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 matches 1-50 of 79)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.640000000000.2	x^10 - 5x^9 + 15x^8 - 30x^7 + 40x^6 - 30x^5 - 10x^4 + 60x^3 - 80x^2 + 60x - 20	\( 2^{16}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.1166400000000.1	x^10 - x^9 + 3x^8 - 8x^7 + 6x^6 - 12x^5 + 21x^4 - 13x^3 + 18x^2 - 11x + 1	\( 2^{12}\cdot 3^{6}\cdot 5^{8} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.1638400000000.1	x^10 - 4x^9 + 6x^8 - 19x^6 + 40x^5 - 42x^4 + 28x^3 - 15x^2 + 8x - 4	\( 2^{22}\cdot 5^{8} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.1822500000000.1	x^10 - 5x^9 + 15x^8 - 20x^7 + 5x^6 + 39x^5 - 65x^4 + 40x^3 - 15x^2 - 5x - 1	\( 2^{8}\cdot 3^{6}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.2073600000000.1	x^10 - 2x^9 + 2x^8 - 4x^7 + 6x^6 - 4x^5 - 6x^4 - 4x^3 + 13x^2 - 2x + 4	\( 2^{16}\cdot 3^{4}\cdot 5^{8} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.12524124635136.1	x^10 - 2x^9 + 7x^8 - 16x^7 + 16x^6 - 16x^5 + 16x^4 - 16x^3 + 22x^2 - 12x + 2	\( 2^{34}\cdot 3^{6} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.16000000000000.1	x^10 - 5x^9 + 5x^8 + 25x^6 - 53x^5 + 55x^4 - 110x^3 + 95x^2 - 25x - 19	\( 2^{16}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.29160000000000.9	x^10 + 5x^8 - 10x^7 + 20x^6 - 10x^5 - 25x^4 + 110x^3 - 130x^2 + 70x + 5	\( 2^{12}\cdot 3^{6}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.45562500000000.1	x^10 - 10x^7 + 10x^6 - 36x^5 + 110x^4 - 40x^3 - 150x^2 + 150x - 31	\( 2^{8}\cdot 3^{6}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.45562500000000.1	x^10 - 10x^8 - 5x^6 - 54x^5 - 50x^4 + 30x^3 + 65x^2 + 30x + 4	\( 2^{8}\cdot 3^{6}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.111236572265625.1	x^10 - 10x^8 - 15x^7 + 70x^6 + 51x^5 - 200x^4 - 30x^3 + 230x^2 - 15x - 101	\( 3^{6}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.729000000000000.1	x^10 - 40x^7 - 50x^6 + 186x^5 + 50x^4 - 100x^3 + 30x^2 - 1	\( 2^{12}\cdot 3^{6}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.743652900000000.1	x^10 - 4x^9 + 12x^8 - 52x^7 + 125x^6 - 198x^5 + 442x^4 - 556x^3 + 531x^2 - 550x + 125	\( 2^{8}\cdot 3^{6}\cdot 5^{8}\cdot 101^{2} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.1024000000000000.2	x^10 - 15x^8 - 20x^7 + 75x^6 + 52x^5 - 155x^4 - 20x^3 + 95x^2 - 9	\( 2^{22}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.1024000000000000.11	x^10 - 5x^9 + 15x^8 - 30x^7 + 45x^6 - 19x^5 - 35x^4 + 10x^3 - 175x^2 - 215x - 181	\( 2^{22}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.1194393600000000.4	x^10 + 5x^8 - 20x^7 + 5x^6 - 68x^5 + 155x^4 - 20x^3 + 305x^2 - 400x - 79	\( 2^{22}\cdot 3^{6}\cdot 5^{8} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.1296000000000000.6	x^10 + 15x^8 - 20x^7 + 120x^6 - 148x^5 + 540x^4 - 560x^3 + 540x^2 - 200x - 124	\( 2^{16}\cdot 3^{4}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.2780914306640625.1	x^10 - 20x^8 - 10x^7 + 145x^6 + 113x^5 - 425x^4 - 355x^3 + 160x^2 + 180x + 31	\( 3^{6}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.3317760000000000.3	x^10 - 10x^8 - 35x^6 - 140x^5 + 270x^4 + 940x^3 + 705x^2 + 60x - 80	\( 2^{22}\cdot 3^{4}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.3317760000000000.13	x^10 + 5x^8 - 20x^7 + 15x^6 - 68x^5 + 165x^4 - 140x^3 + 265x^2 - 480x + 261	\( 2^{22}\cdot 3^{4}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.10.3399254384765625.1	x^10 - 20x^8 + 120x^6 - 18x^5 - 255x^4 + 90x^3 + 135x^2 - 45x - 9	\( 3^{6}\cdot 5^{10}\cdot 691^{2} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.10.7685261806640625.1	x^10 - 20x^8 - 15x^7 + 90x^6 + 63x^5 - 150x^4 - 90x^3 + 90x^2 + 45x - 9	\( 3^{6}\cdot 5^{10}\cdot 1039^{2} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.10.9563006337890625.1	x^10 - 5x^9 - 10x^8 + 60x^7 + 30x^6 - 216x^5 - 15x^4 + 225x^3 - 45x^2 - 45x + 9	\( 3^{6}\cdot 5^{10}\cdot 19^{2}\cdot 61^{2} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.10000000000000000.1	x^10 - 10x^8 - 20x^7 - 90x^6 - 412x^5 - 950x^4 - 940x^3 - 155x^2 + 140x + 16	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.10000000000000000.2	x^10 - 20x^8 + 205x^6 - 164x^5 - 1050x^4 + 1640x^3 + 1225x^2 - 2660x + 944	