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 45 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.7771775074107392.1	x^16 - 6x^15 + 17x^14 - 28x^13 + 26x^12 - 10x^11 - 3x^10 + 2x^9 + x^8 + 6x^7 - 10x^6 + 2x^5 + 6x^4 - 4x^3 - 2x^2 + 2x + 1	\( 2^{16}\cdot 17^{9} \)	$C_4.D_4:C_4$ (as 16T260)	Trivial
16.0.509331051256702042112.1	x^16 - 28x^12 + 374x^8 - 2108x^4 + 4913	\( 2^{32}\cdot 17^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2]$
16.0.2823729921879576880531217.1	x^16 - 5x^15 + 20x^14 - 64x^13 + 175x^12 - 425x^11 + 919x^10 - 1761x^9 + 2532x^8 - 2845x^7 + 2997x^6 - 3154x^5 + 3581x^4 - 3248x^3 + 2377x^2 - 1070x + 213	\( 17^{9}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[10]$ (GRH)
16.0.48154703595510561630166577.2	x^16 + x^14 - x^13 + 48x^12 - 132x^11 + 36x^10 + 132x^9 + 426x^8 - 2193x^7 + 4267x^6 - 5049x^5 + 4012x^4 - 2159x^3 + 748x^2 - 153x + 17	\( 17^{9}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[10]$ (GRH)
16.0.13611751511406706798779957248.1	x^16 + 32x^14 + 416x^12 + 2816x^10 + 10516x^8 + 20800x^6 + 17984x^4 + 2560x^2 + 72	\( 2^{71}\cdot 7^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[218]$ (GRH)
16.16.13611751511406706798779957248.1	x^16 - 32x^14 + 416x^12 - 2816x^10 + 10604x^8 - 22208x^6 + 25024x^4 - 13824x^2 + 2888	\( 2^{71}\cdot 7^{8} \)	$C_4.D_4:C_4$ (as 16T260)	Trivial (GRH)
16.0.13611751511406706798779957248.2	x^16 + 32x^14 + 416x^12 + 2816x^10 + 10604x^8 + 22208x^6 + 25024x^4 + 13824x^2 + 2888	\( 2^{71}\cdot 7^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[130]$ (GRH)
16.16.13611751511406706798779957248.2	x^16 - 32x^14 + 416x^12 - 2816x^10 + 10516x^8 - 20800x^6 + 17984x^4 - 2560x^2 + 72	\( 2^{71}\cdot 7^{8} \)	$C_4.D_4:C_4$ (as 16T260)	Trivial (GRH)
16.0.235840746805304140638847775057.2	x^16 - 8x^15 + 45x^14 - 107x^13 + 261x^12 - 199x^11 + 479x^10 + 5471x^9 - 15947x^8 + 6973x^7 + 98504x^6 - 264952x^5 + 78771x^4 + 150510x^3 + 1483x^2 + 12019x + 62867	\( 17^{13}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 20]$ (GRH)
16.0.1099568479361490150598987419689.2	x^16 - 5x^15 + 32x^14 - 246x^13 + 753x^12 - 2262x^11 + 6443x^10 + 5749x^9 - 50991x^8 + 123309x^7 - 392006x^6 + 333125x^5 + 1091846x^4 - 1121147x^3 + 5869757x^2 - 5886424x + 1545977	\( 11^{12}\cdot 89^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2]$ (GRH)
16.0.4021928999000637617913142677617.7	x^16 - 6x^15 + 18x^14 - 79x^13 + 241x^12 - 744x^11 + 2591x^10 - 4682x^9 + 13197x^8 - 34360x^7 + 62463x^6 - 111143x^5 + 332988x^4 - 223361x^3 + 791589x^2 - 231515x + 1087469	\( 17^{13}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 4]$ (GRH)
16.0.7174452138071971572143971681481.3	x^16 - x^15 - 14x^14 + 51x^13 + 374x^12 - 1690x^11 + 7906x^10 - 41501x^9 + 212754x^8 - 555097x^7 + 2681016x^6 - 4737977x^5 + 22518941x^4 + 2748753x^3 + 166889104x^2 + 120480118x + 21924773	\( 23^{12}\cdot 41^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 12]$ (GRH)
