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 15587)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.9453125.1	x^8 - 2x^7 + 8x^6 - 9x^5 + 15x^4 - 9x^3 + 8x^2 - 2x + 1	\( 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.20000000.1	x^8 - 5x^6 + 10x^4 - 10x^2 + 5	\( 2^{8}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.75078125.1	x^8 - 2x^7 - 7x^6 + 11x^5 + 20x^4 - 14x^3 - 22x^2 + 3x + 11	\( 5^{7}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.320000000.1	x^8 - 10x^6 + 40x^4 - 80x^2 + 80	\( 2^{12}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.4.320000000.1	x^8 - 2x^7 - 2x^6 + 6x^5 - 10x^4 + 6x^3 - 2x^2 - 2x + 1	\( 2^{12}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.393828125.1	x^8 - 2x^7 + 3x^6 + 11x^5 - 30x^4 + 36x^3 + 13x^2 - 142x + 121	\( 5^{7}\cdot 71^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.564736653.1	x^8 - 4x^7 + 7x^6 - 7x^5 + 6x^4 - 5x^3 - 2x^2 + 4x + 3	\( 3^{2}\cdot 13^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.765703125.1	x^8 - 2x^7 - 12x^6 + 16x^5 + 75x^4 - 59x^3 - 217x^2 + 78x + 241	\( 3^{4}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.4.1143828125.1	x^8 - x^7 - 8x^6 + 7x^5 + 15x^4 - 12x^3 - 18x^2 - 4x + 1	\( 5^{7}\cdot 11^{4} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.1340703125.1	x^8 - 2x^7 - 7x^6 - 4x^5 + 70x^4 + 41x^3 - 287x^2 - 62x + 401	\( 5^{7}\cdot 131^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.1620000000.1	x^8 - 15x^6 + 90x^4 - 270x^2 + 405	\( 2^{8}\cdot 3^{4}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.1781328125.1	x^8 - 2x^7 + 18x^6 - 39x^5 + 140x^4 - 219x^3 + 453x^2 - 382x + 451	\( 5^{7}\cdot 151^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.4.2147483648.2	x^8 - 4x^4 + 2	\( 2^{31} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.2147483648.3	x^8 + 4x^4 + 2	\( 2^{31} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.2420000000.1	x^8 - 20x^6 + 150x^4 - 495x^2 + 605	\( 2^{8}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.2420000000.2	x^8 - 15x^6 + 120x^4 - 440x^2 + 605	\( 2^{8}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.2420000000.3	x^8 + 5x^6 - 40x^4 - 110x^2 + 605	\( 2^{8}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.2420000000.4	x^8 + 50x^4 + 605	\( 2^{8}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.2420000000.5	x^8 - 5x^6 - 40x^4 + 110x^2 + 605	\( 2^{8}\cdot 5^{7}\cdot 11^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.2850078125.1	x^8 - 2x^7 - 7x^6 - 9x^5 + 95x^4 + 46x^3 - 372x^2 - 232x + 841	\( 5^{7}\cdot 191^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.3412578125.1	x^8 - 2x^7 + 18x^6 - 9x^5 + 115x^4 + 31x^3 + 408x^2 + 238x + 671	\( 5^{7}\cdot 11^{2}\cdot 19^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.3412578125.2	x^8 - x^7 - 18x^6 + 7x^5 + 130x^4 - 52x^3 - 378x^2 + 431x + 991	\( 5^{7}\cdot 11^{2}\cdot 19^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.3478203125.1	x^8 - 3x^7 + 23x^6 - 36x^5 + 185x^4 - 141x^3 + 633x^2 - 188x + 781	\( 5^{7}\cdot 211^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.4921953125.1	x^8 - 2x^7 - 17x^6 + 26x^5 + 140x^4 - 119x^3 - 597x^2 + 158x + 1441	\( 5^{7}\cdot 251^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.4.5082629877.1	x^8 - 4x^7 + 7x^6 - 7x^5 - 7x^4 + 21x^3 - 2x^2 - 9x + 3	\( 3^{4}\cdot 13^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.4.5120000000.3	x^8 - 5x^4 + 5	\( 2^{16}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.5737578125.1	x^8 - 3x^7 - 17x^6 + 54x^5 + 140x^4 - 326x^3 - 612x^2 + 747x + 1271	\( 5^{7}\cdot 271^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.6081328125.1	x^8 - 2x^7 + 23x^6 - 29x^5 + 220x^4 - 124x^3 + 1013x^2 - 142x + 1801	\( 3^{4}\cdot 5^{7}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.7220000000.1	x^8 - 20x^6 + 220x^4 - 1045x^2 + 1805	\( 2^{8}\cdot 5^{7}\cdot 19^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[4]$
