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 matches 1-50 of 52)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.121260259409849938345984.3	x^20 - 4x^18 + 11x^16 - 12x^14 + 6x^12 + 16x^10 - 18x^8 + 20x^6 + x^4 - 4x^2 - 1	\( -\,2^{28}\cdot 277^{6} \)	20T792	Trivial (GRH)
20.2.150406265394937853264896.1	x^20 - 4x^18 - 2x^17 + 8x^16 + 11x^15 - 31x^14 + 17x^13 + 37x^12 - 55x^11 + 36x^9 - 58x^8 + 19x^7 + 58x^6 - 14x^5 - 22x^4 - x^3 + x^2 + x - 1	\( -\,2^{10}\cdot 2297^{6} \)	20T792	Trivial (GRH)
20.4.4813000492638011304476672.1	x^20 - 10x^18 + 43x^16 - 103x^14 + 155x^12 - 173x^10 + 160x^8 - 100x^6 - 32x^4 + 32x^2 + 32	\( 2^{15}\cdot 2297^{6} \)	20T792	Trivial (GRH)
20.0.455219958061240788416233472.1	x^20 - 7x^18 + 26x^16 - 51x^14 + 65x^12 - 75x^10 + 130x^8 - 204x^6 + 208x^4 - 112x^2 + 32	\( 2^{15}\cdot 4903^{6} \)	20T792	Trivial (GRH)
20.0.4928512504461323575784112128.1	x^20 + 4x^18 + x^16 - 23x^14 - 47x^12 - 73x^10 + 126x^8 + 572x^6 + 568x^4 + 224x^2 + 32	\( 2^{25}\cdot 2297^{6} \)	20T792	Trivial (GRH)
20.4.4928512504461323575784112128.1	x^20 - 8x^18 + 38x^16 - 141x^14 + 374x^12 - 657x^10 + 748x^8 - 564x^6 + 304x^4 - 128x^2 + 32	\( 2^{25}\cdot 2297^{6} \)	20T792	Trivial (GRH)
20.0.4928512504461323575784112128.2	x^20 + 11x^18 + 63x^16 + 230x^14 + 569x^12 + 943x^10 + 974x^8 + 580x^6 + 248x^4 + 128x^2 + 32	\( 2^{25}\cdot 2297^{6} \)	20T792	Trivial (GRH)
20.8.34626601325138198966564814848.1	x^20 - 16x^18 + 106x^16 - 374x^14 + 753x^12 - 870x^10 + 580x^8 - 236x^6 + 28x^4 - 16x^2 + 8	\( 2^{43}\cdot 89^{8} \)	20T792	Trivial (GRH)
20.8.34626601325138198966564814848.2	x^20 - 16x^18 + 113x^16 - 458x^14 + 1161x^12 - 1882x^10 + 1912x^8 - 1148x^6 + 380x^4 - 72x^2 + 8	\( 2^{43}\cdot 89^{8} \)	20T792	Trivial (GRH)
20.0.34626601325138198966564814848.3	x^20 + 16x^18 + 113x^16 + 458x^14 + 1161x^12 + 1882x^10 + 1912x^8 + 1148x^6 + 380x^4 + 72x^2 + 8	\( 2^{43}\cdot 89^{8} \)	20T792	Trivial (GRH)
20.0.34626601325138198966564814848.4	x^20 + 16x^18 + 106x^16 + 374x^14 + 753x^12 + 870x^10 + 580x^8 + 236x^6 + 28x^4 + 16x^2 + 8	\( 2^{43}\cdot 89^{8} \)	20T792	Trivial (GRH)
20.0.177631157333929848863937527808.1	x^20 - 5x^18 + 14x^16 - 41x^14 + 225x^12 - 605x^10 + 732x^8 - 380x^6 + 64x^4 - 32x^2 + 32	\( 2^{25}\cdot 3^{16}\cdot 223^{6} \)	20T792	Trivial (GRH)
20.0.177631157333929848863937527808.2	x^20 + 4x^18 + 8x^16 + 25x^14 + 54x^12 + 79x^10 + 180x^8 + 184x^6 + 184x^4 + 64x^2 + 32	\( 2^{25}\cdot 3^{16}\cdot 223^{6} \)	20T792	Trivial (GRH)
