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
18.2.35099369911034591173.1	x^18 + x^16 - 2x^15 + 4x^13 + 5x^12 - 25x^11 + x^10 + 27x^9 + 41x^8 - 93x^7 + 10x^6 + 54x^5 - 9x^4 - 21x^3 + 2x^2 + 4x - 1	\( 11^{7}\cdot 23^{9} \)	18T301	Trivial
18.2.379379679498607236597.1	x^18 - 8x^15 + 18x^12 - 4x^9 - 10x^6 - 7x^3 - 1	\( 3^{15}\cdot 31^{9} \)	18T301	Trivial
18.0.427054033707557870801891.1	x^18 - 4x^17 + 16x^16 - 46x^15 + 98x^14 - 156x^13 + 95x^12 + 159x^11 - 436x^10 + 622x^9 - 527x^8 + x^7 + 1333x^6 - 1904x^5 + 4570x^4 - 2236x^3 + 2947x^2 - 3243x + 989	\( -\,11^{7}\cdot 23^{12} \)	18T301	$[2]$
18.4.5450990450694506414080000.1	x^18 - 6x^17 + 24x^16 - 62x^15 + 126x^14 - 196x^13 + 214x^12 - 86x^11 - 246x^10 + 650x^9 - 832x^8 + 752x^7 - 664x^6 + 628x^5 - 494x^4 + 276x^3 - 106x^2 + 24x - 2	\( -\,2^{26}\cdot 5^{4}\cdot 37^{9} \)	18T301	Trivial
18.0.6232132441589948716796875.1	x^18 - 4x^17 + 6x^16 + 13x^15 - 60x^14 + 106x^13 + 57x^12 - 464x^11 + 816x^10 + 751x^9 - 3007x^8 + 1460x^7 + 13835x^6 - 23448x^5 + 9184x^4 + 45881x^3 - 42377x^2 + 9060x + 64439	\( -\,5^{9}\cdot 11^{6}\cdot 23^{9} \)	18T301	$[2, 2]$
18.4.73395976223377690632126464.1	x^18 - 6x^17 + 12x^16 - 34x^14 + 44x^13 - 62x^12 + 164x^11 + 72x^10 - 702x^9 + 228x^8 + 1192x^7 - 70x^6 - 1976x^5 - 336x^4 + 1484x^3 - 344x^2 - 1940x - 914	\( -\,2^{26}\cdot 101^{9} \)	18T301	Trivial
18.6.415877567344246400000000000.1	x^18 - 3x^17 + 2x^15 - 22x^14 + 58x^13 - 146x^12 + 348x^11 - 273x^10 + 237x^9 + 624x^8 - 2180x^7 + 4784x^6 - 6080x^5 + 5100x^4 - 1058x^3 - 226x^2 + 368x - 194	\( 2^{16}\cdot 5^{11}\cdot 37^{9} \)	18T301	$[2]$ (GRH)
18.6.764843113371058271302975488.1	x^18 - 12x^16 + 48x^14 - 12x^12 - 432x^10 + 864x^8 + 144x^6 - 1548x^4 + 5292x^2 - 252	\( 2^{26}\cdot 3^{24}\cdot 7^{9} \)	18T301	Trivial
18.0.1294645251195603852036271828992.1	x^18 - 2x^15 + 4x^12 - 8x^9 + 32x^6 - 128x^3 + 512	\( -\,2^{12}\cdot 3^{24}\cdot 47^{9} \)	18T301	$[3, 9]$ (GRH)
18.0.7709257184890088966246072986347.1	x^18 - 3x^17 + 2x^16 + 26x^15 - 89x^14 + 205x^13 + 100x^12 - 616x^11 + 4994x^10 - 13671x^9 + 25036x^8 - 62121x^7 + 135600x^6 - 180678x^5 + 252318x^4 - 345168x^3 + 283896x^2 - 98604x + 12501	\( -\,3^{12}\cdot 53^{4}\cdot 107^{9} \)	18T301	$[2, 2, 24]$ (GRH)
18.18.5302866948897193377940569411551232.1	x^18 - 36x^16 - 2x^15 + 540x^14 + 60x^13 - 4366x^12 - 720x^11 + 20544x^10 + 4432x^9 - 56592x^8 - 14976x^7 + 86852x^6 + 27648x^5 - 65040x^4 - 25640x^3 + 16272x^2 + 8688x + 904	\( 2^{24}\cdot 3^{24}\cdot 47^{9} \)	18T301	Trivial (GRH)
18.18.2020935515475827481967610556932947968.1	x^18 - 83x^16 + 2664x^14 - 42650x^12 + 368002x^10 - 1712361x^8 + 4074420x^6 - 4616838x^4 + 1990521x^2 - 78003	\( 2^{18}\cdot 3^{12}\cdot 53^{4}\cdot 107^{9} \)	18T301	$[2]$ (GRH)