8.0.7220000000.2	x^8 + 85x^4 + 1805	\( 2^{8}\cdot 5^{7}\cdot 19^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.7556328125.1	x^8 - 2x^7 + 23x^6 - 29x^5 + 230x^4 - 124x^3 + 1133x^2 - 162x + 2201	\( 5^{7}\cdot 311^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.7950078125.1	x^8 - x^7 + 27x^6 - 23x^5 + 275x^4 - 172x^3 + 1207x^2 - 404x + 1891	\( 5^{7}\cdot 11^{2}\cdot 29^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.7950078125.2	x^8 - 3x^7 + 33x^6 - 71x^5 + 370x^4 - 546x^3 + 1653x^2 - 1313x + 2131	\( 5^{7}\cdot 11^{2}\cdot 29^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.8559453125.1	x^8 - 3x^7 - 22x^6 + 59x^5 + 215x^4 - 386x^3 - 1042x^2 + 842x + 1991	\( 5^{7}\cdot 331^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.9084453125.1	x^8 - 2x^7 + 28x^6 - 39x^5 + 305x^4 - 239x^3 + 1338x^2 - 132x + 1721	\( 5^{7}\cdot 11^{2}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.9084453125.2	x^8 - 3x^7 + 23x^6 - 31x^5 + 200x^4 - 176x^3 + 1073x^2 - 373x + 2141	\( 5^{7}\cdot 11^{2}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.9084453125.3	x^8 - x^7 - 23x^6 + 27x^5 + 225x^4 - 212x^3 - 1048x^2 + 701x + 2321	\( 5^{7}\cdot 11^{2}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.9084453125.4	x^8 - x^7 - 8x^6 + 27x^5 - 80x^4 - 12x^3 + 622x^2 - 789x + 2441	\( 5^{7}\cdot 11^{2}\cdot 31^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.14512578125.1	x^8 - 3x^7 + 33x^6 - 56x^5 + 350x^4 - 306x^3 + 1678x^2 - 633x + 3641	\( 5^{7}\cdot 431^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[3]$
8.4.14580000000.3	x^8 - 60x^4 - 45x^2 + 45	\( 2^{8}\cdot 3^{6}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.4.14580000000.4	x^8 - 15x^4 + 45	\( 2^{8}\cdot 3^{6}\cdot 5^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.15890703125.1	x^8 - 2x^7 - 32x^6 + 41x^5 + 380x^4 - 249x^3 - 1892x^2 + 483x + 3371	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.15890703125.2	x^8 - 3x^7 - 27x^6 + 64x^5 + 310x^4 - 486x^3 - 1722x^2 + 1237x + 3931	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.15890703125.3	x^8 - x^7 - 33x^6 + 37x^5 + 395x^4 - 382x^3 - 2018x^2 + 1081x + 4051	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.15890703125.4	x^8 - 3x^7 - 27x^6 + 59x^5 + 315x^4 - 421x^3 - 1772x^2 + 1142x + 4061	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.15890703125.5	x^8 - 2x^7 - 27x^6 + 56x^5 + 310x^4 - 499x^3 - 1787x^2 + 1438x + 4201	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.15890703125.6	x^8 - 2x^7 - 27x^6 + 41x^5 + 315x^4 - 344x^3 - 1747x^2 + 1073x + 4331	\( 5^{7}\cdot 11^{2}\cdot 41^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2]$
8.0.16063620352.1	x^8 + 13x^4 + 13	\( 2^{8}\cdot 13^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	Trivial
8.0.16820000000.1	x^8 - 30x^6 + 330x^4 - 1595x^2 + 4205	\( 2^{8}\cdot 5^{7}\cdot 29^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$
8.0.16820000000.2	x^8 + 130x^4 + 4205	\( 2^{8}\cdot 5^{7}\cdot 29^{2} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2]$