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 41438)

Label	Polynomial	Discriminant	Galois group	Class group
10.6.14339628125.1	x^10 - 2x^8 - 4x^7 - 4x^6 + 6x^5 + 9x^4 + 3x^3 - 4x^2 - 5x + 1	\( 5^{5}\cdot 4588681 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.15417264029.1	x^10 - x^9 - 3x^8 + 5x^7 + x^6 - 7x^5 - x^4 + 5x^3 + 3x^2 - x - 1	\( 461\cdot 5783^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.16178522257.1	x^10 - 3x^9 - 2x^8 + 14x^7 - 7x^6 - 19x^5 + 19x^4 + 2x^3 - 11x^2 + 6x - 1	\( 673\cdot 4903^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.16247003125.1	x^10 - x^9 - x^8 + 4x^7 - 4x^6 - 5x^5 + 2x^4 + x^3 + 4x^2 + x - 1	\( 5^{5}\cdot 31\cdot 167711 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.16297628125.1	x^10 - 3x^8 - 2x^7 - x^6 + x^5 + 4x^4 + 5x^3 - 2x^2 - 3x + 1	\( 5^{5}\cdot 41\cdot 131\cdot 971 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.16656903125.1	x^10 - 6x^8 - 2x^7 + 12x^6 + 8x^5 - 8x^4 - 9x^3 - x^2 + 3x + 1	\( 5^{5}\cdot 79\cdot 109\cdot 619 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.16798253125.1	x^10 - 4x^9 + 2x^8 + 9x^7 - 10x^6 - 6x^5 + 12x^4 + 3x^3 - 6x^2 - x + 1	\( 5^{5}\cdot 5375441 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.16851625709.1	x^10 - x^9 - 2x^8 - 6x^6 + 9x^4 + 2x^3 - 3x^2 - 2x + 1	\( 701\cdot 4903^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.16965864077.1	x^10 - x^9 - 4x^8 + 4x^7 + x^6 - x^5 + 11x^4 - 9x^3 - 9x^2 + 7x - 1	\( 557\cdot 5519^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.16987351657.1	x^10 - x^9 - 6x^8 + 7x^7 + 12x^6 - 16x^5 - 12x^4 + 18x^3 + 4x^2 - 7x + 1	\( 53^{2}\cdot 139^{2}\cdot 313 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.17007429581.1	x^10 - 2x^9 + x^8 - 5x^7 + 7x^6 + 3x^5 - 7x^4 + 7x^3 - 4x^2 - 3x + 1	\( 29\cdot 61^{2}\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.17263278125.1	x^10 - 3x^9 - x^8 + 10x^7 - 6x^6 - 5x^5 + 6x^4 - 5x^3 + 3x - 1	\( 5^{5}\cdot 5524249 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.17317491713.1	x^10 - 6x^8 - x^7 + 11x^6 + 3x^5 - 5x^4 - 2x^3 - 3x^2 + 1	\( 137\cdot 11243^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.17898878125.1	x^10 - x^9 - 8x^6 + 2x^5 + 5x^4 + 2x^2 - x - 1	\( 5^{5}\cdot 71\cdot 80671 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.17926403125.1	x^10 - x^9 - 4x^8 + 5x^7 - 3x^5 + 5x^4 - 2x^3 - 3x^2 + 2x + 1	\( 5^{5}\cdot 1129\cdot 5081 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.18171765053.1	x^10 - x^9 - 5x^8 + 10x^6 + 4x^5 - x^4 - 2x^3 - 5x^2 - x + 1	\( 13^{2}\cdot 19\cdot 47\cdot 347^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.18198690625.1	x^10 - x^9 - 4x^8 + 6x^7 + x^6 - 9x^5 + 6x^4 + 3x^3 - 4x^2 + x + 1	\( 5^{5}\cdot 269\cdot 21649 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.18470002897.1	x^10 - 2x^9 - 5x^8 + 11x^7 + 6x^6 - 17x^5 - 6x^4 + 11x^3 + 5x^2 - 2x - 1	\( 97\cdot 13799^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.19246028125.1	x^10 - x^9 - 5x^8 + 6x^7 + 7x^6 - 7x^5 - 9x^4 + 3x^3 + 7x^2 - 1	\( 5^{5}\cdot 6158729 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.19338380893.1	x^10 + 6x^6 - x^5 - 16x^4 - 5x^3 + 9x^2 + 6x + 1	\( 13\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.19388527573.1	x^10 - 3x^8 - x^7 + 2x^6 + x^5 + 3x^3 - 3x + 1	\( 16493\cdot 1175561 \)	$S_{10}$ (as 10T45)	Trivial
10.6.19524450401.1	x^10 - 5x^9 + 6x^8 + 6x^7 - 12x^6 - 6x^5 + 9x^4 + 9x^3 - 4x^2 - 4x + 1	\( 641\cdot 5519^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.19724253125.1	x^10 - 4x^8 + x^6 - 2x^5 + 6x^4 + 4x^3 - 4x^2 - 2x + 1	\( 5^{5}\cdot 59\cdot 106979 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.19817753125.1	x^10 - 4x^8 - 2x^7 + x^6 + 7x^5 + 2x^4 - 8x^3 - 2x^2 + 3x + 1	\( 5^{5}\cdot 1031\cdot 6151 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.19984878125.1	x^10 - 3x^9 + x^8 + 4x^7 - 10x^6 + 10x^5 + 3x^4 - 8x^3 + 7x^2 - 3x - 1	\( 5^{5}\cdot 541\cdot 11821 