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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.9040581643536.1	x^10 - x^9 - 8x^8 + 7x^7 + 18x^6 - 17x^5 - 4x^4 + 26x^3 - 12x - 2	\( 2^{4}\cdot 3^{4}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.144649306296576.1	x^10 - 2x^9 + 2x^8 + 4x^7 + 14x^6 - 16x^5 - 8x^4 - 4x^3 + 16x^2 - 12x + 4	\( 2^{8}\cdot 3^{4}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.144649306296576.2	x^10 - 5x^9 + 10x^8 - 35x^6 + 71x^5 - 24x^4 - 90x^3 + 136x^2 - 24x - 36	\( 2^{8}\cdot 3^{4}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.68122631259765625.1	x^10 + 5x^8 - 20x^7 + 15x^6 - 15x^5 + 175x^4 + 680x^3 + 2850x^2 + 3755x - 6838	\( 5^{10}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.68122631259765625.2	x^10 + 20x^8 - 10x^7 + 70x^6 - 64x^5 - 275x^4 + 510x^3 - 380x^2 + 310x - 101	\( 5^{10}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.68122631259765625.3	x^10 - 20x^8 - 40x^7 + 70x^6 + 358x^5 + 275x^4 - 1530x^3 - 4120x^2 - 3450x - 647	\( 5^{10}\cdot 17^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.167772160000000000.1	x^10 + 60x^6 - 208x^5 + 850x^2 - 8000x - 4672	\( 2^{34}\cdot 5^{10} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.167772160000000000.2	x^10 + 20x^8 - 40x^7 - 50x^6 + 392x^5 - 100x^4 - 360x^3 + 95x^2 - 40x - 112	\( 2^{34}\cdot 5^{10} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.167772160000000000.3	x^10 - 20x^8 - 40x^7 + 370x^6 + 120x^5 - 3100x^4 + 3400x^3 + 6815x^2 - 16200x + 9232	\( 2^{34}\cdot 5^{10} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.167772160000000000.20	x^10 + 60x^6 - 144x^5 - 1550x^2 + 8000x - 10304	\( 2^{34}\cdot 5^{10} \)	$C_5^2 : C_8$ (as 10T18)	$[2]$ (GRH)
10.2.167772160000000000.24	x^10 + 20x^8 - 40x^7 + 210x^6 - 472x^5 + 1500x^4 - 2920x^3 + 2015x^2 + 1080x - 1296	\( 2^{34}\cdot 5^{10} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.23	x^10 - 20x^8 - 40x^7 + 230x^6 + 200x^5 - 900x^4 - 600x^3 + 5025x^2 - 2760x + 1808	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.25	x^10 - 20x^8 - 40x^7 + 270x^6 - 264x^5 + 2500x^4 - 8280x^3 + 5455x^2 - 13800x + 39536	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.28	x^10 - 20x^8 - 120x^7 - 290x^6 - 584x^5 - 1100x^4 - 3720x^3 - 7825x^2 - 11080x - 5648	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.30	x^10 + 20x^8 - 40x^7 + 90x^6 + 664x^5 + 3900x^4 - 1800x^3 - 11775x^2 + 120x - 4208	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.34	x^10 - 20x^8 - 40x^7 + 190x^6 + 488x^5 - 500x^4 - 2680x^3 + 65x^2 + 2040x - 2672	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.4194304000000000000.37	x^10 + 60x^6 - 240x^5 - 350x^2 + 1600x - 1088	\( 2^{34}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.10.6105273987852349696.1	x^10 - 2x^9 - 32x^8 + 56x^7 + 288x^6 - 476x^5 - 800x^4 + 1152x^3 + 816x^2 - 704x - 416	\( 2^{8}\cdot 17^{8}\cdot 43^{4} \)	$C_5^2 : C_8$ (as 10T18)	Trivial
10.2.339738624000000000000.21	x^10 - 20x^8 - 40x^7 + 190x^6 + 152x^5 + 1700x^4 - 6680x^3 + 3935x^2 - 680x + 1264	\( 2^{34}\cdot 3^{4}\cdot 5^{12} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.8	x^10 + 80x^8 + 1960x^6 - 1984x^5 + 19400x^4 - 66000x^3 - 9570x^2 - 554240x - 159488	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.17	x^10 + 40x^8 - 80x^7 + 340x^6 - 2528x^5 - 4000x^4 - 23840x^3 + 43970x^2 - 33280x + 30464	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.18	x^10 + 20x^8 - 200x^7 + 610x^6 - 152x^5 + 3100x^4 - 30600x^3 + 92705x^2 - 108920x + 43408	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.19	x^10 + 20x^8 - 280x^7 + 70x^6 + 456x^5 - 700x^4 + 36760x^3 + 385x^2 - 48840x + 51184	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.20	x^10 - 20x^8 - 200x^7 - 990x^6 - 3224x^5 - 3100x^4 + 15000x^3 + 129505x^2 + 425960x + 491632	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.2621440000000000000000.21	x^10 + 40x^8 - 80x^7 + 140x^6 - 3968x^5 + 12000x^4 - 87840x^3 + 629820x^2 - 1703680x + 1339904	\( 2^{34}\cdot 5^{16} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.10070523904000000000000.1	x^10 + 60x^6 - 80x^5 - 350x^2 - 11200x - 13888	\( 2^{34}\cdot 5^{12}\cdot 7^{4} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.10.1304544800933975062064656.1	x^10 - 4x^9 - 151x^8 + 416x^7 + 7495x^6 - 14680x^5 - 138969x^4 + 218812x^3 + 826960x^2 - 992456x - 289712	\( 2^{4}\cdot 17^{8}\cdot 43^{8} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)
10.2.6294077440000000000000000.1	x^10 - 140x^8 - 40x^7 + 8890x^6 - 43016x^5 + 269500x^4 - 4115720x^3 + 19183745x^2 - 47198760x + 34220816	\( 2^{34}\cdot 5^{16}\cdot 7^{4} \)	$C_5^2 : C_8$ (as 10T18)	Trivial (GRH)