Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions

Results (1-50 of 3085611 matches)

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Label	Polynomial	Discriminant	Galois group	Class group
8.0.1257728.1	x^8 - 2x^7 + 4x^5 - 4x^4 + 3x^2 - 2x + 1	\( 2^{8}\cdot 17^{3} \)	$C_4\wr C_2$ (as 8T17)	trivial
8.0.1265625.1	x^8 - x^7 + x^5 - x^4 + x^3 - x + 1	\( 3^{4}\cdot 5^{6} \)	$C_4\times C_2$ (as 8T2)	trivial
8.0.1282789.1	x^8 - x^7 + 2x^6 - 3x^5 + 3x^4 - 3x^3 + 3x^2 - 2x + 1	\( 1103\cdot 1163 \)	$S_8$ (as 8T50)	trivial
8.0.1327833.1	x^8 - x^7 + x^6 - 2x^5 + 3x^4 - 4x^3 + 4x^2 - 2x + 1	\( 3^{4}\cdot 13^{2}\cdot 97 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.1342413.1	x^8 - x^7 + x^6 + x^4 - 2x^3 + 3x^2 - 3x + 1	\( 3^{4}\cdot 16573 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.1361513.1	x^8 - x^7 + 2x^6 - 3x^5 + 3x^4 - 3x^3 + 2x^2 - x + 1	\( 17\cdot 283^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.1385533.1	x^8 - 2x^7 + 3x^6 - 3x^5 + x^4 + 1	\( 29\cdot 47777 \)	$S_8$ (as 8T50)	trivial
8.0.1424293.1	x^8 - 2x^7 + 2x^6 - x^5 + x^4 - x^3 + 2x^2 - 2x + 1	\( 13\cdot 331^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.1474013.1	x^8 - x^7 + x^6 - x^4 + x^3 - x^2 + 1	\( 617\cdot 2389 \)	$S_8$ (as 8T50)	trivial
8.0.1492101.1	x^8 - x^7 + x^6 - 3x^5 + x^4 - 2x^3 + 3x^2 + 1	\( 3^{4}\cdot 13^{2}\cdot 109 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.1513728.1	x^8 - 2x^7 + x^6 + 2x^5 - 3x^4 - 2x^3 + x^2 + 2x + 1	\( 2^{8}\cdot 3^{4}\cdot 73 \)	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	trivial
8.0.1520789.1	x^8 - x^7 - x^6 + x^4 - x^2 + x + 1	\( 29\cdot 229^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.1578125.1	x^8 - 2x^7 + 3x^5 - x^4 - 3x^3 + 2x + 1	\( 5^{6}\cdot 101 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial
8.0.1590773.1	x^8 - x^7 + 2x^5 - 2x^4 + x^3 + x^2 - 2x + 1	\( 179\cdot 8887 \)	$S_8$ (as 8T50)	trivial
8.0.1601613.1	x^8 - 2x^6 - 3x^5 + 3x^4 + 3x^3 - 2x^2 + 1	\( 3^{6}\cdot 13^{3} \)	$C_4\wr C_2$ (as 8T17)	trivial
8.0.1740113.1	x^8 - 2x^7 + 3x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - x + 1	\( 1740113 \)	$S_8$ (as 8T50)	trivial
8.0.1750329.1	x^8 - 3x^7 + 4x^6 - 3x^5 + 3x^4 - 3x^3 + 4x^2 - 3x + 1	\( 3^{6}\cdot 7^{4} \)	$D_4$ (as 8T4)	trivial
8.0.1763584.1	x^8 - 2x^7 + x^6 + 2x^5 - 3x^4 + 2x^3 + x^2 - 2x + 1	\( 2^{8}\cdot 83^{2} \)	$S_4\times C_2$ (as 8T24)	trivial
8.0.1797309.1	x^8 - 3x^7 + 6x^6 - 8x^5 + 10x^4 - 9x^3 + 7x^2 - 4x + 1	\( 3^{4}\cdot 22189 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.1820637.1	x^8 - x^7 + x^5 - x^4 - 2x^3 + 2x + 1	\( 3^{4}\cdot 7\cdot 13^{2}\cdot 19 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.1867553.1	x^8 - x^7 + x^5 - 2x^4 + x^3 + x^2 - x + 1	\( 1867553 \)	$S_8$ (as 8T50)	trivial
8.0.1890625.1	x^8 - 3x^7 + 6x^6 - 9x^5 + 9x^4 - 7x^3 + 4x^2 - x + 1	\( 5^{6}\cdot 11^{2} \)	$C_2^2:C_4$ (as 8T10)	trivial
8.0.2067245.1	x^8 - x^7 + x^6 - x^4 + x^2 - x + 1	\( 5\cdot 643^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.2105893.1	x^8 - x^7 + 2x^6 - x^5 + x^4 - x^3 + x^2 - 2x + 1	\( 29\cdot 72617 \)	$S_8$ (as 8T50)	trivial
