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 3538)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.662747776000.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 8x^5 - 7x^4 - 2x^3 + 7x^2 - 4x + 1	\( -\,2^{10}\cdot 5^{3}\cdot 173^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[4]$
10.0.3539609321472.1	x^10 - 4x^9 + 24x^7 - 42x^6 + 84x^4 - 120x^3 + 84x^2 - 32x + 8	\( -\,2^{19}\cdot 3^{9}\cdot 7^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.7522959753216.1	x^10 - 6x^8 + 9x^6 - 12x^5 + 24x^4 + 21x^2 + 4x + 18	\( -\,2^{19}\cdot 3^{15} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.7522959753216.2	x^10 - 2x^9 + 3x^8 + 9x^6 - 18x^5 + 9x^4 + 27x^2 - 18x + 9	\( -\,2^{19}\cdot 3^{15} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.10618827964416.1	x^10 - 2x^9 + 3x^8 + 15x^6 - 6x^5 + 15x^4 - 24x^3 + 39x^2 - 34x + 11	\( -\,2^{19}\cdot 3^{10}\cdot 7^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.20155392000000.5	x^10 - 2x^9 + 6x^8 - 16x^7 + 32x^6 - 12x^5 - 18x^4 + 24x^3 + 21x^2 - 2x + 16	\( -\,2^{16}\cdot 3^{9}\cdot 5^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.21134460321792.1	x^10 - 3x^8 + 18x^6 - 30x^4 + 39x^2 - 16x + 3	\( -\,2^{30}\cdot 3^{9} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.21134460321792.2	x^10 - 4x^9 + 9x^8 - 16x^7 + 22x^6 - 24x^5 + 22x^4 - 16x^3 + 21x^2 - 20x + 29	\( -\,2^{30}\cdot 3^{9} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.22672074866688.1	x^10 - 2x^9 + 9x^8 - 24x^7 + 48x^6 - 72x^5 + 138x^4 - 240x^3 + 312x^2 - 232x + 92	\( -\,2^{19}\cdot 3^{9}\cdot 13^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.24207794634752.1	x^10 - x^9 - 2x^8 + 14x^6 - 14x^5 - 16x^4 + 4x^3 + 14x^2 + 2x + 4	\( 2^{24}\cdot 113^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.26748301344768.1	x^10 + 9x^8 + 6x^6 - 30x^4 - 48x^3 - 36x^2 - 16x - 12	\( 2^{24}\cdot 3^{13} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.30229433155584.1	x^10 - 2x^9 - 5x^8 + 8x^7 + 17x^6 - 10x^5 - 27x^4 - 24x^3 + 27x^2 + 54x + 21	\( -\,2^{21}\cdot 3^{8}\cdot 13^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.30233088000000.2	x^10 - 2x^9 + 3x^8 - 6x^7 + 6x^6 - 6x^5 + 12x^4 + 6x^3 + 9x^2 + 4x + 1	\( -\,2^{15}\cdot 3^{10}\cdot 5^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.31492800000000.1	x^10 - 4x^9 + 6x^8 - 9x^6 + 3x^4 + 18x^3 - 12x + 6	\( -\,2^{12}\cdot 3^{9}\cdot 5^{8} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.31701690482688.5	x^10 - 2x^9 - 3x^8 + 12x^6 + 24x^5 - 12x^4 + 24x^2 - 16x + 8	\( -\,2^{29}\cdot 3^{10} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.32248627200000.1	x^10 - 4x^9 + 12x^8 - 24x^7 + 39x^6 - 48x^5 + 48x^4 - 36x^3 + 24x^2 - 12x + 6	\( -\,2^{19}\cdot 3^{9}\cdot 5^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.32520160641024.1	x^10 - 2x^9 + 15x^6 + 