Global number field search results

Further refine search

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 923)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.12500000000.1	x^10 - 5x^9 + 15x^8 - 30x^7 + 45x^6 - 49x^5 + 35x^4 - 10x^3 - 5x^2 + 5x - 1	\( 2^{8}\cdot 5^{11} \)	$F_5$ (as 10T4)	Trivial
10.2.16063620352.1	x^10 - x^9 - 3x^8 + 5x^6 + x^5 - 5x^4 + 3x^2 - x - 1	\( 2^{8}\cdot 13^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.30517578125.1	x^10 - x^5 - 1	\( 5^{15} \)	$F_5$ (as 10T4)	Trivial
10.2.33237432513.1	x^10 - x^9 - 2x^8 + 7x^7 + x^6 - 3x^5 - x^4 + 7x^3 + 2x^2 - x - 1	\( 3^{4}\cdot 17^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.131220000000.2	x^10 - 3x^9 + 5x^8 - 12x^7 + 25x^6 - 33x^5 + 25x^4 - 12x^3 + 5x^2 - 3x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.146418828125.1	x^10 + x^8 + x^6 + 11x^4 + 11x^2 - 5	\( 5^{7}\cdot 37^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.200000000000.1	x^10 + 5x^8 + 5x^6 - 5x^4 - 5x^2 - 5	\( 2^{12}\cdot 5^{11} \)	$F_5$ (as 10T4)	Trivial
10.2.220150628352.1	x^10 + 2x^8 + 10x^6 - 8x^4 - 7x^2 - 2	\( 2^{25}\cdot 3^{8} \)	$F_5$ (as 10T4)	Trivial
10.2.320361328125.1	x^10 - 5x^9 + 5x^8 + 10x^7 - 15x^6 - 8x^5 + 40x^3 - 35x^2 + 10x - 4	\( 3^{8}\cdot 5^{11} \)	$F_5$ (as 10T4)	Trivial
10.2.450375078125.1	x^10 - x^8 + 6x^6 - 11x^4 + 6x^2 - 5	\( 5^{7}\cdot 7^{8} \)	$F_5$ (as 10T4)	Trivial
10.2.491270438912.1	x^10 - 2x^9 + x^8 - 6x^6 - 20x^5 - 6x^4 + x^2 - 2x + 1	\( 2^{25}\cdot 11^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.571220000000.1	x^10 - 5x^9 + 19x^8 - 46x^7 + 89x^6 - 127x^5 + 149x^4 - 130x^3 + 95x^2 - 45x + 5	\( 2^{8}\cdot 5^{7}\cdot 13^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.616443828125.1	x^10 - 3x^9 + 3x^7 + 10x^6 - 23x^5 + 10x^4 + 3x^3 - 3x + 1	\( 5^{7}\cdot 53^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.768320000000.1	x^10 - 3x^9 + 5x^8 + 8x^7 - 35x^6 + 57x^5 - 35x^4 + 8x^3 + 5x^2 - 3x + 1	\( 2^{12}\cdot 5^{7}\cdot 7^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.958348132352.1	x^10 - 4x^9 + 6x^8 - 30x^6 + 72x^5 - 60x^4 + 48x^2 - 64x + 32	\( 2^{25}\cdot 13^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.1012500000000.1	x^10 - 5x^8 - 10x^7 - 15x^6 + 24x^5 + 65x^4 + 30x^3 + 30x^2 + 20x + 4	\( 2^{8}\cdot 3^{4}\cdot 5^{11} \)	$F_5$ (as 10T4)	Trivial
10.2.1394580078125.1	x^10 - 10x^8 + 30x^6 - 11x^5 - 30x^4 + 10x^2 - 1	\( 5^{11}\cdot 13^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.1670420000000.2	x^10 - 2x^9 - x^8 + 14x^7 - 26x^6 + 38x^5 - 54x^4 + 30x^3 - 35x^2 + 20x - 5	\( 2^{8}\cdot 5^{7}\cdot 17^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.1698693120000.1	x^10 - 2x^9 - x^8 + 12x^7 - 17x^6 - 2x^5 + 41x^4 - 48x^3 + 6x^2 + 36x - 18	\( 2^{25}\cdot 3^{4}\cdot 5^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.1770868828125.1	x^10 - 3x^9 + 10x^8 - 27x^7 + 50x^6 - 63x^5 + 50x^4 - 27x^3 + 10x^2 - 3x + 1	\( 3^{4}\cdot 5^{7}\cdot 23^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.2099520000000.5	x^10 - 3x^9 + 2x^8 + 15x^7 - 29x^6 + 30x^5 - 17x^4 + 21x^3 - 4x^2 - 15x - 5	\( 2^{12}\cdot 3^{8}\cdot 5^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.2218612578125.1	x^10 - 3x^9 + 2x^8 + 5x^7 + x^6 - 30x^5 + 38x^4 + 6x^3 - 39x^2 + 25x - 5	\( 5^{7}\cdot 73^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.2621440000000.1	x^10 - 6x^8 + 26x^6 - 56x^4 + 41x^2 - 10	\( 2^{25}\cdot 5^{7} \)	$F_5$ (as 10T4)	$[2]$
