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 20943)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.14710386688.1	x^10 - 4x^9 + 7x^8 - 2x^7 - 7x^6 + 8x^5 + 5x^4 - 6x^3 + 4x + 2	\( -\,2^{12}\cdot 17^{4}\cdot 43 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.15052488704.1	x^10 - x^9 + x^8 - 2x^7 + 4x^6 - 4x^5 + 4x^4 - 2x^3 + x^2 - x + 1	\( -\,2^{14}\cdot 11\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.15052488704.1	x^10 - 4x^9 + 11x^8 - 22x^7 + 31x^6 - 38x^5 + 31x^4 - 22x^3 + 11x^2 - 4x + 1	\( 2^{14}\cdot 11\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.20279160832.1	x^10 + 3x^8 - 2x^7 + 7x^6 - 2x^5 + 7x^4 - 2x^3 + 3x^2 + 1	\( -\,2^{12}\cdot 7\cdot 29^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.20868222976.1	x^10 - 3x^8 - 4x^7 + x^6 + 4x^5 - x^4 - 4x^3 + 3x^2 - 1	\( 2^{12}\cdot 17^{4}\cdot 61 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.22920835072.1	x^10 - x^9 - x^8 + 2x^7 + 7x^6 + 3x^5 + 9x^4 + 8x^3 + 9x^2 + 3x + 1	\( -\,2^{12}\cdot 17^{4}\cdot 67 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.24289243136.1	x^10 - x^9 + 4x^8 + 2x^7 + 2x^6 + 2x^5 + 2x^4 - 2x^3 + x^2 + 3x + 2	\( -\,2^{12}\cdot 17^{4}\cdot 71 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.30104977408.1	x^10 - 2x^9 + 3x^8 - 6x^7 + 9x^6 - 14x^5 + 19x^4 - 16x^3 + 11x^2 - 4x + 1	\( -\,2^{15}\cdot 11\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.31212625617.1	x^10 - x^9 - 2x^7 + 2x^6 - 6x^4 + 3x^3 - 6x^2 + x - 1	\( 3^{8}\cdot 17\cdot 23^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.34552303616.1	x^10 - x^9 - x^8 + 3x^6 + x^5 - 3x^4 + x^2 - x - 1	\( 2^{12}\cdot 17^{4}\cdot 101 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.36604915712.1	x^10 - x^9 + 5x^8 - 8x^7 + 14x^6 - 12x^5 + 6x^4 - 3x^2 + x + 1	\( -\,2^{12}\cdot 17^{4}\cdot 107 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.39452405000.1	x^10 - 3x^9 + 6x^8 - 11x^7 + 12x^6 - 9x^5 + 9x^4 - 6x^3 + 4x^2 - x + 2	\( -\,2^{3}\cdot 5^{4}\cdot 53^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.43446956032.1	x^10 - x^9 + 2x^7 - 6x^6 + 6x^5 + 6x^4 - 2x^3 + 9x^2 - x + 2	\( -\,2^{12}\cdot 17^{4}\cdot 127 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.43789058048.1	x^10 + 6x^8 + 14x^6 + 16x^4 + 5x^2 + 2	\( -\,2^{19}\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.43789058048.1	x^10 - 6x^8 + 14x^6 - 16x^4 + 5x^2 - 2	\( 2^{19}\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.46525874176.1	x^10 - 4x^9 + 8x^8 - 8x^7 + 11x^6 - 8x^5 + 8x^4 - 4x^3 + 5x^2 + 2	\( -\,2^{15}\cdot 17^{5} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.56917140831.1	x^10 - x^9 + 2x^8 - 9x^7 + 11x^6 - 11x^5 + 21x^4 - 23x^3 + 14x^2 - 5x + 1	\( -\,3^{8}\cdot 23^{4}\cdot 31 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.60209954816.1	x^10 - 3x^9 + 8x^8 - 10x^7 + 18x^6 - 18x^5 + 26x^4 - 18x^3 + 15x^2 - 5x + 2	\( -\,2^{16}\cdot 11\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.66025689088.1	x^10 - x^9 - 2x^8 - 6x^7 - x^6 + 5x^5 + 4x^4 - 2x^3 - 3x^2 + x + 2	\( 2^{12}\cdot 17^{4}\cdot 193 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.68078301184.1	x^10 - 3x^9 + 2x^8 + 2x^7 - 5x^6 + 7x^5 - 6x^4 - 2x^3 + 9x^2 - 7x + 4	\( -\,2^{12}\cdot 17^{4}\cdot 199 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.71605435239.1	x^10 - 6x^7 - 3x^6 - 3x^5 + 11x^4 + 18x^3 + 18x^2 + 12x + 3	\( -\,3^{9}\cdot 13\cdot 23^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.77657157632.1	x^10 - 4x^9 + 6x^8 - 4x^7 + 9x^6 - 26x^5 + 26x^4 + 2x^3 - 15x^2 + 2x + 4	\( -\,2^{12}\cdot 17^{4}\cdot 227 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.77657157632.2	x^10 - x^9 - 3x^8 + 2x^7 + 3x^6 + x^5 - 5x^4 - 4x^3 + 12x^2 + 12x + 4	\( -\,2^{12}\cdot 17^{4}\cdot 227 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.81762381824.1	x^10 - x^9 - 6x^8 + 6x^7 + 15x^6 - 19x^5 - 6x^4 + 18x^3 - 2x^2 - 6x + 4	\( -\,2^{12}\cdot 17^{4}\cdot 239 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.83472891904.1	x^10 - 2x^9 + x^8 - 6x^7 + 11x^6 + 10x^5 - 15x^4 - 10x^3 + 8x^2 + 8x + 2	