16.0.8885732870807191282905358804417.6	x^16 - 5x^15 - x^14 - 73x^13 + 777x^12 + 214x^11 - 18728x^10 + 53819x^9 + 54019x^8 - 603079x^7 + 1473030x^6 - 2260599x^5 + 4096231x^4 - 8462844x^3 + 11842379x^2 - 8914295x + 2766731	\( 43^{8}\cdot 97^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2]$ (GRH)
16.0.18102079666797893193942794567137.3	x^16 - 7x^15 - 2x^14 + 28x^13 + 965x^12 - 4442x^11 - 2787x^10 + 24342x^9 + 167258x^8 - 671891x^7 - 1306251x^6 + 10502938x^5 - 15131120x^4 - 20454968x^3 + 94305600x^2 - 123625248x + 63451136	\( 47^{8}\cdot 97^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[10]$ (GRH)
16.0.68157975826732896644627006991473.2	x^16 - 8x^15 - 4x^14 + 168x^13 - 205x^12 - 1318x^11 + 2367x^10 + 5204x^9 - 8907x^8 - 18674x^7 + 18339x^6 + 55724x^5 - 20911x^4 - 95056x^3 + 1840x^2 + 61440x + 65536	\( 17^{15}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 32]$ (GRH)
16.0.68157975826732896644627006991473.10	x^16 - x^15 + 18x^14 - 120x^13 + 562x^12 - 2653x^11 + 11578x^10 - 42501x^9 + 182717x^8 - 553249x^7 + 1972426x^6 - 4224297x^5 + 8773684x^4 - 14208448x^3 + 17704192x^2 - 13786253x + 6662675	\( 17^{15}\cdot 47^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 160]$ (GRH)
16.0.257866565806827685775538626393321.1	x^16 - x^15 + 56x^14 + 41x^13 + 1061x^12 + 5462x^11 + 7309x^10 + 65716x^9 + 440098x^8 + 153755x^7 + 351327x^6 + 10670397x^5 + 19279393x^4 - 105270823x^3 + 45856595x^2 - 151471363x + 282885323	\( 31^{12}\cdot 41^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[6]$ (GRH)
16.0.1162337480711184271576898233831313.1	x^16 - 8x^15 - 4x^14 + 168x^13 - 460x^12 + 212x^11 + 2928x^10 - 11626x^9 + 24158x^8 - 33124x^7 + 30188x^6 - 16764x^5 + 10522x^4 - 11892x^3 + 8606x^2 - 2905x + 375	\( 17^{15}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 16]$ (GRH)
16.0.1162337480711184271576898233831313.3	x^16 - 2x^15 + 21x^14 - 212x^13 + 543x^12 - 1341x^11 + 10451x^10 - 37834x^9 + 69939x^8 + 38860x^7 - 175249x^6 - 165231x^5 + 302225x^4 + 508030x^3 - 673612x^2 - 337425x + 991543	\( 17^{15}\cdot 67^{8} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 16]$ (GRH)
16.0.582477092451999490195840776529155641.2	x^16 - 2x^15 + 75x^14 - 375x^13 + 3106x^12 - 4679x^11 - 108941x^10 + 1419676x^9 - 2696526x^8 - 21246331x^7 + 166298404x^6 - 479007815x^5 - 51797314x^4 + 5658707593x^3 - 7312336230x^2 - 32602890292x + 78854279291	\( 41^{9}\cdot 59^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[6]$ (GRH)
16.0.20273287048130392461673121562633432041.6	x^16 - 2x^15 - 26x^14 - 247x^13 + 2357x^12 - 25713x^11 + 160951x^10 - 425048x^9 + 11589258x^8 - 97134971x^7 + 48261497x^6 + 1424825846x^5 + 1551213890x^4 - 39285105450x^3 + 118568037753x^2 - 144221692018x + 64667028003	\( 23^{12}\cdot 41^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 2, 4, 12]$ (GRH)