20.0.177631157333929848863937527808.3	x^20 + x^18 - 7x^16 + 7x^14 + 18x^12 - 53x^10 + 36x^8 + 28x^6 - 56x^4 + 16x^2 + 32	\( 2^{25}\cdot 3^{16}\cdot 223^{6} \)	20T792	Trivial (GRH)
20.4.1465621300755332525247833251953125.1	x^20 - x^19 - 4x^18 - 13x^17 - 25x^16 - 41x^15 - 86x^14 - 178x^13 - 104x^12 - 50x^11 + 360x^10 + 55x^9 + 350x^8 - 405x^7 + 410x^6 - 350x^5 + 325x^4 - 400x^3 + 250x^2 - 150x + 25	\( 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.8.1465621300755332525247833251953125.1	x^20 - 4x^19 + 4x^18 - 14x^17 - 19x^16 + 165x^15 - 62x^13 - 2018x^12 + 6061x^11 - 11172x^10 + 15863x^9 - 10645x^8 - 5970x^7 + 12319x^6 + 4286x^5 - 20194x^4 + 13941x^3 - 1481x^2 - 1175x + 115	\( 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.10.1512596110450216901523541586560000.1	x^20 - 8x^18 - 28x^16 + 177x^14 + 480x^12 - 373x^10 - 1061x^8 + 306x^6 + 525x^4 - 77x^2 - 9	\( -\,2^{10}\cdot 5^{4}\cdot 36497^{6} \)	20T792	Trivial (GRH)
20.10.1512596110450216901523541586560000.2	x^20 - 3x^18 - 79x^16 + 129x^14 + 1849x^12 - 1062x^10 - 12883x^8 - 6015x^6 + 391x^4 + 320x^2 - 9	\( -\,2^{10}\cdot 5^{4}\cdot 36497^{6} \)	20T792	Trivial (GRH)
20.4.36640532518883313131195831298828125.1	x^20 - 9x^19 + 21x^18 + 67x^17 - 516x^16 + 1340x^15 - 1757x^14 + 724x^13 + 2773x^12 - 10994x^11 + 23618x^10 - 31140x^9 + 26929x^8 - 23202x^7 + 27266x^6 - 19836x^5 - 4569x^4 + 16445x^3 - 5010x^2 - 4815x + 2665	\( 5^{17}\cdot 6029^{6} \)	20T792	$[2, 2]$ (GRH)
20.8.36640532518883313131195831298828125.1	x^20 - 8x^19 + 21x^18 - 47x^17 + 84x^16 + 271x^15 - 601x^14 + 687x^13 - 3054x^12 - 6047x^11 + 5281x^10 - 24x^9 + 10188x^8 + 43649x^7 + 3542x^6 - 43104x^5 - 17217x^4 + 5879x^3 + 2352x^2 - 179x - 49	\( 5^{17}\cdot 6029^{6} \)	20T792	$[2, 2]$ (GRH)
20.0.1732130950652108498309514155453770033.1	x^20 - 4x^19 + 44x^18 - 201x^17 + 936x^16 - 3955x^15 + 13078x^14 - 38360x^13 + 131063x^12 - 199166x^11 + 783658x^10 - 864273x^9 + 1769921x^8 - 3519863x^7 + 111799x^6 - 3876224x^5 + 12202264x^4 + 21517674x^3 + 41684221x^2 + 33419335x + 20136811	\( 61^{6}\cdot 97^{5}\cdot 397^{6} \)	20T792	$[2]$ (GRH)
20.4.1732130950652108498309514155453770033.1	x^20 - 5x^19 + 13x^18 + 2x^17 + 44x^16 + 7x^15 + 43x^14 + 3262x^13 + 1243x^12 - 1035x^11 + 15927x^10 + 30420x^9 + 9124x^8 - 199793x^7 - 166999x^6 + 688157x^5 + 537134x^4 - 1085808x^3 - 893488x^2 + 520727x + 446933	\( 61^{6}\cdot 97^{5}\cdot 397^{6} \)	20T792	Trivial (GRH)
20.0.4077952207063102833961955803138980864.1	x^20 - 7x^19 + 41x^18 - 170x^17 + 629x^16 - 1513x^15 + 4385x^14 - 8216x^13 + 16171x^12 - 14388x^11 + 47814x^10 + 76332x^9 + 132366x^8 + 362904x^7 + 354558x^6 + 562643x^5 + 661900x^4 + 447544x^3 + 684270x^2 + 258768x + 328239	\( 2^{10}\cdot 3^{24}\cdot 7^{6}\cdot 79^{9} \)	20T792	$[2]$ (GRH)
