Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.22687111441835000000000000.1	x^15 + 30x^13 - 10x^12 + 255x^11 - 250x^10 + 100x^9 - 1700x^8 - 3385x^7 + 500x^6 + 11990x^5 + 12550x^4 - 1575x^3 - 15770x^2 - 12600x - 4792	\( -\,2^{12}\cdot 5^{13}\cdot 23^{5}\cdot 89^{3} \)	15T82	Trivial (GRH)
15.1.43519916024000000000000000.1	x^15 + 30x^13 - 10x^12 + 255x^11 - 226x^10 + 400x^9 - 1220x^8 - 625x^7 + 180x^6 + 4438x^5 + 950x^4 - 4495x^3 - 6930x^2 - 2820x - 424	\( -\,2^{18}\cdot 5^{15}\cdot 13^{3}\cdot 19^{5} \)	15T82	Trivial (GRH)
15.5.1260227228582228782433382400.1	x^15 - 7x^14 - 6x^13 + 125x^12 - 97x^11 - 883x^10 + 1522x^9 + 2827x^8 - 14068x^7 - 21146x^6 + 31834x^5 + 78866x^4 + 45191x^3 + 4789x^2 + 60x - 223	\( -\,2^{12}\cdot 5^{2}\cdot 23^{5}\cdot 53^{3}\cdot 113329^{2} \)	15T82	Trivial (GRH)
15.5.7234770832944223158655516672.1	x^15 - 2x^14 - 27x^13 + 66x^12 + 384x^11 - 766x^10 - 4359x^9 + 5278x^8 + 42708x^7 - 56076x^6 - 252571x^5 + 615206x^4 + 442805x^3 - 1963172x^2 + 1900x + 1677206	\( -\,2^{18}\cdot 13^{3}\cdot 19^{5}\cdot 2252389^{2} \)	15T82	Trivial (GRH)
15.3.54509897718560000000000000000.1	x^15 + 30x^13 - 40x^12 + 255x^11 - 888x^10 + 300x^9 - 4560x^8 - 65x^7 + 7840x^6 + 23614x^5 + 16200x^4 - 7135x^3 - 38120x^2 - 33960x - 18064	\( 2^{20}\cdot 5^{16}\cdot 17^{3}\cdot 37^{5} \)	15T82	Trivial (GRH)
15.3.205307886425455460000000000000.1	x^15 + 30x^13 - 70x^12 + 255x^11 - 1266x^10 + 1650x^9 - 2220x^8 + 5765x^7 + 19630x^6 - 69972x^5 + 5400x^4 + 141555x^3 - 86480x^2 - 84420x + 73858	\( 2^{14}\cdot 5^{13}\cdot 23^{6}\cdot 37^{5} \)	15T82	Trivial (GRH)
15.7.449874748329512465067024908812288.1	x^15 - x^14 - 45x^13 - 187x^12 - 215x^11 + 1683x^10 + 6975x^9 + 12185x^8 - 14857x^7 - 41575x^6 + 142641x^5 + 821871x^4 + 1562899x^3 + 1035129x^2 + 89497x - 69121	\( 2^{20}\cdot 13^{4}\cdot 37^{5}\cdot 61^{3}\cdot 30893^{2} \)	15T82	Trivial (GRH)
15.7.1196768921851523490591827382239232.1	x^15 - 5x^14 - 65x^13 + 117x^12 + 2102x^11 + 4902x^10 - 62198x^9 - 170502x^8 + 1255903x^7 + 2178233x^6 - 14942855x^5 - 11450085x^4 + 78014535x^3 + 39062877x^2 - 153874791x - 120960561	\( 2^{24}\cdot 3^{9}\cdot 107^{5}\cdot 137^{3}\cdot 317^{2} \)	15T82	Trivial (GRH)
15.11.288430689287392159449927031844765696.1	x^15 - 4x^14 - 82x^13 + 498x^12 + 4457x^11 - 20812x^10 - 97302x^9 + 419638x^8 + 726751x^7 - 3499132x^6 - 1752538x^5 + 12169158x^4 + 742731x^3 - 17291716x^2 + 715786x + 7403218	\( 2^{20}\cdot 37^{5}\cdot 43^{2}\cdot 139^{2}\cdot 317^{3}\cdot 1867^{2} \)	15T82	Trivial (GRH)
15.15.2250056984849498589655164413542400000.1	x^15 - 4x^14 - 254x^13 + 720x^12 + 24835x^11 - 39488x^10 - 1194256x^9 + 471780x^8 + 29116535x^7 + 18527692x^6 - 324217686x^5 - 460280152x^4 + 1108467941x^3 + 2000962040x^2 - 407455644x - 1153284124	\( 2^{34}\cdot 5^{5}\cdot 37^{5}\cdot 61^{2}\cdot 467^{2}\cdot 863^{2} \)	15T82	Trivial (GRH)
15.11.6726894232542085043013968658644455424.1	x^15 - 6x^14 - 148x^13 + 391x^12 + 6782x^11 + 5664x^10 - 78190x^9 - 247562x^8 - 512976x^7 - 1563298x^6 - 2430874x^5 + 4161024x^4 + 21891109x^3 + 29908420x^2 + 12024364x - 1344637	\( 2^{12}\cdot 13^{3}\cdot 29^{2}\cdot 53^{3}\cdot 229^{5}\cdot 97367^{2} \)	15T82	Trivial (GRH)
15.15.2094858387934572656078862668231684915200.1	x^15 - x^14 - 165x^13 - 243x^12 + 8185x^11 + 18435x^10 - 171625x^9 - 417199x^8 + 1588759x^7 + 3350873x^6 - 5944535x^5 - 6222041x^4 + 7818979x^3 - 971575x^2 - 195583x + 839	\( 2^{20}\cdot 5^{2}\cdot 37^{5}\cdot 61^{3}\cdot 47221^{2}\cdot 47717^{2} \)	15T82	Trivial (GRH)