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 9 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.2954312706550833698643.3	x^18 - 6x^15 + 24x^12 - 74x^9 + 150x^6 + 12x^3 + 1	\( -\,3^{45} \)	$He_3:C_2$ (as 18T21)	Trivial
18.0.11727564985436483639043.1	x^18 - 3x^16 - 6x^15 + 6x^14 + 15x^13 - 6x^12 - 24x^11 - 3x^10 + 43x^9 + 54x^8 - 24x^7 - 12x^6 - 42x^5 + 12x^4 + 15x^3 + 6x^2 + 3x + 1	\( -\,3^{25}\cdot 7^{12} \)	$He_3:C_2$ (as 18T21)	$[3]$
18.0.12100864846032214829641728.2	x^18 - 6x^15 - 18x^14 - 3x^12 + 126x^11 + 288x^10 + 34x^9 + 378x^8 - 540x^7 - 363x^6 + 18x^5 + 540x^4 - 852x^3 + 1224x^2 - 828x + 193	\( -\,2^{12}\cdot 3^{45} \)	$He_3:C_2$ (as 18T21)	Trivial
18.18.70720374548224359605005470978048.1	x^18 - 6x^17 - 24x^16 + 208x^15 + 12x^14 - 2394x^13 + 3125x^12 + 10464x^11 - 24564x^10 - 9916x^9 + 63708x^8 - 28836x^7 - 53993x^6 + 47538x^5 + 8760x^4 - 17236x^3 + 1836x^2 + 1794x - 377	\( 2^{12}\cdot 3^{24}\cdot 7^{8}\cdot 13^{9} \)	$He_3:C_2$ (as 18T21)	$[3]$ (GRH)
18.18.178698494132131643847952616411136.1	x^18 - 9x^17 - 9x^16 + 264x^15 - 288x^14 - 2916x^13 + 5598x^12 + 14526x^11 - 39159x^10 - 27383x^9 + 128403x^8 - 17730x^7 - 188268x^6 + 110070x^5 + 90900x^4 - 76710x^3 - 9855x^2 + 13041x - 623	\( 2^{12}\cdot 3^{37}\cdot 7^{13} \)	$He_3:C_2$ (as 18T21)	Trivial (GRH)
18.0.2954312706550833698643000000000000.1	x^18 - 60x^15 + 360x^14 + 1401x^12 - 14400x^11 + 39600x^10 - 22700x^9 + 193320x^8 - 864000x^7 + 1154967x^6 - 1699200x^5 + 5724000x^4 - 1375800x^3 - 17377920x^2 - 1368000x + 154736383	\( -\,2^{12}\cdot 3^{45}\cdot 5^{12} \)	$He_3:C_2$ (as 18T21)	$[3, 3, 3]$ (GRH)
18.0.13266257117930788904129800273932288.4	x^18 - 48x^15 + 1944x^12 - 28944x^9 + 409536x^6 + 2099520x^3 + 34012224	\( -\,2^{12}\cdot 3^{33}\cdot 17^{12} \)	$He_3:C_2$ (as 18T21)	$[3, 3, 9]$ (GRH)
18.0.50396986113842071567939653456703488.12	x^18 - 60x^15 + 1752x^12 - 33120x^9 + 265824x^6 + 1073088x^3 + 1259712	\( -\,2^{12}\cdot 3^{33}\cdot 19^{12} \)	$He_3:C_2$ (as 18T21)	$[3, 3, 9]$ (GRH)
18.0.149893238403862212943036837746306920448.5	x^18 - 258x^15 + 67464x^12 + 235656x^9 + 364176x^6 + 1555200x^3 + 2985984	\( -\,2^{12}\cdot 3^{33}\cdot 37^{12} \)	$He_3:C_2$ (as 18T21)	$[3, 3, 9]$ (GRH)