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 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.71418001746108874752.1	x^18 - 2x^17 - x^16 + 2x^15 + 2x^14 + 2x^13 + 2x^12 - 18x^11 + 20x^10 + 6x^9 - 30x^7 + 54x^6 - 62x^5 + 62x^4 - 50x^3 + 27x^2 - 8x + 1	\( -\,2^{18}\cdot 3^{9}\cdot 7^{12} \)	$C_3\times S_4$ (as 18T30)	Trivial
18.0.2426051245220667850752.1	x^18 + 3x^16 - 11x^12 - 24x^10 - 6x^8 + 64x^6 + 96x^4 + 48x^2 + 8	\( -\,2^{33}\cdot 3^{24} \)	$C_3\times S_4$ (as 18T30)	Trivial
18.6.14824161510814728000000000.1	x^18 - 3x^17 - 3x^16 + 21x^15 - 33x^14 - 75x^13 + 162x^12 + 183x^11 - 114x^10 + 63x^9 + 285x^8 + 255x^7 + 240x^6 + 114x^5 + 168x^4 + 147x^3 + 12x^2 + 15x + 1	\( 2^{12}\cdot 3^{32}\cdot 5^{9} \)	$C_3\times S_4$ (as 18T30)	Trivial
18.6.45672975569536652017399733.1	x^18 - 3x^17 + 5x^16 - 11x^15 - 38x^14 + 126x^13 - 232x^12 + 539x^11 - 326x^10 - 845x^9 + 1726x^8 - 3000x^7 + 6144x^6 - 2419x^5 - 4313x^4 + 7814x^3 - 8884x^2 - 3258x - 419	\( 7^{12}\cdot 53^{9} \)	$C_3\times S_4$ (as 18T30)	Trivial
18.18.34811183694905557468330328064.1	x^18 - 9x^17 + 186x^15 - 288x^14 - 1332x^13 + 2631x^12 + 4608x^11 - 9063x^10 - 8983x^9 + 13797x^8 + 9882x^7 - 9111x^6 - 5535x^5 + 2250x^4 + 1488x^3 - 81x^2 - 135x - 17	\( 2^{33}\cdot 3^{39} \)	$C_3\times S_4$ (as 18T30)	Trivial (GRH)
18.18.4556898638363530990028531552256.1	x^18 - 3x^17 - 54x^16 + 39x^15 + 1062x^14 + 876x^13 - 7833x^12 - 13659x^11 + 19524x^10 + 58964x^9 + 6090x^8 - 83943x^7 - 59961x^6 + 20367x^5 + 28668x^4 + 1902x^3 - 3390x^2 - 420x + 19	\( 2^{12}\cdot 3^{31}\cdot 23^{9} \)	$C_3\times S_4$ (as 18T30)	Trivial (GRH)