16.0.34993857500868339818743792665125437721.1	x^16 - 6x^15 - 146x^14 + 822x^13 + 9857x^12 - 34753x^11 - 430991x^10 - 170920x^9 + 7676074x^8 + 35576212x^7 + 165000919x^6 + 661782541x^5 + 1624056654x^4 + 1264951561x^3 + 112953200x^2 + 3583260107x + 27286024997	\( 41^{9}\cdot 83^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[30]$ (GRH)
16.0.68989390528102141148007963042095383049.5	x^16 - 24x^14 - 413x^13 + 2537x^12 - 16062x^11 + 269865x^10 - 1530825x^9 + 8165048x^8 - 65792209x^7 + 251387127x^6 - 992861822x^5 + 5518502641x^4 - 11902179377x^3 + 44950407942x^2 - 211399377596x + 288557906703	\( 11^{12}\cdot 89^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 4]$ (GRH)
16.0.728669284860867208184771804455817142281.6	x^16 - 4x^15 + 28x^14 + 555x^13 + 1002x^12 + 30608x^11 + 82171x^10 + 129865x^9 + 14421522x^8 + 42000027x^7 - 204896052x^6 - 2140918182x^5 - 129649338x^4 + 21789615908x^3 + 168484169151x^2 + 477508143788x + 1291248197075	\( 31^{12}\cdot 41^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 12]$ (GRH)
16.0.786647542210626533905079006002056634177.5	x^16 - 6x^15 - 101x^14 + 850x^13 + 1534x^12 - 35066x^11 + 136101x^10 + 39761x^9 - 3371036x^8 + 14774315x^7 - 18720912x^6 - 13870987x^5 + 345816880x^4 - 2092377208x^3 + 5795387679x^2 - 18442347063x + 36752433199	\( 43^{8}\cdot 97^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 4, 8]$ (GRH)
16.0.966064060320802955505014160902035909033.9	x^16 - 2x^15 - 189x^14 - 1329x^13 + 29338x^12 + 275627x^11 - 1814397x^10 - 29359470x^9 + 74993769x^8 + 2204480747x^7 + 76437998x^6 - 96096389750x^5 + 104869687622x^4 + 3826741307380x^3 + 1482211608009x^2 - 59659550358172x + 85829254185005	\( 71^{12}\cdot 73^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 14]$ (GRH)
16.0.1602564097506337056774549158159344838497.9	x^16 - 8x^15 + 161x^14 - 976x^13 + 10885x^12 - 32407x^11 + 364196x^10 - 237490x^9 + 11234971x^8 - 9476184x^7 + 359119764x^6 - 322810806x^5 + 4917795919x^4 + 8350714193x^3 + 12836643115x^2 + 14829382806x + 321671395988	\( 47^{8}\cdot 97^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 20]$ (GRH)
16.0.2866867967976420459213670979269882298249.1	x^16 - 5x^15 - 97x^14 + 523x^13 + 10072x^12 - 18609x^11 - 823046x^10 + 2446813x^9 + 90584933x^8 + 185231148x^7 - 5102562617x^6 - 34254214176x^5 + 16288721013x^4 + 939964804413x^3 + 4836624820184x^2 + 15396026241748x + 26985991018919	\( 67^{12}\cdot 89^{9} \)	$C_4.D_4:C_4$ (as 16T260)	$[2]$ (GRH)
16.0.546464962373097060033371075256437529131129.2	x^16 - 445x^13 + 6942x^12 - 52866x^11 + 213155x^10 - 1125939x^9 + 8058060x^8 - 48094621x^7 + 168888625x^6 - 116994683x^5 - 374685728x^4 - 2204993690x^3 + 34121567244x^2 - 140857502107x + 182391223777	\( 11^{12}\cdot 89^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 32]$ (GRH)
16.0.546464962373097060033371075256437529131129.7	x^16 - 3x^15 - 260x^14 - 440x^13 + 16099x^12 + 73652x^11 + 586457x^10 + 7217528x^9 + 31631282x^8 + 162727605x^7 + 1300334847x^6 + 4874750016x^5 + 18102947155x^4 + 99957289357x^3 + 250721809619x^2 + 542456662935x + 1934079109825	\( 11^{12}\cdot 89^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 32]$ (GRH)