20.4.4077952207063102833961955803138980864.1	x^20 - 9x^19 + 51x^18 - 241x^17 + 347x^16 + 2310x^15 - 14871x^14 + 55324x^13 - 155288x^12 + 351923x^11 - 783138x^10 + 1516694x^9 - 1932499x^8 + 1616791x^7 - 1858545x^6 + 3229947x^5 - 3603968x^4 + 2067065x^3 - 523404x^2 + 32886x - 1687	\( 2^{10}\cdot 3^{24}\cdot 7^{6}\cdot 79^{9} \)	20T792	Trivial (GRH)
20.4.4077952207063102833961955803138980864.2	x^20 - 3x^19 - 9x^18 - 36x^17 - 40x^16 + 1281x^15 + 3528x^14 - 8745x^13 - 48932x^12 - 40878x^11 + 152064x^10 + 569790x^9 + 1176838x^8 + 1366674x^7 - 985131x^6 - 7684281x^5 - 15714352x^4 - 18256686x^3 - 12925395x^2 - 5071794x - 761411	\( 2^{10}\cdot 3^{24}\cdot 7^{6}\cdot 79^{9} \)	20T792	Trivial (GRH)
20.4.4077952207063102833961955803138980864.3	x^20 - 9x^19 + 39x^18 - 130x^17 - 46x^16 + 2109x^15 - 3448x^14 - 3044x^13 - 3224x^12 + 14501x^11 - 4760x^10 - 6985x^9 + 30865x^8 - 3605x^7 - 34213x^6 - 7929x^5 - 20710x^4 - 35695x^3 - 20130x^2 - 2505x + 31	\( 2^{10}\cdot 3^{24}\cdot 7^{6}\cdot 79^{9} \)	20T792	Trivial (GRH)
20.0.36701569863567925505657602228250827776.1	x^20 - 9x^19 + 58x^18 - 298x^17 + 1359x^16 - 5545x^15 + 20061x^14 - 64749x^13 + 192270x^12 - 524678x^11 + 1308351x^10 - 2925404x^9 + 5998134x^8 - 11078268x^7 + 18359979x^6 - 25867084x^5 + 30022761x^4 - 26119411x^3 + 16783114x^2 - 5690010x + 1991149	\( 2^{10}\cdot 3^{26}\cdot 7^{6}\cdot 79^{9} \)	20T792	$[2, 2]$ (GRH)
20.4.36701569863567925505657602228250827776.1	x^20 - 10x^19 + 53x^18 - 141x^17 + 279x^16 - 1035x^15 + 4394x^14 - 2186x^13 - 44057x^12 + 135940x^11 - 173437x^10 + 35093x^9 + 569138x^8 - 1725083x^7 + 2394022x^6 - 1741290x^5 + 631698x^4 - 67251x^3 - 26814x^2 + 10542x - 1329	\( 2^{10}\cdot 3^{26}\cdot 7^{6}\cdot 79^{9} \)	20T792	$[2]$ (GRH)
20.0.36701569863567925505657602228250827776.2	x^20 + 51x^18 + 900x^16 + 7460x^14 + 44808x^12 + 116202x^10 + 21895x^8 - 157653x^6 + 1366068x^4 + 5055210x^2 + 4437351	\( 2^{10}\cdot 3^{26}\cdot 7^{6}\cdot 79^{9} \)	20T792	$[2, 2]$ (GRH)
20.4.599022102118389088243636118689873050397.1	x^20 - 5x^19 + 3x^18 + 105x^17 - 46x^16 - 590x^15 + 4988x^14 + 515x^13 - 6615x^12 + 21964x^11 + 5969x^10 + 156325x^9 - 2130133x^8 + 3555590x^7 - 14109793x^6 + 21121843x^5 - 57181560x^4 + 119955788x^3 - 62037064x^2 + 199399280x - 222407968	\( 13^{13}\cdot 97^{2}\cdot 347^{8} \)	20T792	$[2, 2, 4]$ (GRH)