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.19992528125.1	x^10 - 4x^9 + 4x^8 - 2x^7 + 8x^6 - 7x^5 - x^4 - 4x^3 + 3x^2 + 2x - 1	\( 5^{5}\cdot 6397609 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.20099296489.1	x^10 - x^9 - 4x^8 + 4x^7 + x^6 - 11x^5 + 5x^4 + 10x^3 - 5x^2 - 2x + 1	\( 601\cdot 5783^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20288073637.1	x^10 - 5x^8 - 3x^7 + 4x^6 + 9x^5 + 6x^4 - 11x^3 - 8x^2 + 5x + 1	\( 13^{2}\cdot 347^{2}\cdot 997 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20499149953.1	x^10 - 2x^9 + 6x^7 - 7x^6 - 7x^5 + 7x^4 + 6x^3 - 2x - 1	\( 673\cdot 5519^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20593878125.1	x^10 - x^9 - 3x^8 + x^7 + 2x^6 + 5x^4 + 2x^3 - 6x^2 - x + 1	\( 5^{5}\cdot 6590041 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.20774745637.1	x^10 - 2x^9 - 4x^8 + 11x^7 + 2x^6 - 20x^5 + 5x^4 + 15x^3 - 4x^2 - 4x + 1	\( 17^{2}\cdot 373\cdot 439^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20793824509.1	x^10 - x^9 - 3x^8 - x^7 - x^6 + 5x^5 + x^4 - x^3 + 3x^2 - x - 1	\( 37^{2}\cdot 61\cdot 499^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20812118581.1	x^10 - x^9 - 6x^8 + 5x^7 + 10x^6 - 3x^5 - 11x^4 - 2x^3 + 7x^2 + 2x - 1	\( 79^{2}\cdot 89^{2}\cdot 421 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.20837499904.1	x^10 - x^8 - 5x^6 + x^4 + 4x^2 - 1	\( 2^{10}\cdot 13^{2}\cdot 347^{2} \)	$(C_2^4:A_5) : C_2$ (as 10T37)	Trivial
10.6.21699134293.1	x^10 - 3x^9 + x^8 + 5x^7 - 11x^6 + 15x^5 - 11x^4 + 5x^3 + x^2 - 3x + 1	\( 37\cdot 61^{2}\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.21838337117.1	x^10 - x^9 - 5x^8 + 3x^7 + 5x^6 - 5x^5 - 5x^4 + 3x^3 + 5x^2 - x - 1	\( 653\cdot 5783^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.22236453325.1	x^10 - 3x^8 - x^7 + 8x^5 - 7x^4 - 10x^3 + 19x^2 - 9x + 1	\( 5^{2}\cdot 37\cdot 4903^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.22241589253.1	x^10 - x^9 - 6x^8 + 5x^7 + 5x^6 - 2x^5 + 8x^4 - 11x^3 - 7x^2 + 10x - 1	\( 13^{2}\cdot 347^{2}\cdot 1093 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.22442338621.1	x^10 - x^9 - 2x^8 - x^6 + 2x^5 + 2x^4 + 2x^3 - 3x + 1	\( 277\cdot 81019273 \)	$S_{10}$ (as 10T45)	Trivial
10.6.22456130021.1	x^10 - x^9 - 6x^6 + 3x^5 + 6x^4 - x - 1	\( 13^{2}\cdot 31^{2}\cdot 37^{2}\cdot 101 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.22570503125.1	x^10 - 2x^9 - 2x^8 + 3x^7 + 2x^5 - 2x^4 + x^3 + 4x^2 - 3x - 1	\( 5^{5}\cdot 7222561 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.22749940625.1	x^10 - x^9 - 2x^8 + x^7 - x^6 + x^5 - 2x^4 - 5x^3 + 2x^2 + 4x + 1	\( 5^{5}\cdot 7279981 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.22813399141.1	x^10 - x^9 - 4x^8 + 6x^7 + 4x^6 - 11x^5 - 4x^4 + 6x^3 + 4x^2 - x - 1	\( 13\cdot 73\cdot 4903^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.22818565625.1	x^10 - 4x^9 + 7x^8 - 3x^7 - 9x^6 + 14x^5 - 3x^4 - 10x^3 + 5x^2 + 2x - 1	\( 5^{5}\cdot 2011\cdot 3631 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.23018590625.1	x^10 - 2x^9 - 2x^8 + 9x^7 - 3x^6 - 8x^5 + 3x^4 - x^3 + 3x + 1	\( 5^{5}\cdot 7365949 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.23365118029.1	x^10 - 3x^9 + x^8 + x^7 - 2x^6 + 4x^5 + 5x^4 - 2x^3 - 6x^2 - x + 1	\( 11^{8}\cdot 109 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.6.23448171349.1	x^10 - 3x^9 - 3x^8 + 18x^7 - 8x^6 - 32x^5 + 31x^4 + 14x^3 - 22x^2 + 4x + 1	\( 17^{2}\cdot 421\cdot 439^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.23641503125.1	x^10 - 2x^9 - x^8 + 2x^7 - 4x^6 + 13x^5 + 2x^4 - 18x^3 + 5x + 1	\( 5^{5}\cdot 61\cdot 124021 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.6.23702283053.1	x^10 - 2x^9 - 3x^8 + 10x^7 - 2x^6 - 17x^5 + 12x^4 + 10x^3 - 8x^2 - x + 1	\( 317\cdot 8647^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.6.23836403125.1	x^10 - 2x^9 + x^7 - x^6 + 4x^5 - 4x^4 - 2x^3 + 5x^2 - 1	\( 5^{5}\cdot 7627649 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial