Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1935859745780129267712.1	x^18 - 3x^17 + 3x^16 - 2x^15 - 2x^14 + 20x^13 - 44x^12 + 60x^11 - 71x^10 + 11x^9 + 179x^8 - 318x^7 + 244x^6 - 104x^5 + 74x^4 - 72x^3 + 37x^2 - 9x + 1	\( -\,2^{16}\cdot 3^{9}\cdot 107^{6} \)	18T518	Trivial
18.0.6342687480463779704832.4	x^18 - 6x^16 + 21x^14 - 45x^12 + 63x^10 - 36x^8 - 27x^6 + 81x^4 - 54x^2 + 27	\( -\,2^{12}\cdot 3^{21}\cdot 23^{6} \)	18T518	$[2]$
18.0.7743438983120517070848.1	x^18 - 4x^17 + 5x^16 + 8x^15 - 16x^14 + 4x^13 + 28x^12 - 24x^11 - 10x^10 + 40x^9 - 10x^8 - 24x^7 + 28x^6 + 4x^5 - 16x^4 + 8x^3 + 5x^2 - 4x + 1	\( -\,2^{18}\cdot 3^{9}\cdot 107^{6} \)	18T518	Trivial
18.0.13406281143386163463872.1	x^18 - 2x^17 - x^16 + 3x^15 + 14x^14 - 24x^13 + x^12 - 2x^11 + 52x^10 - 21x^9 + 18x^8 - 166x^7 + 159x^6 + 84x^5 - 82x^4 - 52x^3 + 13x^2 + 12x + 4	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 67^{6} \)	18T518	Trivial
18.6.6465772763757492115341312.1	x^18 - 2x^15 - 15x^14 + 12x^13 - 99x^12 - 132x^11 - 453x^10 - 468x^9 - 540x^8 - 372x^7 - 214x^6 + 90x^5 + 261x^4 + 254x^3 + 225x^2 + 54x + 1	\( 2^{18}\cdot 3^{21}\cdot 11^{9} \)	18T518	Trivial (GRH)
18.2.100731978985180583398735872.1	x^18 + 21x^16 + 129x^14 + 249x^12 - 24x^10 - 60x^8 - 96x^6 - 72x^4 - 36x^2 - 12	\( 2^{26}\cdot 3^{25}\cdot 11^{6} \)	18T518	$[2]$
18.2.155752995546005235447103488.1	x^18 - 6x^16 - 9x^14 + 195x^12 - 657x^10 + 648x^8 + 468x^6 - 567x^4 - 729x^2 - 243	\( 2^{24}\cdot 3^{21}\cdot 31^{6} \)	18T518	$[2]$ (GRH)
18.6.523727593864356861342646272.1	x^18 - 6x^17 + 9x^16 + 30x^15 - 159x^14 + 150x^13 + 666x^12 - 1608x^11 - 678x^10 + 5158x^9 - 2499x^8 - 7212x^7 + 8073x^6 + 2910x^5 - 8451x^4 + 2676x^3 + 2694x^2 - 2250x + 499	\( 2^{18}\cdot 3^{25}\cdot 11^{9} \)	18T518	Trivial (GRH)
18.6.2695700654465561346632000000000.2	x^18 - 8x^17 + 30x^16 - 24x^15 - 274x^14 + 1461x^13 - 3679x^12 + 4958x^11 - 1882x^10 - 4550x^9 + 5911x^8 + 14x^7 - 5757x^6 + 2258x^5 + 4256x^4 - 249x^3 - 913x^2 + 7x + 49	\( 2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 197^{6} \)	18T518	Trivial (GRH)
18.6.24898334997800010149166707638272.2	x^18 - 69x^14 - 272x^12 - 57x^10 + 1026x^8 + 1001x^6 - 528x^4 - 552x^2 - 2	\( 2^{35}\cdot 3^{24}\cdot 37^{6} \)	18T518	$[2]$ (GRH)
18.10.67392516361639033665800000000000.1	x^18 - x^17 - 28x^16 + 113x^15 - 44x^14 - 976x^13 + 2632x^12 + 991x^11 - 12209x^10 + 10813x^9 + 14918x^8 - 31699x^7 + 14158x^6 + 21115x^5 - 37843x^4 + 13449x^3 + 15071x^2 - 13805x + 3169	\( 2^{12}\cdot 5^{11}\cdot 7^{8}\cdot 197^{6} \)	18T518	Trivial (GRH)
18.10.99593339991200040596666830553088.1	x^18 + 18x^16 - 436x^12 + 156x^10 + 2784x^8 - 3260x^6 + 360x^4 + 432x^2 - 32	\( 2^{37}\cdot 3^{24}\cdot 37^{6} \)	18T518	$[2]$ (GRH)
18.6.132089332068812505984968000000000.1	x^18 - x^17 - 8x^16 + 59x^15 - 59x^14 - 167x^13 + 1679x^12 - 2068x^11 - 7749x^10 + 11813x^9 + 9580x^8 - 19454x^7 - 25962x^6 + 3227x^5 - 2570x^4 + 3410x^3 + 325x^2 - 50x + 125	\( 2^{12}\cdot 5^{9}\cdot 7^{10}\cdot 197^{6} \)	18T518	Trivial (GRH)
18.14.172524841885795926184448000000000.1	x^18 - 2x^17 - 40x^16 + 116x^15 + 520x^14 - 2120x^13 - 1700x^12 + 15608x^11 - 11544x^10 - 38968x^9 + 74216x^8 - 17332x^7 - 71204x^6 + 95336x^5 - 62448x^4 + 19496x^3 + 2944x^2 - 2504x - 344	\( 2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 197^{6} \)	18T518	$[2]$ (GRH)
18.6.172524841885795926184448000000000.1	x^18 + 15x^16 - 944x^12 - 5030x^10 - 6970x^8 + 9624x^6 + 28120x^4 + 13645x^2 - 125	\( 2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 197^{6} \)	18T518	Trivial (GRH)
18.14.172524841885795926184448000000000.2	x^18 - 34x^16 - 6x^15 + 412x^14 + 4x^13 - 2956x^12 - 584x^11 + 13776x^10 + 12052x^9 - 32688x^8 - 55452x^7 + 33180x^6 + 98800x^5 - 14432x^4 - 70904x^3 + 7616x^2 + 14920x - 1240	\( 2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 197^{6} \)	18T518	$[2]$ (GRH)
18.18.136343282447952855576836891027177472.1	x^18 - 72x^16 - 4x^15 + 1932x^14 + 204x^13 - 25080x^12 - 5904x^11 + 169518x^10 + 75028x^9 - 580464x^8 - 402456x^7 + 841186x^6 + 816576x^5 - 240000x^4 - 429608x^3 - 80412x^2 + 30312x + 7972	\( 2^{37}\cdot 3^{24}\cdot 37^{8} \)	18T518	$[2]$ (GRH)
18.18.263783607028943356478904541770678272.1	x^18 - 52x^16 + 1009x^14 - 9848x^12 + 53555x^10 - 168338x^8 + 306779x^6 - 310144x^4 + 151404x^2 - 22898	\( 2^{43}\cdot 37^{6}\cdot 43^{8} \)	18T518	Trivial (GRH)