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
18.6.10834375376002294480896.2	x^18 - 5x^16 + 15x^14 - 30x^12 + 44x^10 - 51x^8 + 43x^6 - 25x^4 + 8x^2 - 1	\( 2^{30}\cdot 3^{6}\cdot 7^{12} \)	18T269	Trivial
18.6.19408409961765342806016.2	x^18 - 3x^16 + 9x^14 - 24x^12 + 48x^10 - 69x^8 + 65x^6 - 39x^4 + 12x^2 - 1	\( 2^{36}\cdot 3^{24} \)	18T269	Trivial
18.14.1256584347701942722269184.1	x^18 - 5x^16 - 13x^14 + 139x^12 - 363x^10 + 412x^8 - 183x^6 + x^4 + 11x^2 - 1	\( 2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T269	Trivial (GRH)
18.14.1546494554874388003652089.1	x^18 - 2x^17 - 8x^16 + 21x^15 + 2x^14 - 62x^13 + 90x^12 + 20x^11 - 141x^10 + 98x^9 - 36x^8 - 104x^7 + 183x^6 + 32x^5 - 110x^4 - 2x^3 + 20x^2 - 1	\( 7^{12}\cdot 53^{6}\cdot 71^{2} \)	18T269	Trivial (GRH)
18.6.1546494554874388003652089.1	x^18 - x^17 + 4x^15 + 7x^14 + x^13 - 16x^12 - 71x^11 - 48x^10 + 14x^9 + 119x^8 + 154x^7 + 35x^6 - 59x^5 - 89x^4 + 19x^3 + 39x^2 - 13x + 1	\( 7^{12}\cdot 53^{6}\cdot 71^{2} \)	18T269	Trivial
18.10.2886523956915912859821961.1	x^18 - 2x^17 - 4x^16 + 15x^15 - 25x^14 + 4x^13 + 84x^12 - 187x^11 + 233x^10 + 66x^9 - 764x^8 + 899x^7 - 249x^6 - 593x^5 + 1475x^4 - 1152x^3 - 325x^2 + 776x - 251	\( 7^{12}\cdot 53^{6}\cdot 97^{2} \)	18T269	Trivial (GRH)
18.6.2886523956915912859821961.1	x^18 - 5x^17 + x^16 + 36x^15 - 78x^14 + 28x^13 + 90x^12 - 132x^11 - 20x^10 + 313x^9 - 350x^8 + 257x^7 + 243x^6 - 251x^5 + 4x^4 + 87x^3 + 25x^2 + 3x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{2} \)	18T269	Trivial
18.10.5927359907702450033438209.1	x^18 - 4x^17 + 4x^16 + 14x^15 - 62x^14 + 98x^13 - 13x^12 - 217x^11 + 430x^10 - 491x^9 + 289x^8 + 313x^7 - 811x^6 + 490x^5 + 163x^4 - 293x^3 + 76x^2 + 20x - 8	\( 7^{12}\cdot 53^{6}\cdot 139^{2} \)	18T269	Trivial (GRH)
18.6.5927359907702450033438209.1	x^18 - 2x^17 - 8x^16 + 3x^15 + 32x^14 + 29x^13 - 34x^12 + 22x^11 - 278x^10 + 101x^9 - 356x^8 + 689x^7 - 213x^6 + 494x^5 + 183x^4 - 386x^3 + 225x^2 - 208x + 127	\( 7^{12}\cdot 53^{6}\cdot 139^{2} \)	18T269	Trivial
18.10.80421398252924334225227776.3	x^18 - 7x^16 - 4x^14 + 116x^12 - 193x^10 - 132x^8 + 284x^6 + 39x^4 - 32x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T269	Trivial (GRH)
18.10.80421398252924334225227776.4	x^18 + 2x^16 - 13x^14 - 13x^12 + 55x^10 - 6x^8 - 45x^6 + 17x^4 + 2x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T269	Trivial (GRH)
18.6.80421398252924334225227776.5	x^18 - 28x^14 - 54x^12 + 49x^10 + 189x^8 + 132x^6 + 7x^4 - 14x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T269	Trivial
18.18.2634685428164054113552687169536.2	x^18 - 43x^16 + 719x^14 - 6297x^12 + 32271x^10 - 101072x^8 + 193941x^6 - 219697x^4 + 133035x^2 - 32761	\( 2^{18}\cdot 7^{12}\cdot 53^{6}\cdot 181^{2} \)	18T269	Trivial (GRH)
18.18.7378817931230277278673861083136.2	x^18 - 36x^16 + 513x^14 - 3795x^12 + 16143x^10 - 41196x^8 + 63314x^6 - 56565x^4 + 26625x^2 - 5041	\( 2^{30}\cdot 3^{24}\cdot 13^{6}\cdot 71^{2} \)	18T269	Trivial (GRH)
18.6.64995426171445808748564578304000000.1	x^18 + 45x^16 + 203x^14 - 16894x^12 - 265698x^10 - 683793x^8 + 5082399x^6 + 1591569x^4 - 9668484x^2 - 1750329	\( 2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12} \)	18T269	Trivial (GRH)
18.6.8153107601695937311094624312805556224000000.1	x^18 - 138x^16 - 68853x^14 - 6124047x^12 - 149831913x^10 + 3421153032x^8 + 176355676530x^6 + 503949705963x^4 - 40426599583227x^2 - 262254607552729	\( 2^{30}\cdot 3^{32}\cdot 5^{6}\cdot 11^{6}\cdot 23^{6} \)	18T269	$[4]$ (GRH)