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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.140546066200987919382387150626943.1	x^21 - 6x^20 + 12x^19 + 3x^18 - 60x^17 + 108x^16 - 18x^15 - 225x^14 + 357x^13 - 89x^12 - 387x^11 + 522x^10 - 121x^9 - 312x^8 + 315x^7 - 47x^6 - 108x^5 + 75x^4 - 8x^3 - 12x^2 + 6x - 1	\( -\,3^{18}\cdot 23^{7}\cdot 10322161^{2} \)	21T156	Trivial (GRH)
21.3.171648210515488829655228363467583.1	x^21 - 6x^20 + 12x^19 + 5x^18 - 66x^17 + 108x^16 + 6x^15 - 261x^14 + 345x^13 - 11x^12 - 453x^11 + 474x^10 - 33x^9 - 336x^8 + 279x^7 - 19x^6 - 108x^5 + 69x^4 - 6x^3 - 12x^2 + 6x - 1	\( -\,3^{18}\cdot 7^{4}\cdot 23^{7}\cdot 232801^{2} \)	21T156	Trivial (GRH)
21.9.23171591614509185999699336548662164736.1	x^21 - 6x^20 + 12x^19 + 4x^18 - 63x^17 + 108x^16 - 10x^15 - 243x^14 + 363x^13 - 59x^12 - 435x^11 + 519x^10 - 66x^9 - 336x^8 + 297x^7 - 29x^6 - 108x^5 + 72x^4 - 7x^3 - 12x^2 + 6x - 1	\( 2^{8}\cdot 3^{18}\cdot 229^{7}\cdot 241^{2}\cdot 349^{2} \)	21T156	Trivial (GRH)
21.9.117718325734535571649220304350791680000.1	x^21 - 6x^20 + 12x^19 + 5x^18 - 66x^17 + 108x^16 + 3x^15 - 261x^14 + 354x^13 - 17x^12 - 462x^11 + 492x^10 - 24x^9 - 345x^8 + 279x^7 - 16x^6 - 108x^5 + 69x^4 - 6x^3 - 12x^2 + 6x - 1	\( 2^{14}\cdot 3^{18}\cdot 5^{4}\cdot 37^{7}\cdot 559081^{2} \)	21T156	Trivial (GRH)
21.7.273490175308145649218316559765231007672934873279971520512.1	x^21 - 2x^20 - 54x^19 + 135x^18 + 1157x^17 - 3586x^16 - 11893x^15 + 48699x^14 + 49421x^13 - 358369x^12 + 92229x^11 + 1341255x^10 - 1573377x^9 - 1749879x^8 + 4607869x^7 - 1997427x^6 - 2688590x^5 + 3784011x^4 - 2037535x^3 + 590098x^2 - 105404x + 11177	\( -\,2^{12}\cdot 23^{7}\cdot 79397^{2}\cdot 174007^{2}\cdot 320532929081^{2} \)	21T156	Trivial (GRH)
21.7.755870767257884461296368938259663318174024298914692856768.1	x^21 - x^20 - 18x^19 - 3x^18 + 331x^17 - 538x^16 - 2964x^15 + 3682x^14 + 20931x^13 - 41558x^12 - 62536x^11 + 203841x^10 + 8690x^9 - 80214x^8 + 106730x^7 - 255609x^6 + 173098x^5 - 478605x^4 - 347452x^3 + 14115x^2 - 174087x - 60237	\( -\,2^{6}\cdot 23^{7}\cdot 3484502293^{2}\cdot 16902292269377^{2} \)	21T156	Trivial (GRH)
21.21.10180793702309956451402616388520823146632889469649989663981568.1	x^21 - 4x^20 - 62x^19 + 189x^18 + 1681x^17 - 3408x^16 - 25763x^15 + 27349x^14 + 238657x^13 - 54441x^12 - 1321059x^11 - 619089x^10 + 3989997x^9 + 4432703x^8 - 4738321x^7 - 10274281x^6 - 2570366x^5 + 6167033x^4 + 5960453x^3 + 2161528x^2 + 310542x + 8117	\( 2^{18}\cdot 37^{7}\cdot 109^{2}\cdot 18169^{2}\cdot 40897^{2}\cdot 249727200731^{2} \)	21T156	Trivial (GRH)
21.21.33892626352023444868618939918566086658794963687233335938252800.1	x^21 - 8x^20 - 46x^19 + 443x^18 + 633x^17 - 9908x^16 + 1593x^15 + 113179x^14 - 126711x^13 - 670395x^12 + 1329837x^11 + 1638285x^10 - 5996879x^9 + 1362401x^8 + 10533483x^7 - 11794543x^6 - 70574x^5 + 7974959x^4 - 5871123x^3 + 1812636x^2 - 236758x + 9175	\( 2^{18}\cdot 5^{2}\cdot 37^{7}\cdot 3907^{2}\cdot 1889135899773996787^{2} \)	21T156	Trivial (GRH)