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 109722)

Label	Polynomial	Discriminant	Galois group	Class group
8.8.282300416.1	x^8 - 4x^7 + 14x^5 - 8x^4 - 12x^3 + 7x^2 + 2x - 1	\( 2^{12}\cdot 41^{3} \)	$C_4\wr C_2$ (as 8T17)	Trivial
8.8.309593125.1	x^8 - 4x^7 - x^6 + 17x^5 - 5x^4 - 23x^3 + 6x^2 + 9x - 1	\( 5^{4}\cdot 19\cdot 29^{2}\cdot 31 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.324000000.1	x^8 - 7x^6 + 14x^4 - 8x^2 + 1	\( 2^{8}\cdot 3^{4}\cdot 5^{6} \)	$C_4\times C_2$ (as 8T2)	Trivial
8.8.410338673.1	x^8 - x^7 - 7x^6 + 6x^5 + 15x^4 - 10x^3 - 10x^2 + 4x + 1	\( 17^{7} \)	$C_8$ (as 8T1)	Trivial
8.8.432640000.1	x^8 - 2x^7 - 7x^6 + 16x^5 + 4x^4 - 18x^3 + 2x^2 + 4x - 1	\( 2^{12}\cdot 5^{4}\cdot 13^{2} \)	$Q_8:C_2$ (as 8T11)	Trivial
8.8.442050625.1	x^8 - 2x^7 - 12x^6 + 26x^5 + 17x^4 - 36x^3 - 5x^2 + 11x - 1	\( 5^{4}\cdot 29^{4} \)	$D_4$ (as 8T4)	Trivial
8.8.456768125.1	x^8 - 2x^7 - 7x^6 + 11x^5 + 14x^4 - 18x^3 - 8x^2 + 9x - 1	\( 5^{4}\cdot 11\cdot 29^{2}\cdot 79 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.483345053.1	x^8 - x^7 - 7x^6 + 4x^5 + 15x^4 - 3x^3 - 9x^2 + 1	\( 483345053 \)	$S_8$ (as 8T50)	Trivial
8.8.494613125.1	x^8 - x^7 - 7x^6 + 4x^5 + 13x^4 - 4x^3 - 7x^2 + x + 1	\( 5^{4}\cdot 29^{2}\cdot 941 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.582918125.1	x^8 - 2x^7 - 6x^6 + 9x^5 + 11x^4 - 9x^3 - 6x^2 + 2x + 1	\( 5^{4}\cdot 29^{2}\cdot 1109 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.656505625.1	x^8 - 3x^7 - 4x^6 + 13x^5 + 5x^4 - 13x^3 - 4x^2 + 3x + 1	\( 5^{4}\cdot 29^{2}\cdot 1249 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.661518125.1	x^8 - x^7 - 7x^6 + 5x^5 + 15x^4 - 7x^3 - 10x^2 + 2x + 1	\( 5^{4}\cdot 439\cdot 2411 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.707295133.1	x^8 - 8x^6 - 2x^5 + 19x^4 + 7x^3 - 13x^2 - 4x + 1	\( 9973\cdot 70921 \)	$S_8$ (as 8T50)	Trivial
8.8.733968125.1	x^8 - 2x^7 - 6x^6 + 10x^5 + 11x^4 - 11x^3 - 7x^2 + 2x + 1	\( 5^{4}\cdot 11\cdot 106759 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.740605625.1	x^8 - x^7 - 9x^6 + 8x^5 + 21x^4 - 12x^3 - 14x^2 + 4x + 1	\( 5^{4}\cdot 29^{2}\cdot 1409 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.803680625.1	x^8 - 2x^7 - 9x^6 + 12x^5 + 22x^4 - 24x^3 - 14x^2 + 14x - 1	\( 5^{4}\cdot 11\cdot 29^{2}\cdot 139 