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 both matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.44993926732918647221096386680603027343750000000000.1	x^15 - 49225x^10 + 1533984375x^5 - 714892578125	\( -\,2^{10}\cdot 5^{28}\cdot 11^{13}\cdot 509^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5, 360]$ (GRH)
15.15.2368379989452191012928309708195070432434082031250000000000.1	x^15 - 11275x^13 - 124025x^12 + 45081960x^11 + 891723965x^10 - 76578988200x^9 - 2216106307965x^8 + 44485161759555x^7 + 2079870790777010x^6 + 8195553887899983x^5 - 457716480374582000x^4 - 5640651315561778120x^3 + 1700941616424112590x^2 + 316610688507343605265x + 1257096395450004601701	\( 2^{10}\cdot 3^{5}\cdot 5^{25}\cdot 11^{13}\cdot 41^{13} \)	$S_3 \times C_5$ (as 15T4)	$[5, 5, 55]$ (GRH)