20.0.1536248413078669172228161404553498984448.1	x^20 + 92x^18 + 3910x^16 + 100969x^14 + 1720880x^12 + 19740109x^10 + 150942702x^8 + 742339744x^6 + 2190048840x^4 + 3414091920x^2 + 2099120288	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	$[2, 4]$ (GRH)
20.12.1536248413078669172228161404553498984448.1	x^20 - 34x^18 + 158x^16 + 8709x^14 - 134662x^12 + 31087x^10 + 13516974x^8 - 117496492x^6 + 399562688x^4 - 513140784x^2 + 181584800	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	Trivial (GRH)
20.0.1536248413078669172228161404553498984448.2	x^20 - 36x^18 - 467x^16 + 29249x^14 - 218667x^12 - 1917945x^10 + 17764684x^8 + 152218424x^6 + 401056456x^4 + 448187008x^2 + 181584800	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	$[2, 2]$ (GRH)
20.12.1536248413078669172228161404553498984448.2	x^20 - 97x^18 + 3251x^16 - 41309x^14 + 102918x^12 + 652329x^10 - 2776726x^8 - 3070008x^6 + 27702296x^4 - 37090928x^2 + 7263392	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	Trivial (GRH)
20.0.1536248413078669172228161404553498984448.3	x^20 + 19x^18 - 389x^16 - 5238x^14 + 173235x^12 + 3934197x^10 + 33352428x^8 + 146487108x^6 + 348632568x^4 + 415025456x^2 + 181584800	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	$[2, 2]$ (GRH)
20.12.1536248413078669172228161404553498984448.3	x^20 - 114x^18 + 5125x^16 - 122322x^14 + 1714658x^12 - 14458085x^10 + 71168110x^8 - 186941576x^6 + 222464072x^4 - 78051696x^2 + 7263392	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	Trivial (GRH)
20.0.1536248413078669172228161404553498984448.4	x^20 + 86x^18 + 3052x^16 + 59699x^14 + 746450x^12 + 6611147x^10 + 41550500x^8 + 170926636x^6 + 468542464x^4 + 511890528x^2 + 181584800	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	$[2, 2]$ (GRH)
20.12.1536248413078669172228161404553498984448.4	x^20 - 69x^18 + 1475x^16 - 8555x^14 - 26916x^12 - 311583x^10 + 7710224x^8 - 41988252x^6 + 295085304x^4 - 492303184x^2 + 181584800	\( 2^{25}\cdot 61^{9}\cdot 397^{6} \)	20T792	Trivial (GRH)
20.0.1573698888766283323386134528000000000000000.1	x^20 + 118x^18 + 4847x^16 + 78494x^14 + 395639x^12 + 771620x^10 + 671980x^8 + 255350x^6 + 33985x^4 + 810x^2 + 5	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[4, 2964]$ (GRH)
20.12.1573698888766283323386134528000000000000000.1	x^20 - 68x^18 + 946x^16 + 15060x^14 - 412215x^12 + 2198310x^10 + 3630180x^8 - 30380910x^6 - 44084680x^4 + 14024500x^2 + 3125	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.16.1573698888766283323386134528000000000000000.1	x^20 - 10x^19 - 20x^18 + 444x^17 - 976x^16 - 1086x^15 + 8874x^14 - 96892x^13 + 423991x^12 + 103412x^11 - 