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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1357192521131719482421875.1	x^18 - 3x^17 + 9x^16 - 18x^15 + 36x^14 - 81x^13 + 144x^12 - 378x^11 + 765x^10 - 1164x^9 + 2070x^8 - 2997x^7 + 3186x^6 - 3294x^5 + 2997x^4 - 1917x^3 + 1053x^2 - 540x + 144	\( -\,3^{33}\cdot 5^{12} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	Trivial
18.0.6785962605658597412109375.1	x^18 - 6x^17 + 21x^16 - 66x^15 + 195x^14 - 471x^13 + 897x^12 - 1500x^11 + 2334x^10 - 3010x^9 + 2928x^8 - 2337x^7 + 1545x^6 - 57x^5 - 1326x^4 + 1068x^3 - 24x^2 - 240x + 64	\( -\,3^{33}\cdot 5^{13} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[2]$
18.2.54226471004352000000000000.1	x^18 - 6x^17 + 6x^16 + 36x^15 - 93x^14 - 48x^13 + 468x^12 - 648x^11 + 105x^10 + 730x^9 - 1515x^8 + 2658x^7 - 3384x^6 + 1992x^5 + 471x^4 - 1116x^3 + 162x^2 + 264x - 47	\( 2^{18}\cdot 3^{25}\cdot 5^{12} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	Trivial
18.2.271132355021760000000000000.1	x^18 + 15x^16 + 57x^14 - 18x^13 + 6x^12 - 132x^11 - 21x^10 + 74x^9 - 273x^8 + 54x^7 + 150x^6 - 66x^5 + 132x^4 + 108x^3 + 54x^2 + 18x + 1	\( 2^{18}\cdot 3^{25}\cdot 5^{13} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[2]$
18.0.10490752768731680375385103017603.1	x^18 + 36x^16 + 486x^14 + 3123x^12 + 10017x^10 + 15795x^8 + 12420x^6 + 4698x^4 + 729x^2 + 27	\( -\,3^{37}\cdot 13^{12} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[27]$ (GRH)
18.0.136379785993511844880006339228839.1	x^18 - 9x^17 + 90x^16 - 516x^15 + 2727x^14 - 10773x^13 + 37410x^12 - 105237x^11 + 255627x^10 - 516022x^9 + 885375x^8 - 1260243x^7 + 1486950x^6 - 1418553x^5 + 1073547x^4 - 618753x^3 + 255672x^2 - 67293x + 8272	\( -\,3^{37}\cdot 13^{13} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[3, 36]$ (GRH)
18.18.2820436287545773260125000000000000.1	x^18 - x^17 - 49x^16 + 50x^15 + 825x^14 - 811x^13 - 6474x^12 + 5979x^11 + 25635x^10 - 21240x^9 - 51109x^8 + 33299x^7 + 50891x^6 - 18700x^5 - 24960x^4 + 720x^3 + 4900x^2 + 1300x + 100	\( 2^{12}\cdot 5^{15}\cdot 41^{12} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[3]$ (GRH)
18.18.115637887789376703665125000000000000.1	x^18 - 5x^17 - 42x^16 + 155x^15 + 740x^14 - 1705x^13 - 7075x^12 + 7640x^11 + 38470x^10 - 5760x^9 - 113412x^8 - 61340x^7 + 150504x^6 + 184160x^5 - 14440x^4 - 142160x^3 - 99600x^2 - 28960x - 3120	\( 2^{12}\cdot 5^{15}\cdot 41^{13} \)	$C_2\times C_3:S_3.C_2$ (as 18T27)	$[6]$ (GRH)