8.0.2118069.1	x^8 - x^7 - x^3 + 2x^2 - x + 1	\( 3^{4}\cdot 79\cdot 331 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2149173.1	x^8 - x^7 - 2x^6 + 2x^5 + x^3 + x^2 - 2x + 1	\( 3^{4}\cdot 13^{2}\cdot 157 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.2178981.1	x^8 - x^7 - x^6 + 2x^5 + x^4 - 2x^3 - x^2 + x + 1	\( 3^{6}\cdot 7^{2}\cdot 61 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.2193125.1	x^8 - 2x^7 + 4x^6 - 5x^5 + 5x^4 - 5x^3 + 4x^2 - 2x + 1	\( 5^{4}\cdot 11^{2}\cdot 29 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.2217213.1	x^8 - x^7 - x^6 - x^5 + 3x^4 - x + 1	\( 3^{4}\cdot 31\cdot 883 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2313441.1	x^8 - x^7 + 2x^6 + 3x^5 - x^4 + 3x^3 + 2x^2 - x + 1	\( 3^{4}\cdot 13^{4} \)	$D_4$ (as 8T4)	trivial
8.0.2314413.1	x^8 - x^6 - x^5 - x^3 + 2x + 1	\( 3^{4}\cdot 28573 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2477709.1	x^8 - x^7 + 3x^5 - x^3 + 2x^2 + 2x + 1	\( 3^{4}\cdot 13^{2}\cdot 181 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.2560000.1	x^8 - 2x^7 + 2x^6 + 2x^5 - 2x^4 + 2x^3 + 2x^2 - 2x + 1	\( 2^{12}\cdot 5^{4} \)	$D_4$ (as 8T4)	trivial
8.0.2671805.1	x^8 - x^5 + x^4 - x^3 + 1	\( 5\cdot 17^{2}\cdot 43^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.2708009.1	x^8 - x^7 - x^6 + x^5 + x^4 - x^3 - x^2 + x + 1	\( 41\cdot 257^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.2712933.1	x^8 - 3x^7 + 3x^6 - x^5 + x^4 - 2x^2 + x + 1	\( 3^{4}\cdot 33493 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2824713.1	x^8 - 3x^7 + 2x^6 + 3x^5 - 4x^4 + x^2 + 1	\( 3^{4}\cdot 43\cdot 811 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2828125.1	x^8 - x^7 - x^6 - 2x^5 + 4x^4 + x^3 + x^2 - 3x + 1	\( 5^{6}\cdot 181 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial
8.0.2844928.1	x^8 - 2x^7 + 2x^6 - 2x^4 + 2x^3 + x^2 - 2x + 1	\( 2^{8}\cdot 11113 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.2963293.1	x^8 - 3x^7 + 5x^6 - 6x^5 + 7x^4 - 6x^3 + 5x^2 - 3x + 1	\( 37\cdot 283^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.2970513.1	x^8 - 2x^7 + 2x^6 - 2x^5 + 3x^4 - 3x^2 + x + 1	\( 3^{4}\cdot 7\cdot 13^{2}\cdot 31 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial
8.0.2985984.1	x^8 - 2x^7 + 2x^6 - 2x^5 + 7x^4 - 10x^3 + 8x^2 - 4x + 1	\( 2^{12}\cdot 3^{6} \)	$D_4$ (as 8T4)	trivial
8.0.3057993.1	x^8 - 2x^7 + 3x^6 - 2x^5 + x^3 + 2x^2 - 3x + 1	\( 3^{4}\cdot 19\cdot 1987 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.3134053.1	x^8 - x^7 + x^6 - 2x^5 + 3x^4 - 2x^3 + x^2 - x + 1	\( 13\cdot 491^{2} \)	$C_2 \wr S_4$ (as 8T44)	trivial
8.0.3167829.1	x^8 - 3x^7 + 4x^6 - 4x^4 + 3x^3 + 2x^2 - 3x + 1	\( 3^{4}\cdot 7\cdot 37\cdot 151 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.3198933.1	x^8 - x^7 - x^6 + 4x^4 - x^3 - 3x^2 + x + 1	\( 3^{4}\cdot 73\cdot 541 \)	$S_4\wr C_2$ (as 8T47)	trivial
8.0.3203125.1	x^8 - x^7 + 2x^6 + 2x^5 + 3x^3 + 2x^2 + x + 1	\( 5^{7}\cdot 41 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial
8.0.3207681.1	x^8 - 3x^7 + 4x^6 - 3x^5 + 2x^4 - x^2 + 1	\( 3^{4}\cdot 199^{2} \)	$S_4\times C_2$ (as 8T24)	trivial
8.0.3211264.1	x^8 - 4x^7 + 8x^6 - 8x^5 + 7x^4 - 8x^3 + 8x^2 - 4x + 1	\( 2^{16}\cdot 7^{2} \)	$D_4\times C_2$ (as 8T9)	trivial
8.0.3240000.1	x^8 - 3x^7 + 3x^6 + x^5 - 2x^4 - 3x^3 + 7x^2 - 4x + 1	\( 2^{6}\cdot 3^{4}\cdot 5^{4} \)	$Q_8:C_2$ (as 8T11)	trivial

  There are too many results (3085611) to download.