4839034x^10 + 10102328x^9 + 4472351x^8 - 42902680x^7 + 55364452x^6 - 8823476x^5 - 36540381x^4 + 26209548x^3 + 1106448x^2 - 5759886x + 1170971	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.4.1573698888766283323386134528000000000000000.1	x^20 + 44x^18 - 392x^16 - 45802x^14 - 811216x^12 - 5737870x^10 - 16710835x^8 - 15936160x^6 + 2704550x^4 + 1185460x^2 + 18605	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2, 12]$ (GRH)
20.8.1573698888766283323386134528000000000000000.1	x^20 - 60x^18 + 926x^16 - 1740x^14 - 82851x^12 + 971250x^10 - 4739000x^8 + 11032730x^6 - 8282560x^4 - 6225980x^2 + 4675445	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.12.1573698888766283323386134528000000000000000.2	x^20 - 24x^18 - 692x^16 + 14592x^14 + 54704x^12 - 2093120x^10 + 10440640x^8 - 6575360x^6 - 46650880x^4 + 57113600x^2 + 1479680	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.16.1573698888766283323386134528000000000000000.2	x^20 - 64x^18 + 858x^16 + 12552x^14 - 242251x^12 - 504290x^10 + 12051880x^8 - 26972430x^6 + 20315340x^4 - 5140000x^2 + 262205	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.4.1573698888766283323386134528000000000000000.2	x^20 + 56x^18 - 40x^17 + 418x^16 + 256x^15 - 12528x^14 + 7152x^13 - 10256x^12 + 168320x^11 + 1858096x^10 + 4196096x^9 - 3159072x^8 - 56532608x^7 - 101853504x^6 + 125400896x^5 + 1020137072x^4 + 2614386304x^3 + 3601583424x^2 + 3332373376x + 1112892896	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2, 2]$ (GRH)
20.8.1573698888766283323386134528000000000000000.2	x^20 - 10x^19 + 58x^18 + 98x^17 - 1319x^16 - 1612x^15 + 10716x^14 + 7198x^13 + 18958x^12 - 85574x^11 - 158274x^10 - 64134x^9 + 730917x^8 + 1590992x^7 - 4526036x^6 + 271408x^5 + 5280429x^4 - 3426440x^3 + 1178700x^2 - 569000x + 133225	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[4]$ (GRH)
20.4.1573698888766283323386134528000000000000000.3	x^20 + 34x^18 + 53x^16 - 7882x^14 - 81016x^12 - 168780x^10 + 511955x^8 + 1183990x^6 + 751455x^4 + 172570x^2 + 12005	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2, 2]$ (GRH)
20.8.1573698888766283323386134528000000000000000.3	x^20 + 8x^18 - 1054x^16 - 7710x^14 + 295855x^12 + 1997460x^10 - 19325825x^8 - 60641840x^6 + 284653495x^4 + 45854450x^2 + 666125	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2]$ (GRH)
20.4.1573698888766283323386134528000000000000000.4	x^20 - 8x^18 - 350x^16 + 3394x^14 + 10679x^12 - 179100x^10 - 533765x^8 - 3852120x^6 - 841405x^4 - 20830x^2 + 245	\( 2^{30}\cdot 5^{15}\cdot 6029^{6} \)	20T792	$[2, 2]$ (GRH)