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
18.2.76848453272063549952000.1	x^18 - 12x^15 + 72x^13 - 63x^12 - 72x^11 + 36x^10 + 88x^9 - 36x^8 - 72x^7 + 63x^6 + 72x^5 - 12x^3 - 1	\( 2^{12}\cdot 3^{36}\cdot 5^{3} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial
18.2.78692816150593075150848.1	x^18 + 9x^16 + 36x^14 + 75x^12 + 36x^10 - 117x^8 - 21x^6 + 54x^4 + 36x^2 - 8	\( 2^{19}\cdot 3^{36} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial
18.0.157385632301186150301696.1	x^18 - 9x^16 + 36x^14 - 69x^12 + 72x^10 - 9x^8 - 165x^6 + 108x^4 + 144x^2 + 64	\( -\,2^{20}\cdot 3^{36} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial
18.0.230545359816190649856000.1	x^18 - 9x^15 + 36x^13 + 45x^12 - 234x^10 - 225x^9 + 252x^8 + 630x^7 + 498x^6 - 756x^5 - 1224x^4 + 252x^3 + 792x^2 + 216x + 24	\( -\,2^{12}\cdot 3^{37}\cdot 5^{3} \)	$C_2\times C_3:S_4$ (as 18T66)	$[2]$
18.12.144433874233348438770904326156288.1	x^18 - 9x^17 + 9x^16 + 120x^15 - 441x^14 + 711x^13 - 612x^12 - 2313x^11 + 10953x^10 - 17092x^9 + 11511x^8 - 1287x^7 - 9777x^6 + 22230x^5 - 21960x^4 + 8988x^3 - 576x^2 - 468x + 76	\( -\,2^{12}\cdot 3^{37}\cdot 23^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial (GRH)
18.12.542180903814533417438934859788288.1	x^18 - 36x^16 + 270x^14 - 234x^13 + 789x^12 + 4914x^11 - 13086x^10 - 30444x^9 + 49734x^8 + 31626x^7 - 263913x^6 + 65610x^5 + 1140426x^4 + 594792x^3 - 1422036x^2 - 1667628x - 493749	\( -\,2^{12}\cdot 3^{33}\cdot 47^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	$[3]$ (GRH)
18.6.2310941987733575020334469218500608.1	x^18 - 36x^15 - 585x^14 + 1728x^13 - 1650x^12 - 5670x^11 + 49131x^10 - 75340x^9 + 229878x^8 - 169380x^7 + 448401x^6 - 212940x^5 + 549954x^4 - 288762x^3 + 334836x^2 - 186912x - 10622	\( 2^{16}\cdot 3^{37}\cdot 23^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial (GRH)
18.0.2891631487010844893007652585537536.1	x^18 + 57x^16 + 1236x^14 + 13444x^12 + 82062x^10 + 297342x^8 + 651252x^6 + 843588x^4 + 593001x^2 + 173889	\( -\,2^{16}\cdot 3^{32}\cdot 47^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	$[6, 24]$ (GRH)
18.6.6018078093056184948787680256512000.1	x^18 - 288x^14 - 1020x^12 + 17280x^10 + 112320x^8 + 168816x^6 - 34560x^4 - 57600x^2 - 8000	\( 2^{12}\cdot 3^{36}\cdot 5^{3}\cdot 23^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	Trivial (GRH)
18.18.8674894461032534679022957756612608.1	x^18 - 6x^17 - 42x^16 + 238x^15 + 738x^14 - 3708x^13 - 6681x^12 + 29718x^11 + 33048x^10 - 132374x^9 - 91158x^8 + 327990x^7 + 143671x^6 - 430524x^5 - 128340x^4 + 256128x^3 + 54270x^2 - 38430x - 597	\( 2^{16}\cdot 3^{33}\cdot 47^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	$[3]$ (GRH)
18.0.32923515554977373578036580514267136.1	x^18 - 6x^17 + 51x^16 - 146x^15 + 734x^14 - 934x^13 + 5142x^12 + 210x^11 + 27604x^10 + 30598x^9 + 124796x^8 + 255754x^7 + 593654x^6 + 1154974x^5 + 2414142x^4 + 3055670x^3 + 3388775x^2 + 3140424x + 2055213	\( -\,2^{20}\cdot 7^{12}\cdot 197^{8} \)	$C_2\times C_3:S_4$ (as 18T66)	$[2, 2, 6, 90]$ (GRH)
18.18.135906679889509709971359671520264192.1	x^18 - 9x^17 - 24x^16 + 384x^15 - 33x^14 - 6540x^13 + 5677x^12 + 57606x^11 - 65787x^10 - 282822x^9 + 343368x^8 + 778449x^7 - 922425x^6 - 1149072x^5 + 1244082x^4 + 819388x^3 - 744636x^2 - 218364x + 156356	\( 2^{16}\cdot 3^{32}\cdot 47^{9} \)	$C_2\times C_3:S_4$ (as 18T66)	$[3]$ (GRH)