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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.11569850838123915570577408.1	x^20 - 6x^19 + 26x^18 - 76x^17 + 196x^16 - 406x^15 + 768x^14 - 1210x^13 + 1773x^12 - 2182x^11 + 2502x^10 - 2324x^9 + 2084x^8 - 1198x^7 + 1278x^6 + 584x^5 + 1948x^4 + 1966x^3 + 3238x^2 + 1738x + 2213	\( 2^{30}\cdot 220873^{3} \)	20T1022	Trivial (GRH)
20.2.12643669953134424130859375.1	x^20 - x^19 + 5x^18 + 8x^17 - x^16 + 31x^15 + 53x^14 - 79x^13 + 251x^12 - 99x^11 - 19x^10 + 404x^9 - 301x^8 + 171x^7 + 184x^6 - 97x^5 + 23x^4 + 100x^3 - 30x^2 - 4x - 1	\( -\,5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T1022	Trivial (GRH)
20.6.12643669953134424130859375.2	x^20 - 6x^19 + 17x^18 - 26x^17 - x^16 + 108x^15 - 316x^14 + 596x^13 - 778x^12 + 593x^11 + 141x^10 - 1079x^9 + 1334x^8 - 706x^7 - 89x^6 + 406x^5 - 337x^4 + 144x^3 - 33x^2 - x + 1	\( -\,5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T1022	Trivial (GRH)
20.0.3149070808568813267726079513.1	x^20 - 6x^19 + 13x^18 - 10x^17 - 14x^16 + 160x^15 - 434x^14 + 683x^13 - 967x^12 - 870x^11 + 6845x^10 - 13758x^9 + 29955x^8 - 41275x^7 + 50182x^6 - 94915x^5 + 84960x^4 - 27434x^3 + 82905x^2 + 7751x + 21061	\( 3^{10}\cdot 37^{3}\cdot 109^{3}\cdot 241^{5} \)	20T1022	Trivial (GRH)
20.4.9700708256022096688369140625.1	x^20 - x^19 - 10x^18 + 12x^17 + 43x^16 - 22x^15 - 357x^14 + 349x^13 + 1009x^12 - 333x^11 - 5079x^10 + 3434x^9 + 9295x^8 + 201x^7 - 27900x^6 + 16553x^5 + 14016x^4 - 18410x^3 - 210x^2 + 11975x + 3725	\( 5^{10}\cdot 199^{5}\cdot 1471^{3} \)	20T1022	Trivial (GRH)
20.10.203483763895883268631630859375.1	x^20 - 2x^19 - 23x^18 + 65x^17 + 131x^16 - 605x^15 + 131x^14 + 2165x^13 - 3133x^12 - 2441x^11 + 10512x^10 - 4943x^9 - 14841x^8 + 19019x^7 + 7904x^6 - 24322x^5 + 18x^4 + 14615x^3 - 1589x^2 - 2902x + 619	\( -\,5^{10}\cdot 27517559^{3} \)	20T1022	Trivial (GRH)
20.4.224790888456601610240000000000.1	x^20 - 20x^16 + 76x^14 + 90x^12 - 1852x^10 + 2154x^8 + 5515x^6 - 44476x^4 + 280001	\( 2^{20}\cdot 5^{10}\cdot 280001^{3} \)	20T1022	Trivial (GRH)
20.4.2179984560030696704042470703125.1	x^20 - 5x^19 + 16x^18 - 28x^17 + 7x^16 + 88x^15 - 181x^14 + 263x^13 + 152x^12 - 1268x^11 + 2296x^10 - 1109x^9 + 2666x^8 + 12546x^7 + 1372x^6 - 9571x^5 - 16045x^4 - 3379x^3 + 3725x^2 - 1074x + 2309	\( 5^{10}\cdot 60662149^{3} \)	20T1022	Trivial (GRH)
20.8.2179984560030696704042470703125.1	x^20 - 4x^19 - 12x^18 + 55x^17 + 16x^16 - 278x^15 + 211x^14 + 520x^13 - 617x^12 - 156x^11 - 963x^10 + 1894x^9 + 6819x^8 - 10810x^7 - 11511x^6 + 19668x^5 + 3528x^4 - 12445x^3 + 4377x^2 + 100x - 244	\( 5^{10}\cdot 60662149^{3} \)	20T1022	Trivial (GRH)