\( -\,2^{14}\cdot 17^{4}\cdot 61 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.83472891904.1	x^10 - x^9 - 5x^8 + 4x^7 + 6x^6 - 10x^5 - 6x^4 + 4x^3 + 5x^2 - x - 1	\( 2^{14}\cdot 17^{4}\cdot 61 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.84841299968.1	x^10 - 4x^9 + 10x^8 - 22x^7 + 37x^6 - 50x^5 + 58x^4 - 50x^3 + 31x^2 - 12x + 2	\( -\,2^{15}\cdot 17^{4}\cdot 31 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.84841299968.1	x^10 - 2x^9 + 3x^8 - 2x^7 + x^6 - 2x^5 - 3x^4 - 2x^3 + 4x - 2	\( 2^{15}\cdot 17^{4}\cdot 31 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.87578116096.1	x^10 - 3x^8 + 4x^6 + 8x^4 - 3x^2 + 1	\( -\,2^{20}\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.87578116096.2	x^10 + x^8 + 4x^6 + 4x^4 + 5x^2 + 1	\( -\,2^{20}\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.87578116096.3	x^10 + 2x^6 + 4x^4 - 3x^2 + 4	\( -\,2^{20}\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.93051748352.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 10x^5 - 10x^4 + 6x^2 - 2x - 2	\( 2^{16}\cdot 17^{5} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.93637876851.1	x^10 - x^9 + 6x^8 - 8x^7 + 8x^6 - 3x^5 + 8x^4 - 8x^3 + 6x^2 - x + 1	\( -\,3^{9}\cdot 17\cdot 23^{4} \)	$C_2 \wr A_5$ (as 10T36)	$[2]$
10.0.99893788672.1	x^10 - 4x^9 + 11x^8 - 20x^7 + 25x^6 - 24x^5 + 25x^4 - 20x^3 + 11x^2 - 4x + 1	\( -\,2^{14}\cdot 17^{4}\cdot 73 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.99893788672.1	x^10 - x^9 - 4x^8 + 4x^7 + 4x^6 - 4x^5 - 4x^4 - 4x^3 - 2x^2 - 2x - 4	\( 2^{14}\cdot 17^{4}\cdot 73 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.101262196736.1	x^10 - 2x^9 + 5x^8 - 4x^7 - x^6 + 14x^5 - 9x^4 + 12x^2 - 8x + 8	\( -\,2^{15}\cdot 17^{4}\cdot 37 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.107189850112.1	x^10 - 3x^9 + x^8 + 10x^7 - 17x^6 + 3x^5 + 17x^4 - 12x^3 - 4x^2 + 6x + 2	\( 2^{12}\cdot 29^{4}\cdot 37 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.112027271168.1	x^10 + 2x^8 + 8x^4 - 12x^2 + 8	\( -\,2^{15}\cdot 43^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.112209461248.1	x^10 + 4x^8 - 8x^7 + 11x^6 - 20x^5 + 28x^4 - 36x^3 + 29x^2 - 12x + 2	\( 2^{15}\cdot 17^{4}\cdot 41 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.116656787456.1	x^10 - x^9 - 7x^8 - 2x^7 + 11x^6 + 7x^5 - 3x^4 - 4x^3 - 4x^2 - 2x + 2	\( 2^{12}\cdot 11\cdot 17^{4}\cdot 31 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.117683093504.1	x^10 - 4x^8 - 2x^7 + 13x^6 + 2x^5 - 28x^4 + 14x^3 + 19x^2 - 20x + 4	\( 2^{15}\cdot 17^{4}\cdot 43 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.119393603584.1	x^10 - x^9 + x^8 + 6x^6 - 10x^4 + 4x^3 + x^2 + 5x + 1	\( 2^{12}\cdot 17^{4}\cdot 349 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.120419909632.1	x^10 - 2x^9 - 2x^8 + 8x^7 - 28x^5 + 48x^4 - 44x^3 + 30x^2 - 16x + 4	\( 2^{17}\cdot 11\cdot 17^{4} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.126686539269.1	x^10 - x^9 + 3x^8 + 4x^7 - x^6 + 12x^5 + 13x^4 + 8x^3 + 21x^2 + 18x + 3	\( 3^{9}\cdot 23^{5} \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.128630358016.1	x^10 - 4x^9 + 7x^8 - 4x^7 - 3x^6 + 4x^5 + 7x^4 - 8x^3 - 4x^2 + 8x + 4	\( -\,2^{15}\cdot 17^{4}\cdot 47 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.128630358016.2	x^10 - 2x^9 - 2x^7 + 11x^6 + 4x^5 + 2x^4 - 16x^3 - 4x^2 + 8	\( -\,2^{15}\cdot 17^{4}\cdot 47 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.140946030592.1	x^10 - x^9 + 2x^8 - 4x^7 + 4x^6 + 8x^4 - 8x^3 - 14x^2 + 6x + 8	\( -\,2^{14}\cdot 17^{4}\cdot 103 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.2.140946030592.1	x^10 - 2x^9 - 2x^8 + 6x^7 + x^6 - 4x^5 - 2x^4 - 6x^3 - 5x^2 - 2x - 2	\( 2^{14}\cdot 17^{4}\cdot 103 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.143340744704.1	x^10 - x^9 + 5x^8 - 8x^7 + 15x^6 - 31x^5 + 43x^4 - 44x^3 + 29x^2 - 9x + 1	\( -\,2^{12}\cdot 17^{4}\cdot 419 \)	$C_2 \wr A_5$ (as 10T36)	Trivial
10.0.143340744704.2	x^10 - 2x^9 + 2x^8 + 7x^6 - 18x^5 + 38x^4 - 40x^3 + 29x^2 - 10x + 4	\( -\,2^{12}\cdot 17^{4}\cdot 419 \)	$C_2 \wr A_5$ (as 10T36)	Trivial