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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.8173509334225000000.1	x^18 + x^16 - 6x^14 - 5x^12 + 2x^10 + 7x^8 + 18x^6 + 7x^4 - 3x^2 + 1	\( -\,2^{6}\cdot 5^{8}\cdot 83^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial
18.0.54866869729378238464.1	x^18 + 2x^16 + 3x^14 + 4x^12 + 18x^10 + 41x^8 + 53x^6 + 39x^4 + 11x^2 + 1	\( -\,2^{16}\cdot 307^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial
18.6.671400859182742683648.1	x^18 - x^17 - 9x^16 + 9x^15 + 34x^14 - 25x^13 - 65x^12 + 16x^11 + 57x^10 + 48x^9 - 18x^8 - 86x^7 - 9x^6 + 49x^5 + 13x^4 - 11x^3 - 5x^2 + 2x + 1	\( 2^{14}\cdot 3^{9}\cdot 113^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial
18.6.2685603436730970734592.1	x^18 - 4x^17 + x^16 + 7x^15 - 12x^13 + 20x^12 - 37x^11 + 29x^10 + 15x^9 - 5x^8 - 9x^7 - 22x^6 + 27x^5 - 30x^4 + 14x^3 - 3x^2 - x + 1	\( 2^{16}\cdot 3^{9}\cdot 113^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial
18.12.535438019832160469313491712.1	x^18 - 3x^17 - 17x^16 + 61x^15 + 91x^14 - 424x^13 - 219x^12 + 1431x^11 + 374x^10 - 2812x^9 - 406x^8 + 2977x^7 + 282x^6 - 1317x^5 - 200x^4 + 100x^3 + 16x^2 + 17x + 1	\( -\,2^{8}\cdot 3^{17}\cdot 503^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)
18.0.68835522420844686611068124224.1	x^18 - 5x^17 + 22x^16 - 72x^15 + 250x^14 - 614x^13 + 1227x^12 - 1923x^11 + 3257x^10 - 5266x^9 + 6472x^8 - 4339x^7 - 429x^6 + 1253x^5 - 785x^4 - 6372x^3 + 6668x^2 + 400x + 5696	\( -\,2^{6}\cdot 32009^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	$[4]$ (GRH)
18.12.68835522420844686611068124224.1	x^18 - 5x^17 - 19x^16 + 157x^15 - 138x^14 - 1018x^13 + 2248x^12 + 1960x^11 - 9145x^10 + 1080x^9 + 16119x^8 - 6506x^7 - 13454x^6 + 5204x^5 + 5064x^4 - 1088x^3 - 280x^2 + 288x + 32	\( -\,2^{6}\cdot 32009^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)
18.6.3579577017830391873800000000000.1	x^18 - 2x^17 - 11x^16 - 2x^15 + 310x^14 - 405x^13 - 3568x^12 + 9026x^11 + 14204x^10 - 58815x^9 - 15539x^8 + 189202x^7 - 64469x^6 - 273183x^5 + 156303x^4 + 150741x^3 - 81162x^2 - 9963x - 729	\( 2^{12}\cdot 5^{11}\cdot 17^{8}\cdot 37^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)
18.0.281950299835779836358935036821504.1	x^18 + 37x^16 + 542x^14 + 4115x^12 + 17965x^10 + 46965x^8 + 73217x^6 + 64362x^4 + 27348x^2 + 3481	\( -\,2^{18}\cdot 32009^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	$[2, 2, 224]$ (GRH)
18.6.75345346281286616442657800000000000.1	x^18 - 5x^17 - 50x^16 + 287x^15 + 840x^14 - 5401x^13 - 14811x^12 + 89776x^11 + 155150x^10 - 1214856x^9 - 284084x^8 + 10748536x^7 - 11983740x^6 - 43606048x^5 + 107242976x^4 - 5419904x^3 - 197999872x^2 + 214803968x - 99042304	\( 2^{12}\cdot 5^{11}\cdot 37^{6}\cdot 59^{8} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)
18.18.225106712174089155532536320000000000.1	x^18 - 8x^17 - 69x^16 + 742x^15 + 463x^14 - 21374x^13 + 45054x^12 + 180264x^11 - 794484x^10 + 245930x^9 + 3537283x^8 - 6602254x^7 + 1171173x^6 + 8772146x^5 - 10063201x^4 + 2750688x^3 + 2007202x^2 - 1514508x + 284953	\( 2^{18}\cdot 5^{10}\cdot 17^{11}\cdot 37^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)
18.18.1809732592884732626462062694400000000.1	x^18 - 102x^16 - 160x^15 + 3693x^14 + 10566x^13 - 50868x^12 - 218556x^11 + 150759x^10 + 1637522x^9 + 1419528x^8 - 3120024x^7 - 5455849x^6 - 857994x^5 + 2308524x^4 + 626660x^3 - 347892x^2 - 55974x + 17858	\( 2^{18}\cdot 3^{24}\cdot 5^{8}\cdot 29^{3}\cdot 37^{6} \)	$C_2\times (C_3\times A_4):S_3$ (as 18T156)	Trivial (GRH)