12x^5 + 18x^4 + 12x^3 + 12x^2 + 8x + 2	\( -\,2^{15}\cdot 3^{10}\cdot 7^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.2.39958937600000.1	x^10 - 2x^9 + 3x^8 + 12x^7 - 23x^6 - 14x^5 + 37x^4 + 12x^3 - 21x^2 + 10x + 11	\( 2^{19}\cdot 5^{5}\cdot 29^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.50388480000000.3	x^10 + 3x^8 - 12x^7 + 21x^6 - 42x^5 + 105x^4 - 204x^3 + 246x^2 - 158x + 42	\( -\,2^{15}\cdot 3^{9}\cdot 5^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.50388480000000.4	x^10 - 2x^9 + 15x^8 - 18x^7 + 66x^6 - 42x^5 + 138x^4 - 30x^3 + 117x^2 - 4x + 47	\( -\,2^{15}\cdot 3^{9}\cdot 5^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.0.53496602689536.1	x^10 - 4x^9 + 6x^8 + 12x^2 + 16x + 8	\( -\,2^{25}\cdot 3^{13} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.59374943502336.1	x^10 - 2x^9 - 2x^8 - 2x^7 + 27x^6 - 36x^5 + 10x^4 + 16x^3 + 52x^2 - 128x + 72	\( -\,2^{15}\cdot 3^{4}\cdot 7^{5}\cdot 11^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.71328803586048.3	x^10 - 2x^9 + 3x^8 - 12x^6 + 24x^5 - 12x^4 + 21x^2 - 74x + 55	\( -\,2^{27}\cdot 3^{12} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.0.77760000000000.2	x^10 - 5x^6 - 8x^5 + 10x^2 + 20x + 10	\( -\,2^{15}\cdot 3^{5}\cdot 5^{10} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.90275517038592.1	x^10 - 4x^9 + 6x^8 + 36x^2 + 48x + 24	\( -\,2^{21}\cdot 3^{16} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.96745881600000.1	x^10 + 6x^8 - 12x^7 - 9x^6 - 12x^5 + 12x^4 - 3x^2 + 44x - 36	\( 2^{19}\cdot 3^{10}\cdot 5^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.102036672000000.4	x^10 - 2x^9 + 6x^8 - 6x^7 + 3x^6 + 12x^5 + 9x^4 + 36x^3 + 72x^2 + 48x + 48	\( -\,2^{12}\cdot 3^{13}\cdot 5^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.103195607040000.3	x^10 - 4x^9 + 6x^8 - 12x^2 - 16x - 8	\( 2^{23}\cdot 3^{9}\cdot 5^{4} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.103873473183744.1	x^10 - 4x^9 + 3x^8 + 18x^7 - 27x^6 - 12x^5 - 3x^4 - 6x^3 + 12x^2 + 88x + 44	\( 2^{15}\cdot 3^{9}\cdot 11^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.103873473183744.2	x^10 - 2x^9 + 9x^8 - 24x^7 + 39x^6 - 90x^5 + 111x^4 - 132x^3 + 156x^2 - 72x + 60	\( 2^{15}\cdot 3^{9}\cdot 11^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.112385789001728.1	x^10 + 10x^8 - 8x^7 + 23x^6 - 48x^5 - 38x^4 + 56x^3 + 33x^2 + 8x + 16	\( -\,2^{19}\cdot 11^{8} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.120135498046875.1	x^10 - 5x^9 + 15x^8 - 30x^7 + 45x^6 - 51x^5 + 30x^4 - 15x^2 - 15x + 42	\( -\,3^{9}\cdot 5^{14} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.120367356051456.1	x^10 - 2x^9 + 3x^8 - 24x^6 + 120x^5 - 192x^4 + 144x^3 - 60x^2 + 8x - 4	\( 2^{23}\cdot 3^{15} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.0.134369280000000.9	x^10 - 4x^9 + x^8 + 12x^7 - 