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.852038125.1	x^8 - 10x^6 - 5x^5 + 17x^4 + 5x^3 - 10x^2 + 1	\( 5^{4}\cdot 29^{2}\cdot 1621 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.877268125.1	x^8 - 3x^7 - 6x^6 + 20x^5 + 5x^4 - 25x^3 - x^2 + 7x + 1	\( 5^{4}\cdot 29^{2}\cdot 1669 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.898293125.1	x^8 - x^7 - 9x^6 + 10x^5 + 15x^4 - 10x^3 - 9x^2 + x + 1	\( 5^{4}\cdot 29^{2}\cdot 1709 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.1000118125.1	x^8 - 3x^7 - 4x^6 + 14x^5 + 5x^4 - 19x^3 - x^2 + 7x - 1	\( 5^{4}\cdot 31\cdot 41\cdot 1259 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1024000000.1	x^8 - 8x^6 + 19x^4 - 12x^2 + 1	\( 2^{16}\cdot 5^{6} \)	$C_4\times C_2$ (as 8T2)	Trivial
8.8.1032588125.1	x^8 - 9x^6 - 2x^5 + 23x^4 + 9x^3 - 17x^2 - 9x - 1	\( 5^{4}\cdot 1652141 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1064390625.1	x^8 - 13x^6 + 44x^4 - 17x^2 + 1	\( 3^{4}\cdot 5^{6}\cdot 29^{2} \)	$C_2^2:C_4$ (as 8T10)	Trivial
8.8.1077044573.1	x^8 - x^7 - 8x^6 + 8x^5 + 16x^4 - 17x^3 - 2x^2 + 5x - 1	\( 11\cdot 97913143 \)	$S_8$ (as 8T50)	Trivial
8.8.1095205625.1	x^8 - 3x^7 - 5x^6 + 18x^5 + 2x^4 - 23x^3 + 2x^2 + 8x - 1	\( 5^{4}\cdot 349\cdot 5021 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1098290293.1	x^8 - 3x^7 - 4x^6 + 16x^5 + x^4 - 23x^3 + 7x^2 + 5x - 1	\( 7523\cdot 145991 \)	$S_8$ (as 8T50)	Trivial
8.8.1104338125.1	x^8 - 2x^7 - 8x^6 + 15x^5 + 17x^4 - 31x^3 - 9x^2 + 17x - 1	\( 5^{4}\cdot 11\cdot 29^{2}\cdot 191 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.1114390153.1	x^8 - 8x^6 - 2x^5 + 16x^4 + 3x^3 - 10x^2 + 1	\( 347\cdot 3211499 \)	$S_8$ (as 8T50)	Trivial
8.8.1121463125.1	x^8 - 3x^7 - 4x^6 + 15x^5 + 2x^4 - 18x^3 + 5x + 1	\( 5^{4}\cdot 19\cdot 94439 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1136700613.1	x^8 - x^7 - 7x^6 + 4x^5 + 14x^4 - 4x^3 - 8x^2 + x + 1	\( 89\cdot 1301\cdot 9817 \)	$S_8$ (as 8T50)	Trivial
8.8.1142440000.1	x^8 - 3x^7 - 5x^6 + 15x^5 + 8x^4 - 15x^3 - 5x^2 + 4x + 1	\( 2^{6}\cdot 5^{4}\cdot 13^{4} \)	$Q_8:C_2$ (as 8T11)	Trivial
8.8.1152784549.1	x^8 - 4x^7 - x^6 + 15x^5 - 3x^4 - 16x^3 + 4x^2 + 4x - 1	\( 7\cdot 19^{2}\cdot 43\cdot 103^{2} \)	$C_2 \wr S_4$ (as 8T44)	Trivial
