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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.236549479975054182819.1	x^18 - 2x^17 + 3x^16 - 4x^15 + 6x^14 - 6x^13 + 4x^12 - 4x^9 + 3x^8 - 3x^7 + 6x^6 + 3x^5 + 4x^4 + 4x^3 + 3x^2 + 1	\( -\,3^{9}\cdot 23^{6}\cdot 433^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.4.734206470812912109375.1	x^18 + 3x^16 - 3x^14 - 3x^13 + 6x^12 - 21x^11 + 21x^10 + 2x^9 - 27x^8 + 48x^7 - 36x^6 + 6x^5 + 15x^4 - 21x^3 + 15x^2 - 6x + 1	\( -\,3^{24}\cdot 5^{9}\cdot 11^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.4.3703509525672326171875.1	x^18 - 3x^17 + 2x^16 - x^15 - 4x^14 + 10x^13 - 5x^12 - 7x^11 - 15x^10 + 21x^9 + 8x^8 - 19x^7 - 12x^6 + 11x^5 + 11x^4 - 4x^3 - 3x^2 + 7x + 1	\( -\,5^{9}\cdot 31^{7}\cdot 41^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.2.4047139580139001953125.1	x^18 - x^17 + x^16 - 2x^15 + 7x^14 - 2x^13 + 3x^12 - 7x^11 + 10x^10 + 2x^9 + 6x^8 - 3x^7 - 7x^6 + 4x^5 - 2x^4 + 5x^3 - 3x^2 - 1	\( 5^{9}\cdot 23^{6}\cdot 241^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.0.9476762676643233792000.1	x^18 - 6x^17 + 18x^16 - 30x^15 + 27x^14 - 24x^13 + 126x^12 - 510x^11 + 1257x^10 - 2158x^9 + 2772x^8 - 2754x^7 + 2145x^6 - 1308x^5 + 618x^4 - 222x^3 + 60x^2 - 12x + 2	\( -\,2^{28}\cdot 3^{24}\cdot 5^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.2.13453464775849822265625.1	x^18 - 3x^17 + 12x^16 - 15x^15 + 36x^14 - 24x^13 + 75x^12 - 27x^11 + 69x^10 - 44x^9 + 45x^8 - 27x^7 + 15x^6 - 12x^5 + 9x^4 + 3x^3 + 9x^2 - 1	\( 3^{24}\cdot 5^{9}\cdot 29^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.0.5975336823211392744554496.1	x^18 - 3x^17 + 6x^16 - 3x^15 - 18x^14 + 24x^13 + 63x^12 - 27x^11 - 54x^10 - 47x^9 - 99x^8 + 9x^7 + 171x^6 + 222x^5 + 330x^4 + 207x^3 + 144x^2 + 42x + 14	\( -\,2^{19}\cdot 3^{24}\cdot 7^{9} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.6.10927177744449669001953125.1	x^18 - 3x^17 + 2x^16 - 13x^15 + 24x^14 + 8x^13 + 61x^12 - 46x^11 - 228x^10 - 49x^9 - 30x^8 + 473x^7 + 722x^6 - 528x^5 - 887x^4 + 103x^3 + 306x^2 + 56x - 31	\( 5^{9}\cdot 59^{7}\cdot 131^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial
18.6.11919189767769141150744576.1	x^18 - 6x^16 - 6x^15 + 24x^14 + 36x^13 - 33x^12 - 84x^11 - 114x^10 + 280x^9 + 408x^8 - 804x^7 - 597x^6 + 1044x^5 + 354x^4 - 1002x^3 - 594x^2 + 24x + 41	\( 2^{33}\cdot 3^{24}\cdot 17^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.0.96873331012983000000000000.1	x^18 - 6x^17 + 15x^16 - 15x^15 + 18x^14 - 72x^13 + 147x^12 - 399x^11 + 849x^10 - 901x^9 + 822x^8 - 597x^7 - 6x^6 - 387x^5 + 2007x^4 - 2679x^3 + 1716x^2 - 564x + 79	\( -\,2^{12}\cdot 3^{24}\cdot 5^{12}\cdot 7^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.12.1089427651175529674612670464.1	x^18 - 4x^17 - 16x^16 + 72x^15 + 60x^14 - 464x^13 + 30x^12 + 1376x^11 - 344x^10 - 2424x^9 + 736x^8 + 2400x^7 - 904x^6 - 1168x^5 + 600x^4 + 224x^3 - 160x^2 + 8	\( -\,2^{33}\cdot 37^{6}\cdot 367^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.12.1997957520642764463811854336.1	x^18 - 12x^16 - 12x^15 - 12x^14 + 24x^13 + 144x^12 - 96x^11 + 72x^10 + 320x^9 - 864x^8 - 48x^7 + 804x^6 - 384x^5 + 144x^3 - 96x^2 + 8	\( -\,2^{33}\cdot 3^{24}\cdot 7^{7} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.6.7444172137965405517922697216.1	x^18 - 6x^16 - 12x^15 + 15x^14 + 56x^12 + 180x^11 - 126x^10 - 272x^9 - 708x^8 - 24x^7 + 1956x^6 + 384x^5 - 1824x^4 - 1344x^3 + 1152x^2 + 2304x + 768	\( 2^{26}\cdot 3^{21}\cdot 13^{9} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.18.207921161448365080828304162816.1	x^18 - 6x^17 - 17x^16 + 142x^15 + 63x^14 - 1270x^13 + 388x^12 + 5398x^11 - 3598x^10 - 11248x^9 + 10173x^8 + 10424x^7 - 12147x^6 - 2766x^5 + 5745x^4 - 754x^3 - 608x^2 + 80x + 25	\( 2^{33}\cdot 37^{6}\cdot 2113^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.6.913386706821601472305592008704.1	x^18 - 27x^16 - 6x^15 + 204x^14 - 72x^13 - 834x^12 + 1212x^11 + 2619x^10 - 4672x^9 - 3573x^8 + 8226x^7 - 798x^6 - 5520x^5 + 14976x^4 - 11364x^3 - 2208x^2 + 4392x - 956	\( 2^{34}\cdot 3^{25}\cdot 13^{7} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)
18.18.32897258484594691238896111328125.1	x^18 - 43x^16 - 6x^15 + 693x^14 + 185x^13 - 5330x^12 - 1876x^11 + 20823x^10 + 7986x^9 - 40733x^8 - 14559x^7 + 36698x^6 + 11414x^5 - 11235x^4 - 4162x^3 + 95x^2 + 39x + 1	\( 5^{9}\cdot 257^{6}\cdot 3881^{3} \)	$S_3\times S_3\wr C_2$ (as 18T150)	Trivial (GRH)