16.0.1224893067851117776958601403290228616174361.5	x^16 - 2x^15 + 48x^14 - 2242x^13 + 5449x^12 + 91997x^11 + 2833808x^10 + 28541268x^9 + 249012444x^8 + 1583635463x^7 + 8992149138x^6 + 37628617532x^5 + 136700965336x^4 + 330648863904x^3 + 494720800128x^2 + 444135049728x + 190379307008	\( 31^{12}\cdot 41^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 320]$ (GRH)
16.0.1224893067851117776958601403290228616174361.7	x^16 - 2x^15 + 48x^14 + 1407x^13 - 4637x^12 - 125221x^11 - 576572x^10 - 622524x^9 + 21634972x^8 + 250742109x^7 + 1385098477x^6 + 2042810745x^5 - 7327431717x^4 - 35655384702x^3 + 2592547372x^2 + 47330809200x + 227541079872	\( 31^{12}\cdot 41^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 4160]$ (GRH)
16.0.1645941051244254531415289228525803373267801.6	x^16 - 2x^15 + 40x^14 - 219x^13 - 26089x^12 + 290065x^11 + 9936127x^10 + 59571195x^9 - 428796243x^8 - 5933432448x^7 + 11182903017x^6 + 411196014948x^5 + 1496275591245x^4 - 4239496133880x^3 - 28777843094468x^2 + 23625665057905x + 281742122142543	\( 41^{13}\cdot 59^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 60]$ (GRH)
16.0.7401566724659785057512888367473350870971393.5	x^16 - 8x^15 + 30x^14 - 70x^13 + 6928x^12 - 41022x^11 + 20192x^10 + 274360x^9 + 4546826x^8 - 20283562x^7 + 50381510x^6 - 78549692x^5 + 119367930x^4 - 132257608x^3 + 19413309680x^2 - 19356775495x + 162278712581	\( 43^{8}\cdot 97^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 32]$ (GRH)
16.0.7401566724659785057512888367473350870971393.6	x^16 - 2x^15 + 14x^14 - 1156x^13 - 3665x^12 + 28405x^11 + 24577x^10 + 15125453x^9 + 28754614x^8 + 534487532x^7 + 3912204275x^6 - 1279043207x^5 + 170125614243x^4 - 447528584932x^3 + 3007775646743x^2 - 5241373973535x + 2866358222303	\( 43^{8}\cdot 97^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[8, 32]$ (GRH)
16.0.98884277765511220794553278305197522019930681.4	x^16 - 4x^15 + 5x^14 + 2645x^13 + 46435x^12 - 121864x^11 - 15460825x^10 + 60514795x^9 + 1211493195x^8 - 9810178344x^7 + 9233730823x^6 + 175446845335x^5 - 859514035076x^4 - 92057160074x^3 + 13325887212862x^2 - 45824508231069x + 80918703349713	\( 41^{13}\cdot 83^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 12]$ (GRH)
16.0.2766826907141591867309101193151875470463173481.3	x^16 - 4x^15 + 69x^14 - 224x^13 - 17038x^12 - 109940x^11 + 310090x^10 + 15872553x^9 + 111233592x^8 + 352966659x^7 + 472182745x^6 - 4522699120x^5 - 4193139084x^4 + 98354585839x^3 + 353322548342x^2 + 406935393270x + 387255219875	\( 41^{15}\cdot 59^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 4, 16]$ (GRH)
16.0.2766826907141591867309101193151875470463173481.5	x^16 - 6x^15 - 19x^14 + 2442x^13 - 15576x^12 - 644417x^11 + 18522881x^10 - 304305287x^9 + 3194261138x^8 - 23486633086x^7 + 87603516131x^6 + 237616125806x^5 - 2336821044932x^4 - 142328996665x^3 + 15997195291737x^2 + 22845585920160x + 36644678113511	\( 41^{15}\cdot 59^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 2, 2, 16]$ (GRH)