8.8.1153988125.1	x^8 - 2x^7 - 7x^6 + 11x^5 + 12x^4 - 16x^3 - 5x^2 + 6x - 1	\( 5^{4}\cdot 101^{2}\cdot 181 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.1166547493.1	x^8 - x^7 - 7x^6 + 6x^5 + 14x^4 - 9x^3 - 9x^2 + 3x + 1	\( 1166547493 \)	$S_8$ (as 8T50)	Trivial
8.8.1183423341.1	x^8 - x^7 - 8x^6 + 9x^5 + 17x^4 - 20x^3 - 8x^2 + 10x - 1	\( 3\cdot 19^{2}\cdot 103^{3} \)	$C_2 \wr S_4$ (as 8T44)	Trivial
8.8.1202043125.1	x^8 - 3x^7 - 4x^6 + 16x^5 - 21x^3 + 9x^2 + 2x - 1	\( 5^{4}\cdot 41\cdot 61\cdot 769 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1225026133.1	x^8 - 3x^7 - 4x^6 + 18x^5 - 6x^4 - 17x^3 + 9x^2 + 2x - 1	\( 83\cdot 14759351 \)	$S_8$ (as 8T50)	Trivial
8.8.1243893125.1	x^8 - x^7 - 8x^6 + 3x^5 + 18x^4 - x^3 - 12x^2 - 2x + 1	\( 5^{4}\cdot 1990229 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1255718125.1	x^8 - 2x^7 - 8x^6 + 19x^5 + 10x^4 - 41x^3 + 13x^2 + 10x - 1	\( 5^{4}\cdot 29^{2}\cdot 2389 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.1261609229.1	x^8 - 2x^7 - 6x^6 + 12x^5 + 9x^4 - 19x^3 - x^2 + 6x - 1	\( 397\cdot 3177857 \)	$S_8$ (as 8T50)	Trivial
8.8.1292203125.1	x^8 - 4x^7 - x^6 + 17x^5 - 6x^4 - 21x^3 + 6x^2 + 8x + 1	\( 3^{4}\cdot 5^{6}\cdot 1021 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	Trivial
8.8.1299600812.1	x^8 - 2x^7 - 6x^6 + 10x^5 + 12x^4 - 13x^3 - 8x^2 + 3x + 1	\( 2^{2}\cdot 324900203 \)	$S_8$ (as 8T50)	Trivial
8.8.1317743125.1	x^8 - x^7 - 8x^6 + 7x^5 + 19x^4 - 14x^3 - 12x^2 + 8x - 1	\( 5^{4}\cdot 2108389 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.8.1318279381.1	x^8 - x^7 - 7x^6 + 5x^5 + 14x^4 - 6x^3 - 9x^2 + x + 1	\( 1318279381 \)	$S_8$ (as 8T50)	Trivial
8.8.1326417388.1	x^8 - 2x^7 - 6x^6 + 10x^5 + 12x^4 - 13x^3 - 9x^2 + 4x + 2	\( 2^{2}\cdot 43\cdot 2777^{2} \)	$C_2 \wr S_4$ (as 8T44)	Trivial
8.8.1348097653.1	x^8 - 2x^7 - 6x^6 + 11x^5 + 11x^4 - 17x^3 - 6x^2 + 6x + 1	\( 7^{2}\cdot 27512197 \)	$S_8$ (as 8T50)	Trivial
8.8.1358954496.1	x^8 - 8x^6 + 20x^4 - 16x^2 + 1	\( 2^{24}\cdot 3^{4} \)	$C_4\times C_2$ (as 8T2)	Trivial
8.8.1359341129.1	x^8 - 8x^6 - x^5 + 18x^4 + 2x^3 - 12x^2 - x + 2	\( 1359341129 \)	$S_8$ (as 8T50)	Trivial
8.8.1377663125.1	x^8 - 12x^6 + 33x^4 - 5x^3 - 22x^2 + 5x + 1	\( 5^{4}\cdot 29^{2}\cdot 2621 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.8.1381875749.1	x^8 - 3x^7 - 4x^6 + 14x^5 + 4x^4 - 18x^3 + x^2 + 5x - 1	\( 1381875749 \)	$S_8$ (as 8T50)	Trivial

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