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
18.6.36644198070556426025390625.1	x^18 - 12x^15 + 36x^14 - 33x^12 + 117x^11 - 171x^10 - 2x^9 + 135x^8 - 81x^7 - 30x^6 + 36x^5 + 81x^4 - 393x^3 + 531x^2 - 270x + 44	\( 3^{36}\cdot 5^{12} \)	$C_3^2:S_3.C_2$ (as 18T49)	Trivial (GRH)
18.6.36644198070556426025390625.2	x^18 - 12x^15 + 9x^14 + 54x^13 - 18x^12 + 72x^11 - 261x^10 - 14x^9 + 135x^8 - 270x^7 + 840x^6 - 1116x^5 + 1269x^4 - 1026x^3 + 576x^2 - 252x + 49	\( 3^{36}\cdot 5^{12} \)	$C_3^2:S_3.C_2$ (as 18T49)	Trivial (GRH)
18.18.16096057926792443193781494140625.1	x^18 - 6x^17 - 18x^16 + 141x^15 + 108x^14 - 1227x^13 - 438x^12 + 5220x^11 + 1956x^10 - 11198x^9 - 5475x^8 + 11283x^7 + 6315x^6 - 5184x^5 - 3051x^4 + 930x^3 + 552x^2 - 24x - 16	\( 3^{26}\cdot 5^{12}\cdot 11^{10} \)	$C_3^2:S_3.C_2$ (as 18T49)	Trivial (GRH)
18.18.1303780692070187898696301025390625.1	x^18 - 3x^17 - 63x^16 + 147x^15 + 1245x^14 - 1968x^13 - 9306x^12 + 9264x^11 + 28194x^10 - 15305x^9 - 31773x^8 + 6729x^7 + 13914x^6 - 786x^5 - 2355x^4 + 57x^3 + 144x^2 - 6x - 1	\( 3^{30}\cdot 5^{12}\cdot 11^{10} \)	$C_3^2:S_3.C_2$ (as 18T49)	Trivial (GRH)