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
21.3.8666156601021353004160055862582708672653223.1	x^21 - 72x^14 - 435x^7 + 1	\( -\,3^{28}\cdot 7^{35} \)	$C_3\times F_7$ (as 21T9)	$[2, 546]$ (GRH)
21.3.2803860759981050190158681909505960217064638670151364262388173263.1	x^21 - 7x^20 + 21x^19 - 34x^18 + 29x^17 + 30908x^16 - 227299x^15 + 331614x^14 - 11256581x^13 - 100744748x^12 + 250586819x^11 - 1122038804x^10 + 8083253229x^9 - 7342418196x^8 - 1136578032834x^7 + 596900678473x^6 + 16991239839504x^5 - 27591656221276x^4 - 9543020500384x^3 + 370902066797360x^2 - 862711219086080x - 660800505832768	\( -\,7^{17}\cdot 13^{18}\cdot 41^{18} \)	$F_7$ (as 21T4)	$[14, 14, 14]$ (GRH)