330x^17 - 2629x^16 + 9945x^15 - 21697x^14 + 61691x^13 - 337490x^12 + 1367751x^11 - 3880770x^10 + 9707987x^9 - 27063618x^8 + 86251922x^7 - 249930855x^6 + 516125610x^5 - 636836088x^4 + 367896053x^3 + 18430223x^2 - 116740442x + 35136283	\( -\,7^{17}\cdot 43^{18} \)	$F_7$ (as 21T4)	$[7]$ (GRH)
21.3.42600210199743647641790494093640979042918020345647.1	x^21 - 2067x^14 - 766753x^7 - 62748517	\( -\,7^{35}\cdot 13^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.42600210199743647641790494093640979042918020345647.2	x^21 - 2171x^14 + 1219335x^7 - 62748517	\( -\,7^{35}\cdot 13^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.42600210199743647641790494093640979042918020345647.3	x^21 - 325x^14 - 221897x^7 + 62748517	\( -\,7^{35}\cdot 13^{18} \)	$F_7$ (as 21T4)	$[2, 2, 2]$ (GRH)
21.3.2099320095095383219362534880897373365668616194446503.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 3384x^16 - 22661x^15 + 85004x^14 - 409885x^13 - 188418x^12 - 2604021x^11 - 6603224x^10 + 30173537x^9 - 75034142x^8 - 399264676x^7 + 477537789x^6 + 583377214x^5 - 1978514300x^4 + 979864648x^3 + 3374286608x^2 - 5170051936x + 2015987008	\( -\,7^{17}\cdot 113^{18} \)	$F_7$ (as 21T4)	$[7]$ (GRH)
21.3.17184371679714375406342276014583508152741413197410183.1	x^21 - 7x^20 + 21x^19 - 34x^18 - 860x^17 + 4693x^16 - 12259x^15 - 14067x^14 + 37681x^13 - 3477004x^12 + 389109x^11 + 23235788x^10 - 37794391x^9 + 399984668x^8 + 105257496x^7 - 6303984553x^6 + 3887930312x^5 + 9054965094x^4 - 95684899751x^3 + 28879725259x^2 + 175769815592x - 322494640909	\( -\,7^{17}\cdot 127^{18} \)	$F_7$ (as 21T4)	$[7]$ (GRH)
21.3.2374450721934441204800704599474362981402341385467744663.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 9692x^16 + 37133x^15 - 111234x^14 - 306733x^13 + 2227436x^12 - 15927429x^11 + 48390428x^10 - 36546963x^9 - 117158588x^8 - 3295825882x^7 + 13211621361x^6 - 7267451240x^5 - 59139292492x^4 + 73337235104x^3 + 87604194608x^2 - 76802664064x - 146043093056	\( -\,7^{17}\cdot 167^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.79725153240997641482803881969926742124712205514640391823.1	x^21 - 25955x^14 - 81483649x^7 - 17249876309	\( -\,7^{35}\cdot 29^{18} \)	$F_7$ (as 21T4)	$[7]$ (GRH)
21.3.159864073705644817826866721926705417106647399937729252767.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 12232x^16 - 36395x^15 + 28738x^14 - 856933x^13 - 5891416x^12 + 24379691x^11 - 5679616x^10 + 73289981x^9 - 350840512x^8 - 12471465894x^7 + 5267658761x^6 + 83230171864x^5 + 22083422172x^4 - 43889160896x^3 - 214646951456x^2 - 858652083072x + 745947224512	\( -\,7^{17}\cdot 211^{18} \)	$F_7$ (as 21T4)	$[7, 7, 7]$ (GRH)
21.3.432667441118225293081744612251055070987538949548395174983.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 6696x^16 + 39331x^15 - 66028x^14 - 967981x^13 + 7864242x^12 - 17206833x^11 - 16939676x^10 + 352134365x^9 - 809756522x^8 - 16153054924x^7 + 78811833717x^6 + 8157442846x^5 - 535267042184x^4 + 402334865128x^3 + 1100178148832x^2 - 2037042160384x - 256310093312	\( -\,7^{17}\cdot 223^{18} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.3637421813338787913991133669958840202605967577382248356207.1	x^21 - 7x^20 + 21x^19 - 34x^18 - 1728x^17 + 8277x^16 - 26511x^15 + 228637x^14 - 2299843x^13 + 43252952x^12 - 358447607x^11 + 1629066924x^10 - 4992150763x^9 + 6624085180x^8 - 9335801376x^7 + 136223349179x^6 - 270952034724x^5 + 131571710354x^4 - 3552798817939x^3 + 6818751637159x^2 + 1165451658700x + 7016855542291	\( -\,7^{17}\cdot 251^{18} \)	$F_7$ (as 21T4)	$[2, 2, 2]$ (GRH)
21.3.58922863816834248701730948403017453588761267745332101431343.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 17000x^16 + 76879x^15 + 25168x^14 - 3960985x^13 - 7944166x^12 + 40651037x^11 + 81259502x^10 - 506512648x^9 - 2778664855x^8 - 84195862092x^7 + 400745644202x^6 + 655623718393x^5 - 7349761489371x^4 + 529795117999x^3 + 53152215171034x^2 - 12893672008602x - 131863811763929	\( -\,7^{17}\cdot 293^{18} \)	$F_7$ (as 21T4)	$[7, 7]$ (GRH)
21.3.95689349211490968068273743174738670497010473255536509295007.1	x^21 - 89483x^14 + 103438607x^7 + 271818611107	\( -\,7^{35}\cdot 43^{18} \)	$F_7$ (as 21T4)	$[7]$ (GRH)
