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
18.2.79129515469685653504.1	x^18 - 3x^16 + x^14 + 8x^12 - 20x^10 + 25x^8 - 17x^6 + 5x^4 + 2x^2 - 1	\( 2^{18}\cdot 7^{6}\cdot 37^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial
18.2.970168002150400000000.1	x^18 - 7x^16 + 23x^14 - 44x^12 + 46x^10 - 19x^8 + 31x^6 - 15x^4 + 4x^2 - 1	\( 2^{24}\cdot 5^{8}\cdot 23^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial
18.2.3266763321003968139264.1	x^18 - x^17 + 2x^16 - 12x^15 + 7x^14 + 7x^13 + 60x^12 - 7x^11 - 10x^10 - 97x^9 - 10x^8 - 7x^7 + 60x^6 + 7x^5 + 7x^4 - 12x^3 + 2x^2 - x + 1	\( 2^{12}\cdot 3^{12}\cdot 107^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial
18.2.15034518472210440781824.1	x^18 + x^12 - 1	\( 2^{18}\cdot 3^{18}\cdot 23^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial
18.6.962209182221468210036736.1	x^18 - 18x^16 + 135x^14 - 536x^12 + 1167x^10 - 1242x^8 + 297x^6 + 324x^4 - 64	\( 2^{24}\cdot 3^{18}\cdot 23^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.6.5768629464666860572114944.1	x^18 - 18x^16 + 135x^14 - 540x^12 + 1215x^10 - 1458x^8 + 745x^6 - 96x^4 + 144x^2 - 64	\( 2^{24}\cdot 3^{18}\cdot 31^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.6.13380662562832253498425344.1	x^18 - 7x^16 - 6x^15 - 5x^14 - 14x^13 + 42x^12 + 112x^11 - 94x^10 + 266x^9 - 447x^8 + 158x^7 - 207x^6 + 118x^5 + 181x^4 - 72x^3 - 20x^2 - 10x + 1	\( 2^{24}\cdot 3^{12}\cdot 107^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial
18.6.239272477618363922259221151744.1	x^18 - 14x^16 + 14x^14 + 343x^12 + 1176x^10 - 15435x^8 - 3087x^6 + 120050x^4 + 84035x^2 - 117649	\( 2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 67^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.6.539140130893112269326400000000.1	x^18 - 3x^17 - 8x^16 - 8x^15 + 147x^14 + 29x^13 - 640x^12 + 613x^11 - 3104x^10 + 7689x^9 - 160x^8 - 21097x^7 + 42574x^6 - 50637x^5 + 42545x^4 - 24556x^3 + 8980x^2 - 1705x - 125	\( 2^{12}\cdot 5^{8}\cdot 7^{8}\cdot 197^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.6.778072968681250317161459613696.1	x^18 - 24x^16 - 4x^15 + 261x^14 + 108x^13 - 1604x^12 - 1152x^11 + 6225x^10 + 7744x^9 - 12690x^8 - 29208x^7 - 6671x^6 + 27936x^5 + 31944x^4 + 13632x^3 + 1440x^2 - 576x - 128	\( 2^{30}\cdot 3^{24}\cdot 37^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.18.1503855547469708539369307904147456.1	x^18 - 8x^17 - 34x^16 + 406x^15 + 5x^14 - 7212x^13 + 10378x^12 + 54168x^11 - 126883x^10 - 165800x^9 + 611032x^8 + 53790x^7 - 1264603x^6 + 612252x^5 + 830632x^4 - 718892x^3 + 140512x^2 + 9184x - 3136	\( 2^{20}\cdot 3^{14}\cdot 7^{10}\cdot 101^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)
18.18.2208317976138187855160934400000000.1	x^18 - 36x^16 + 419x^14 - 2155x^12 + 5331x^10 - 6514x^8 + 3808x^6 - 959x^4 + 71x^2 - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{8}\cdot 197^{6} \)	$C_3:S_3:S_4$ (as 18T154)	Trivial (GRH)