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.10000000000000000.6	x^10 - 20x^7 + 50x^6 - 400x^4 - 500x^3 - 175x^2 - 320	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.10000000000000000.8	x^10 + 15x^6 - 44x^5 + 25x^2 - 480x + 304	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.10000000000000000.12	x^10 - 20x^7 + 95x^6 + 56x^5 - 400x^4 - 700x^3 + 2065x^2 + 2560x + 704	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.10000000000000000.13	x^10 - 20x^8 + 130x^6 - 136x^5 - 300x^4 + 1360x^3 - 275x^2 - 6440x - 5056	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.10000000000000000.14	x^10 - 20x^8 + 205x^6 - 16x^5 - 1050x^4 + 160x^3 + 2725x^2 - 1240x - 1216	\( 2^{16}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.17866833472265625.1	x^10 - 2x^9 - 2x^8 + 11x^7 - 50x^6 + 41x^5 + 103x^4 - 82x^3 + 16x^2 + 30x - 25	\( 3^{6}\cdot 5^{8}\cdot 89^{4} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.6.21743271936000000.1	x^10 - 4x^9 - 6x^8 + 32x^7 + 4x^6 - 16x^5 - 184x^4 + 128x^3 + 306x^2 - 360x + 100	\( 2^{34}\cdot 3^{4}\cdot 5^{6} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial
10.2.29859840000000000.18	x^10 - 5x^9 + 35x^8 - 90x^7 + 255x^6 - 57x^5 - 645x^4 + 90x^3 + 765x^2 + 45x - 369	\( 2^{22}\cdot 3^{6}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.29859840000000000.57	x^10 - 5x^9 - 5x^8 - 10x^7 + 25x^6 - 19x^5 - 175x^4 - 330x^3 + 2675x^2 - 4965x + 3769	\( 2^{22}\cdot 3^{6}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.82944000000000000.3	x^10 - 10x^8 + 45x^6 - 68x^5 - 750x^4 - 1020x^3 - 5x^2 + 540x + 176	\( 2^{22}\cdot 3^{4}\cdot 5^{12} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.167772160000000000.1	x^10 - 20x^8 - 40x^7 - 50x^6 + 424x^5 + 100x^4 - 760x^3 + 95x^2 + 360x - 144	\( 2^{34}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.167772160000000000.2	x^10 - 20x^8 - 40x^7 - 30x^6 + 392x^5 + 100x^4 - 200x^3 + 1185x^2 - 1400x - 1552	\( 2^{34}\cdot 5^{10} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.195689447424000000.19	x^10 - 4x^9 + 16x^8 - 40x^7 - 74x^6 - 160x^5 - 92x^4 - 952x^3 + 625x^2 - 4092x + 1476	\( 2^{34}\cdot 3^{6}\cdot 5^{6} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.195689447424000000.24	x^10 + 22x^8 + 204x^6 + 888x^4 + 1026x^2 - 1440x - 900	\( 2^{34}\cdot 3^{6}\cdot 5^{6} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.250000000000000000.11	x^10 - 30x^8 - 20x^7 + 195x^6 - 136x^5 - 1950x^4 - 1960x^3 + 1985x^2 + 3140x + 944	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.250000000000000000.12	x^10 - 30x^8 - 20x^7 + 195x^6 + 804x^5 - 1950x^4 - 1460x^3 + 3585x^2 - 160x - 976	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.250000000000000000.15	x^10 + 30x^8 - 60x^7 + 345x^6 - 552x^5 + 2700x^4 - 5280x^3 + 12585x^2 - 9820x + 656	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.250000000000000000.16	x^10 + 20x^8 - 20x^7 + 70x^6 - 276x^5 - 700x^4 - 460x^3 + 385x^2 + 1140x + 1264	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.250000000000000000.17	x^10 + 20x^8 - 80x^7 + 70x^6 - 944x^5 + 1300x^4 - 240x^3 - 2015x^2 - 4240x + 3904	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.250000000000000000.18	x^10 - 20x^8 - 60x^7 + 145x^6 + 428x^5 - 50x^4 - 380x^3 + 7185x^2 - 2520x + 5776	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.250000000000000000.19	x^10 - 20x^8 - 60x^7 + 70x^6 + 508x^5 + 700x^4 - 2180x^3 - 9215x^2 - 15420x - 6704	\( 2^{16}\cdot 5^{18} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.543581798400000000.1	x^10 - 20x^8 - 40x^7 + 210x^6 + 72x^5 - 980x^4 + 1400x^3 - 985x^2 + 440x - 104	\( 2^{34}\cdot 3^{4}\cdot 5^{8} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	$[2]$ (GRH)
10.2.599695360000000000.1	x^10 - 5x^9 - 5x^8 + 30x^7 + 25x^6 - 51x^5 + 425x^4 + 270x^3 - 3675x^2 - 3335x - 1501	\( 2^{22}\cdot 5^{10}\cdot 11^{4} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.6.640000000000000000.3	x^10 - 10x^8 - 40x^7 - 35x^6 + 212x^5 - 50x^4 - 660x^3 + 785x^2 + 740x - 944	\( 2^{22}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)
10.2.640000000000000000.12	x^10 + 20x^8 - 40x^7 + 100x^6 - 440x^5 + 400x^4 - 400x^3 + 675x^2 - 400x + 80	\( 2^{22}\cdot 5^{16} \)	$(C_5^2 : C_8):C_2$ (as 10T28)	Trivial (GRH)