21.3.6055813052022442741267437386720431302520208823407199686319727.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 5335x^17 - 68226x^16 + 370487x^15 - 976238x^14 + 9992983x^13 - 167147434x^12 + 1254295567x^11 - 5119024426x^10 + 16406088995x^9 - 124794841242x^8 + 1235524808890x^7 - 7765632654107x^6 + 28259771083054x^5 - 48713312542188x^4 - 12644866212328x^3 + 193183257790096x^2 - 276127419440096x + 122588921675584	\( -\,7^{17}\cdot 379^{18} \)	$F_7$ (as 21T4)	$[7, 7, 7, 7, 7]$ (GRH)
21.3.639931573735145678269077305601948179707569066438710730266948047.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 42220x^16 - 238849x^15 + 507776x^14 - 9461221x^13 + 30949290x^12 - 118397153x^11 + 849128436x^10 + 3360629141x^9 - 17534305986x^8 - 639064890904x^7 - 84897810087x^6 + 8605795373014x^5 + 21486789774576x^4 - 76273061749528x^3 - 178475909056704x^2 + 177581658222976x + 629094860366336	\( -\,7^{17}\cdot 491^{18} \)	$F_7$ (as 21T4)	n/a
21.3.2803860759981050190158681909505960217064638670151364262388173263.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 30908x^16 - 227299x^15 + 331614x^14 - 11256581x^13 - 100744748x^12 + 250586819x^11 - 1122038804x^10 + 8083253229x^9 - 7342418196x^8 - 1136578032834x^7 + 596900678473x^6 + 16991239839504x^5 - 27591656221276x^4 - 9543020500384x^3 + 370902066797360x^2 - 862711219086080x - 660800505832768	\( -\,7^{17}\cdot 13^{18}\cdot 41^{18} \)	$F_7$ (as 21T4)	$[14, 14, 14]$ (GRH)
21.3.13238447676394874558196094904430889210811997401754826436629096687.1	x^21 - 57851x^14 + 30304711x^7 + 27136050989627	\( -\,7^{35}\cdot 83^{18} \)	$F_7$ (as 21T4)	n/a
21.3.24344854108509137895346177549498986990410149857662202745929382807.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 34864x^16 - 57451x^15 + 891810x^14 - 16216613x^13 + 111348616x^12 - 1168389061x^11 + 7475278120x^10 - 2937883611x^9 - 48950465208x^8 - 1285942710366x^7 + 6911521990801x^6 - 1175582555784x^5 - 35643871943428x^4 - 19183703267008x^3 - 9595175213344x^2 - 215779097824640x - 84881631489088	\( -\,7^{17}\cdot 601^{18} \)	$F_7$ (as 21T4)	n/a
21.3.39066061807525750900462785203767943376542499971141582990405683063.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 53056x^16 - 387753x^15 + 1715360x^14 - 20945477x^13 - 106972970x^12 - 574361697x^11 - 3215159260x^10 + 18233746589x^9 - 44219027574x^8 - 1367906097928x^7 - 307347689851x^6 + 10689969421306x^5 - 11010699170856x^4 - 17385833768968x^3 + 157072709296608x^2 - 428208522920192x + 293698546559488	\( -\,7^{17}\cdot 617^{18} \)	$F_7$ (as 21T4)	n/a
21.3.2057504513883865290828006783622225388610315551093969843772003838087.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 66140x^16 + 197181x^15 + 519746x^14 - 38250611x^13 + 728885410x^12 - 5190026793x^11 + 29182239326x^10 - 68615906434x^9 + 126081016179x^8 - 6211611183364x^7 + 23232341812268x^6 + 42625508333359x^5 + 56176184509851x^4 - 383224347675253x^3 - 3177193347653934x^2 - 1410935175422024x + 6295917838747831	\( -\,7^{17}\cdot 769^{18} \)	$F_7$ (as 21T4)	n/a
21.3.27983264514794111999474435672403673823086010489813254087627154702167.1	x^21 - 1173353x^14 - 82982043713x^7 - 532875860165503	\( -\,7^{35}\cdot 127^{18} \)	$F_7$ (as 21T4)	n/a
21.3.698659295573481696443702685323246063670561579560848034212460416254103.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 150952x^16 + 1091081x^15 - 1885902x^14 - 82474679x^13 + 1782947986x^12 - 8271270553x^11 + 14713958422x^10 + 36609721794x^9 - 157374528081x^8 - 29032774648716x^7 + 146378771353312x^6 + 403041892117935x^5 - 1511275454987137x^4 + 2913800887665479x^3 - 25119733760908906x^2 - 90692100544127768x + 135973981979723027	\( -\,7^{17}\cdot 1063^{18} \)	$F_7$ (as 21T4)	n/a
21.3.14693654444550188334618410219169833396067319235696680397949255095300047.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 - 214036x^16 + 1591903x^15 - 8455612x^14 - 78804229x^13 + 2442806710x^12 - 18581839787x^11 + 108000335718x^10 - 222335916920x^9 + 284300561201x^8 - 44833968691560x^7 + 248434219855942x^6 + 39614286391869x^5 - 1260636204184623x^4 + 2502989432053803x^3 - 12369631255580718x^2 - 62218052737609482x - 26412654578702301	\( -\,7^{17}\cdot 1259^{18} \)	$F_7$ (as 21T4)	n/a