16.0.27434520006428699643943668849708793135373210953.7	x^16 - 3x^15 + 1243x^14 + 544x^13 + 612545x^12 + 1854491x^11 + 160968008x^10 + 783771762x^9 + 23302576816x^8 + 121079233072x^7 + 2150065913720x^6 + 6160562935376x^5 + 65896886115085x^4 + 110526109065100x^3 + 2915744632504734x^2 - 8522534230317664x + 56812866336026263	\( 71^{12}\cdot 73^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 4, 56]$ (GRH)
16.0.166224470923824362155644060831037034515503474761.1	x^16 - 6x^15 - 60x^14 - 3257x^13 + 48712x^12 - 89769x^11 - 3124258x^10 + 48276837x^9 + 79402250x^8 - 1118934092x^7 + 17677601785x^6 + 36052562864x^5 + 142489068976x^4 + 247366851315x^3 + 313772956188x^2 + 374090699762x + 448464248273	\( 41^{15}\cdot 83^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 4, 16]$ (GRH)
16.0.166224470923824362155644060831037034515503474761.6	x^16 - 4x^15 - 259x^14 - 2479x^13 + 75130x^12 + 1956747x^11 + 25630993x^10 + 220167189x^9 + 2277412340x^8 + 32214962714x^7 + 489495293654x^6 + 5568200365384x^5 + 49556273455148x^4 + 319122527760339x^3 + 1553171376434168x^2 + 4893603985587031x + 9312471101944163	\( 41^{15}\cdot 83^{12} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 2, 2, 2, 80]$ (GRH)
16.0.179873720961956854769314815076056959198372636009.5	x^16 - 2x^15 - 74x^14 + 6167x^13 - 120134x^12 + 784396x^11 + 7526907x^10 - 240575709x^9 + 6418777262x^8 - 65084516877x^7 + 955574028589x^6 - 10483386432081x^5 + 56327674930810x^4 - 646734985272706x^3 + 1851579194059094x^2 - 19004907231570663x + 636936648311835307	\( 67^{12}\cdot 89^{13} \)	$C_4.D_4:C_4$ (as 16T260)	$[4, 4]$ (GRH)
16.0.1424779743739660246627742650217447173810309649827289.2	x^16 - 8x^15 + 30x^14 + 6249x^13 + 374025x^12 + 2734522x^11 + 2204199x^10 - 866862815x^9 - 3534340512x^8 - 33095688555x^7 + 681690587107x^6 - 1054372576950x^5 + 42709216585313x^4 - 183630121999979x^3 + 2159497799389466x^2 - 8100247836751296x + 59350353865950707	\( 67^{12}\cdot 89^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 4, 48]$ (GRH)
16.0.1424779743739660246627742650217447173810309649827289.4	x^16 - 6x^15 - 417x^14 + 5113x^13 + 219047x^12 - 4116907x^11 + 73569971x^10 + 1033057887x^9 - 22022514513x^8 + 143085855695x^7 + 1048437250287x^6 - 21501492709695x^5 + 70407651610811x^4 - 3212027220574933x^3 + 68539999241660465x^2 - 372235254486644566x + 683884486037949879	\( 67^{12}\cdot 89^{15} \)	$C_4.D_4:C_4$ (as 16T260)	$[2, 4, 48]$ (GRH)
16.8.6985872701411915091439460916010822936571645898168438313975808.1	x^16 - 8752x^14 - 7200731392x^12 + 36863389517120x^10 + 13611700064197971142x^8 - 7267228884846036391424x^6 - 3384507326332862097584407792x^4 + 11574363150647086989170162447488x^2 + 83142230203097022619741298888816802	\( 2^{71}\cdot 7^{8}\cdot 150513919^{4} \)	$C_4.D_4:C_4$ (as 16T260)	n/a