20.2.13257848864777881917440000000000.1	x^20 - 20x^18 + 215x^16 - 1334x^14 + 3750x^12 + 12104x^10 - 131906x^8 + 311575x^6 + 276812x^4 - 1568255x^2 - 1089911	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T1022	$[5]$ (GRH)
20.6.13257848864777881917440000000000.1	x^20 - 6x^18 - 18x^16 + 342x^14 - 2619x^12 + 6954x^10 - 9606x^8 + 193990x^6 - 1035092x^4 + 1895136x^2 - 1089911	\( -\,2^{20}\cdot 5^{10}\cdot 1039^{3}\cdot 1049^{3} \)	20T1022	Trivial (GRH)
20.4.19867324198595974862892094631712900390625.1	x^20 - 4x^19 + 120x^18 - 455x^17 + 2959x^16 - 15417x^15 - 126061x^14 - 215365x^13 - 5912224x^12 - 11246243x^11 - 43052462x^10 - 319740577x^9 + 1019228952x^8 + 10583460950x^7 + 89634505875x^6 + 650613452731x^5 + 3108087294944x^4 + 11858163795028x^3 + 30961063038531x^2 + 66656193013587x + 125053657678981	\( 5^{10}\cdot 4588681^{5} \)	20T1022	$[4]$ (GRH)
20.8.692690229709114777272320000000000000000000000.1	x^20 - 80x^16 - 2400x^14 - 15105x^12 + 315400x^10 - 346600x^8 - 11759900x^6 + 93816450x^4 - 231354400x^2 + 167811200	\( 2^{57}\cdot 5^{22}\cdot 17^{10} \)	20T1022	$[2]$ (GRH)
20.0.78130637554327275128616443231859804160000000000.1	x^20 + 529x^18 + 138365x^16 + 22839038x^14 + 2068594443x^12 + 87853088411x^10 + 3672413853363x^8 + 361572835120248x^6 + 15138792734705123x^4 + 184040238341354934x^2 + 676348299686920069	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 199^{5}\cdot 401^{5} \)	20T1022	$[2, 2, 2, 4]$ (GRH)
20.2.1729797948719255084072017529251001251840000000000.1	x^20 + 538x^18 + 59526x^16 - 8411745x^14 - 1395371322x^12 + 9530036138x^10 + 8603288846964x^8 + 351613585853425x^6 - 1875817034507589x^4 - 321799222643246666x^2 - 4337852776485437971	\( -\,2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 1630891^{5} \)	20T1022	n/a
20.2.161565819652412899832686999834204280821760000000000.1	x^20 + 1215x^18 + 511759x^16 + 17027900x^14 - 63291398882x^12 - 26248097666138x^10 - 5251386273851037x^8 - 601902913742794431x^6 - 39929780990644264941x^4 - 1419239447710082479566x^2 - 20836737422938446707879	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{5} \)	20T1022	n/a
20.0.19031596686524690994504794774570696832010240000000000.1	x^20 - 2047x^18 + 895458x^16 + 491864356x^14 - 205994049190x^12 - 70140281045427x^10 + 8237200478417331x^8 + 4647879416771177895x^6 + 551837397237621960474x^4 + 24788321856472354874337x^2 + 364338580053661358017501	\( 2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 349^{5}\cdot 10771^{5} \)	20T1022	n/a
20.4.56048985368357082097694845902442652817568000000000000000.1	x^20 + 2998x^18 - 590506x^16 - 9158944433x^14 - 9101711382939x^12 - 2415557541551610x^10 + 545904341348455920x^8 + 333331964079477992575x^6 + 47773773343213035028450x^4 + 2520112834651844975036250x^2 + 43950182127057497055453625	\( 2^{20}\cdot 5^{15}\cdot 1039^{5}\cdot 67931^{5} \)	20T1022	n/a