Global number field search results

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

Results (displaying all 4 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.9.1115970269016553289813936756281.1	x^21 - 2x^20 - 10x^19 + 31x^18 - 24x^17 - 152x^16 + 288x^15 + 7x^14 - 127x^13 + 465x^12 - 466x^11 + 1998x^10 + 1430x^9 + 2635x^8 + 613x^7 - 570x^6 - 1087x^5 - 669x^4 + 195x^3 + 193x^2 + 93x - 53	\( 13^{16}\cdot 109^{6} \)	$C_3\times \PSL(2,7)$ (as 21T22)	Trivial (GRH)
21.9.1115970269016553289813936756281.2	x^21 - x^20 - 12x^19 + 8x^18 + 49x^17 - 14x^16 - 94x^15 + 123x^14 - 7x^13 - 1078x^12 + 1150x^11 + 1019x^10 - 4414x^9 + 6562x^8 + 4203x^7 - 14456x^6 + 3035x^5 + 9936x^4 - 5649x^3 - 1996x^2 + 1631x - 79	\( 13^{16}\cdot 109^{6} \)	$C_3\times \PSL(2,7)$ (as 21T22)	Trivial (GRH)
21.21.204156663640790261439595720457863561216.1	x^21 - 2x^20 - 38x^19 + 69x^18 + 568x^17 - 933x^16 - 4319x^15 + 6417x^14 + 18052x^13 - 24428x^12 - 41833x^11 + 52044x^10 + 51770x^9 - 58979x^8 - 31596x^7 + 30977x^6 + 9259x^5 - 5733x^4 - 1455x^3 + 114x^2 + 17x - 1	\( 2^{30}\cdot 7^{14}\cdot 809^{6} \)	$C_3\times \PSL(2,7)$ (as 21T22)	Trivial (GRH)
21.21.204156663640790261439595720457863561216.2	x^21 - 40x^19 - 8x^18 + 579x^17 + 128x^16 - 4024x^15 - 828x^14 + 14642x^13 + 3152x^12 - 29068x^11 - 6976x^10 + 31979x^9 + 8240x^8 - 19278x^7 - 4888x^6 + 6120x^5 + 1376x^4 - 924x^3 - 168x^2 + 48x + 8	\( 2^{30}\cdot 7^{14}\cdot 809^{6} \)	$C_3\times \PSL(2,7)$ (as 21T22)	Trivial (GRH)