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
15.5.70908197723388671875.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 374x^5 + 100x^4 + 120x^3 - 50x^2 + 5x - 1	\( -\,5^{15}\cdot 19^{2}\cdot 23^{5} \)	15T68	Trivial
15.5.105716774627685546875.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 376x^5 + 100x^4 + 130x^3 - 50x^2 - 5x + 3	\( -\,5^{15}\cdot 11^{2}\cdot 31^{5} \)	15T68	Trivial
15.1.1196084830291748046875.1	x^15 + 15x^13 + 90x^11 + 275x^9 + 450x^7 + 376x^5 + 130x^3 + 5x - 1	\( -\,5^{15}\cdot 31^{5}\cdot 37^{2} \)	15T68	Trivial
15.1.2003696745086669921875.1	x^15 + 15x^13 + 90x^11 + 275x^9 + 450x^7 + 374x^5 + 120x^3 - 5x - 1	\( -\,5^{15}\cdot 23^{5}\cdot 101^{2} \)	15T68	Trivial (GRH)
15.11.19218853520172119140625.1	x^15 - 15x^13 + 90x^11 - 275x^9 + 450x^7 - 379x^5 + 145x^3 - 20x - 1	\( 5^{15}\cdot 229^{5} \)	15T68	Trivial (GRH)
15.11.34214932039093017578125.1	x^15 - 15x^13 + 90x^11 - x^10 - 275x^9 + 10x^8 + 450x^7 - 35x^6 - 379x^5 + 50x^4 + 145x^3 - 25x^2 - 20x + 3	\( 5^{15}\cdot 257^{5} \)	15T68	Trivial (GRH)
15.7.554751656000000000000000.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 387x^5 + 100x^4 + 185x^3 - 50x^2 - 60x + 8	\( 2^{18}\cdot 5^{15}\cdot 37^{5} \)	15T68	Trivial (GRH)
15.3.603551401169600830078125.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 384x^5 + 100x^4 + 170x^3 - 50x^2 - 45x + 19	\( 3^{2}\cdot 5^{13}\cdot 7^{2}\cdot 257^{5} \)	15T68	Trivial
15.7.936090281689727783203125.1	x^15 - 15x^13 + 90x^11 - 2x^10 - 275x^9 + 20x^8 + 450x^7 - 70x^6 - 380x^5 + 100x^4 + 150x^3 - 50x^2 - 25x + 9	\( 3^{7}\cdot 5^{15}\cdot 107^{5} \)	15T68	Trivial
15.3.15088785029240020751953125.1	x^15 - 15x^13 + 90x^11 - 5x^10 - 275x^9 + 50x^8 + 450x^7 - 175x^6 - 384x^5 + 250x^4 + 170x^3 - 125x^2 - 45x + 37	\( 3^{2}\cdot 5^{15}\cdot 7^{2}\cdot 257^{5} \)	15T68	Trivial
15.15.213074598225018500000000000000.1	x^15 - 40x^13 + 500x^11 - 72x^10 - 2600x^9 + 720x^8 + 6000x^7 - 2480x^6 - 5836x^5 + 3200x^4 + 1620x^3 - 1200x^2 + 160x + 4	\( 2^{14}\cdot 5^{15}\cdot 37^{7}\cdot 67^{2} \)	15T68	Trivial (GRH)
15.15.2893656810637015092296465010514625000000000000.1	x^15 - 680x^13 + 171320x^11 - 119968x^10 - 20002000x^9 + 43344480x^8 + 1125484800x^7 - 4314358400x^6 - 24576836416x^5 + 139423692800x^4 + 63114118080x^3 - 1090492454400x^2 + 290797987840x + 2806200582656	\( 2^{12}\cdot 5^{15}\cdot 19^{5}\cdot 73^{8}\cdot 103^{5} \)	15T68	$[2]$ (GRH)