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
18.10.14610422921440715006545693.1	x^18 - 6x^17 + 2x^16 + 73x^15 - 248x^14 + 287x^13 + 261x^12 - 1401x^11 + 2256x^10 - 2010x^9 + 924x^8 + 481x^7 - 1802x^6 + 2007x^5 - 871x^4 - 128x^3 + 217x^2 - 45x + 1	\( 19^{16}\cdot 37^{3} \)	18T264	Trivial
18.10.14610422921440715006545693.2	x^18 - x^17 - 14x^16 + 6x^15 + 68x^14 - 9x^13 - 141x^12 + 26x^11 + 173x^10 - 51x^9 - 166x^8 + x^7 + 27x^6 - 101x^5 - 83x^4 + 25x^3 + 41x^2 + 8x - 1	\( 19^{16}\cdot 37^{3} \)	18T264	Trivial
18.6.14610422921440715006545693.2	x^18 - 8x^17 + 33x^16 - 91x^15 + 179x^14 - 222x^13 + 3x^12 + 746x^11 - 2111x^10 + 3836x^9 - 5477x^8 + 6230x^7 - 5361x^6 + 2930x^5 - 88x^4 - 1877x^3 + 2125x^2 - 962x + 151	\( 19^{16}\cdot 37^{3} \)	18T264	Trivial
18.4.75613185918270483380568064.1	x^18 + 7x^16 + 7x^14 - 45x^12 - 100x^10 + 13x^8 + 170x^6 + 139x^4 + 36x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T264	Trivial
18.8.75613185918270483380568064.1	x^18 + x^16 - 27x^14 - 7x^12 + 173x^10 - 4x^8 - 229x^6 - 124x^4 - 14x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T264	Trivial
18.12.75613185918270483380568064.2	x^18 - 3x^16 - 15x^14 + 56x^12 - 9x^10 - 111x^8 + 88x^6 + x^4 - 8x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T264	Trivial (GRH)
18.8.75613185918270483380568064.2	x^18 + 5x^16 - 10x^14 - 39x^12 + 34x^10 + 78x^8 - 45x^6 - 27x^4 + x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T264	Trivial (GRH)
18.12.75613185918270483380568064.3	x^18 - 2x^16 - 13x^14 + 18x^12 + 51x^10 - 43x^8 - 45x^6 + 45x^4 - 12x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T264	Trivial (GRH)
18.4.258151783382020583032356864.1	x^18 + 9x^16 + 18x^14 - 45x^12 - 198x^10 - 216x^8 - 75x^6 + 9x^4 + 9x^2 + 1	\( -\,2^{18}\cdot 3^{44} \)	18T264	Trivial
18.14.416191250312479879983411857.1	x^18 - 5x^17 - 12x^16 + 69x^15 + 45x^14 - 261x^13 - 123x^12 + 403x^11 + 241x^10 - 422x^9 - 271x^8 + 558x^7 + 127x^6 - 506x^5 + 24x^4 + 170x^3 - 34x^2 - 6x + 1	\( 19^{16}\cdot 113^{3} \)	18T264	Trivial (GRH)
18.6.416191250312479879983411857.2	x^18 - 8x^17 + 35x^16 - 120x^15 + 292x^14 - 507x^13 + 524x^12 - 58x^11 - 708x^10 + 1210x^9 - 819x^8 - 45x^7 - 87x^6 + 161x^5 + 312x^4 + 13x^3 + 375x^2 - 151x - 1	\( 19^{16}\cdot 113^{3} \)	18T264	Trivial
18.14.774455350146061749097070592.1	x^18 - 9x^16 + 9x^14 + 66x^12 - 144x^10 + 216x^6 - 189x^4 + 54x^2 - 3	\( 2^{18}\cdot 3^{45} \)	18T264	Trivial (GRH)
18.0.103514451522112291747997679616.1	x^18 + 25x^16 + 263x^14 + 1528x^12 + 5404x^10 + 12064x^8 + 16994x^6 + 14559x^4 + 6882x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T264	$[2, 162]$ (GRH)
18.0.3830034706318154794675914145792.2	x^18 + 46x^16 + 875x^14 + 8918x^12 + 52728x^10 + 183435x^8 + 367668x^6 + 408591x^4 + 229992x^2 + 50653	\( -\,2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T264	$[2, 2, 468]$ (GRH)
18.18.3830034706318154794675914145792.2	x^18 - 46x^16 + 875x^14 - 8918x^12 + 52728x^10 - 183435x^8 + 367668x^6 - 408591x^4 + 229992x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T264	Trivial (GRH)
18.18.3830034706318154794675914145792.3	x^18 - 51x^16 + 1023x^14 - 10328x^12 + 56951x^10 - 181204x^8 + 339994x^6 - 369260x^4 + 213564x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T264	Trivial (GRH)