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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.3.571298992310032855209.1	x^15 - 4x^14 + 12x^13 - 24x^12 + 35x^11 - 66x^10 + 91x^9 - 93x^8 + 174x^7 - 76x^6 + 180x^5 - 85x^4 + 61x^3 - 61x^2 - 17x - 1	\( 3^{5}\cdot 11^{4}\cdot 107^{7} \)	15T40	Trivial
15.3.8364388546411191033114969.1	x^15 - 6x^14 + 33x^13 - 125x^12 + 309x^11 - 531x^10 + 628x^9 - 378x^8 - 204x^7 + 673x^6 - 657x^5 + 333x^4 - 64x^3 - 27x^2 + 15x + 1	\( 3^{5}\cdot 11^{8}\cdot 107^{7} \)	15T40	Trivial
15.15.163182013910625833582031250000000000.1	x^15 - 175x^13 - 150x^12 + 8100x^11 + 13476x^10 - 112175x^9 - 214350x^8 + 573440x^7 + 1242740x^6 - 862375x^5 - 2510850x^4 - 427285x^3 + 563840x^2 - 88100x + 3524	\( 2^{10}\cdot 5^{18}\cdot 37^{5}\cdot 881^{4} \)	15T40	Trivial (GRH)
15.15.2101141399534246351499964130000000000.1	x^15 - 7x^14 - 297x^13 + 3108x^12 + 11225x^11 - 198002x^10 + 134362x^9 + 3284150x^8 - 2555513x^7 - 25199016x^6 + 139474x^5 + 73214629x^4 + 42035037x^3 - 35952686x^2 - 18776851x + 981137	\( 2^{10}\cdot 5^{10}\cdot 19^{12}\cdot 37^{7} \)	15T40	Trivial (GRH)
15.5.464317130069216763190044343471527099609375.1	x^15 - 1870x^12 - 32010x^11 + 777876x^10 - 6851625x^9 + 30190710x^8 - 74603760x^7 + 2486105930x^6 - 13069638582x^5 - 50184822600x^4 - 124388611655x^3 + 1660824701580x^2 + 7902686294580x + 5476184846968	\( -\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7} \)	15T40	$[5, 5, 5]$ (GRH)
15.5.464317130069216763190044343471527099609375.2	x^15 - 330x^13 - 4620x^12 + 12650x^11 + 1106633x^10 + 4277350x^9 - 70074125x^8 - 1077527385x^7 + 10086284725x^6 + 100194176808x^5 + 168219899100x^4 - 16147355822675x^3 - 69620528681495x^2 + 79865978259705x + 368982332191957	\( -\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7} \)	15T40	$[5, 5, 5]$ (GRH)
15.1.505587397847240362501152000000000000000000.1	x^15 - 15x^13 - 30x^12 + 75x^11 + 2880x^10 - 36275x^9 - 455490x^8 + 794220x^7 + 7999460x^6 - 29685606x^5 - 73095900x^4 + 981089960x^3 + 5043879720x^2 + 10724525400x + 9378358624	\( -\,2^{23}\cdot 3^{20}\cdot 5^{18}\cdot 1459^{4} \)	15T40	$[15]$ (GRH)
15.1.2290959479641121893981744591147824672000000000000000000.1	x^15 + 105x^13 - 5640x^12 - 157785x^11 + 1914312x^10 + 332396675x^9 - 2590483680x^8 - 83929544010x^7 - 85198013200x^6 + 3532946629590x^5 - 2532704653800x^4 - 265590632403700x^3 - 1765231283268600x^2 - 5044667439936000x - 6241061091507200	\( -\,2^{23}\cdot 3^{20}\cdot 5^{18}\cdot 1459^{8} \)	15T40	$[15]$ (GRH)