60x^5 + 66x^4 + 36x^3 + 27x^2 + 9	\( -\,2^{18}\cdot 3^{8}\cdot 5^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.139314069504000.1	x^10 - 2x^9 + 3x^8 + 27x^6 + 18x^5 - 3x^4 - 96x^3 + 33x^2 + 46x + 13	\( -\,2^{21}\cdot 3^{12}\cdot 5^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.139314069504000.2	x^10 - 4x^9 + 12x^7 + 6x^6 - 24x^5 + 6x^4 + 36x^3 + 21x^2 - 20x + 14	\( -\,2^{21}\cdot 3^{12}\cdot 5^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.0.142657607172096.5	x^10 - 4x^9 + 3x^8 - 6x^6 + 24x^5 + 6x^4 + 45x^2 + 12x + 15	\( -\,2^{28}\cdot 3^{12} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.142826025627648.1	x^10 - 2x^9 - 9x^8 + 24x^7 + 9x^6 - 66x^5 + 57x^4 - 42x^3 + 42x^2 - 2x + 10	\( 2^{12}\cdot 3^{9}\cdot 11^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.161243136000000.4	x^10 - 2x^9 + 3x^8 + 12x^6 - 24x^5 + 12x^4 + 48x^2 - 32x + 16	\( -\,2^{19}\cdot 3^{9}\cdot 5^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.161243136000000.7	x^10 - 4x^9 + 6x^8 + 75x^2 + 100x + 50	\( -\,2^{19}\cdot 3^{9}\cdot 5^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.163470238547968.2	x^10 - 2x^9 + 11x^8 + 14x^6 + 12x^5 + 10x^4 + 32x^3 + 53x^2 + 30x - 9	\( 2^{23}\cdot 11^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.4.163840000000000.1	x^10 - 10x^8 + 35x^6 - 12x^5 - 50x^4 + 60x^3 + 15x^2 - 60x + 40	\( -\,2^{24}\cdot 5^{10} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.2.173440856752128.1	x^10 - 2x^9 + 3x^8 - 6x^6 + 12x^5 - 30x^4 - 15x^2 - 2x - 41	\( 2^{19}\cdot 3^{9}\cdot 7^{5} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.2.176637542400000.1	x^10 - 2x^9 + 3x^8 - 24x^7 + 24x^6 - 40x^5 + 94x^4 - 88x^3 + 116x^2 - 16x + 76	\( 2^{19}\cdot 3^{4}\cdot 5^{5}\cdot 11^{3} \)	$(A_6 : C_2) : C_2$ (as 10T35)	$[2]$
10.0.177054207934464.1	x^10 - 2x^9 - 5x^8 + 2x^7 + 35x^6 - 28x^5 - 21x^4 - 18x^3 + 36x^2 + 6x + 6	\( -\,2^{15}\cdot 3^{8}\cdot 7^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.177054207934464.2	x^10 - 4x^9 + 6x^8 - 6x^7 + 21x^4 - 12x^3 + 48x^2 - 16x + 16	\( -\,2^{15}\cdot 3^{8}\cdot 7^{7} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.4.180912911484375.1	x^10 - 4x^9 - 9x^8 + 60x^7 - 45x^6 - 180x^5 + 420x^4 - 390x^3 + 195x^2 - 50x + 5	\( -\,3^{9}\cdot 5^{7}\cdot 7^{6} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.196830000000000.8	x^10 + 15x^6 - 78x^5 + 180x^4 - 240x^3 + 240x^2 - 160x + 48	\( -\,2^{10}\cdot 3^{9}\cdot 5^{10} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial (GRH)
10.0.203119913336832.1	x^10 - 4x^9 + 18x^8 - 24x^7 + 6x^6 + 12x^4 + 24x^3 + 9x^2 + 4x + 2	\( -\,2^{19}\cdot 3^{18} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial
10.0.203119913336832.2	x^10 - 4x^9 + 12x^7 + 24x^6 + 12x^4 + 24x^3 + 36x^2 + 16x + 8	\( -\,2^{19}\cdot 3^{18} \)	$(A_6 : C_2) : C_2$ (as 10T35)	Trivial