10.2.3889620000000.1	x^10 - x^9 - 5x^8 + 10x^7 - 15x^6 + 19x^5 - 9x^4 + 10x^3 + 35x^2 - 25x + 5	\( 2^{8}\cdot 3^{4}\cdot 5^{7}\cdot 7^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.4078173828125.1	x^10 - 5x^9 + 10x^8 - 5x^7 - 10x^6 + x^5 + 10x^4 - 5x^3 - 10x^2 - 5x - 1	\( 5^{11}\cdot 17^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.4372847132672.1	x^10 - 4x^9 + 4x^8 - 4x^7 + 15x^6 - 16x^5 + 26x^4 - 56x^3 + 50x^2 - 48x + 28	\( 2^{25}\cdot 19^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.4415968335104.1	x^10 - 3x^9 + 7x^8 - 12x^7 - 7x^6 + 61x^5 - 69x^4 + 32x^3 - 21x^2 + 7x - 5	\( 2^{8}\cdot 29^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.4901737578125.1	x^10 - 4x^9 + 13x^8 - 30x^7 + 46x^6 - 55x^5 + 47x^4 - 8x^3 - 9x^2 - 5x + 5	\( 5^{7}\cdot 89^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.5596820000000.1	x^10 - 4x^9 + 3x^8 + 10x^7 - 14x^6 - 20x^5 - 8x^4 + 232x^3 - 344x^2 + 80x + 80	\( 2^{8}\cdot 5^{7}\cdot 23^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.9139520000000.1	x^10 + x^8 + x^6 - 9x^4 - 9x^2 - 5	\( 2^{12}\cdot 5^{7}\cdot 13^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.9389905805312.1	x^10 - 4x^9 + 8x^8 - 12x^7 - 5x^6 - 32x^5 + 78x^4 + 38x^2 - 48x + 68	\( 2^{25}\cdot 23^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.9496142578125.1	x^10 - 5x^8 - 10x^7 + 15x^5 + 5x^4 - 30x^3 - 45x^2 - 25x - 5	\( 3^{4}\cdot 5^{11}\cdot 7^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.10039762720000.1	x^10 - 5x^9 + 5x^8 + 10x^7 - 11x^6 - 23x^5 + 19x^4 + 22x^3 - 27x^2 + 9x - 1	\( 2^{8}\cdot 5^{4}\cdot 13^{7} \)	$F_5$ (as 10T4)	Trivial
10.2.11027981328125.1	x^10 + x^8 + x^6 + 21x^4 + 21x^2 - 20	\( 5^{7}\cdot 109^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.14145620000000.1	x^10 - 5x^9 + 19x^8 - 46x^7 + 89x^6 - 127x^5 + 139x^4 - 110x^3 + 55x^2 - 15x - 5	\( 2^{8}\cdot 5^{7}\cdot 29^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.14639743828125.1	x^10 - x^9 - 4x^8 + 23x^7 - 6x^6 - x^5 + 54x^4 + 65x^3 - 50x^2 + 35x + 5	\( 3^{8}\cdot 5^{7}\cdot 13^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.16200000000000.2	x^10 - 5x^8 - 5x^6 - 22x^5 + 30x^4 + 60x^3 + 60x^2 + 200x + 176	\( 2^{12}\cdot 3^{4}\cdot 5^{11} \)	$F_5$ (as 10T4)	Trivial
10.2.16746787578125.1	x^10 - 3x^9 + 6x^8 + 11x^7 - 29x^6 - 15x^5 - 6x^4 - 55x^3 + 65x^2 + 200x + 100	\( 5^{7}\cdot 11^{8} \)	$F_5$ (as 10T4)	$[5]$
10.2.18470420000000.1	x^10 - 5x^9 + 9x^8 - 6x^7 - x^6 + 3x^5 + 19x^4 - 40x^3 + 20x^2 - 80	\( 2^{8}\cdot 5^{7}\cdot 31^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.19073486328125.3	x^10 - 5	\( 5^{19} \)	$F_5$ (as 10T4)	Trivial
10.2.21634600078125.1	x^10 - 5x^9 + 9x^8 - 6x^7 - x^6 + 3x^5 - 6x^4 + 10x^3 - 5x^2 - 5	\( 3^{4}\cdot 5^{7}\cdot 43^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.23718420000000.1	x^10 - 4x^8 + 16x^6 - 44x^4 - 4x^2 - 20	\( 2^{8}\cdot 3^{4}\cdot 5^{7}\cdot 11^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.24302560546048.1	x^10 - 3x^9 + 5x^8 - 8x^7 + 3x^6 - 17x^5 + 73x^4 + 26x^3 + 5x^2 + 11x + 3	\( 2^{8}\cdot 37^{7} \)	$F_5$ (as 10T4)	Trivial
10.10.30012500000000.1	x^10 - 15x^8 + 60x^6 - 4x^5 - 60x^4 + 15x^2 - 1	\( 2^{8}\cdot 5^{11}\cdot 7^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.30012500000000.1	x^10 - 5x^9 + 15x^8 - 30x^7 + 75x^6 - 141x^5 + 225x^4 - 240x^3 + 375x^2 - 275x + 59	\( 2^{8}\cdot 5^{11}\cdot 7^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.32057708828125.2	x^10 - 5x^9 + 11x^8 - 14x^7 + 28x^6 - 56x^5 + 51x^4 - 15x^3 + 2x^2 - 3x - 1	\( 5^{7}\cdot 17^{7} \)	$F_5$ (as 10T4)	$[2]$
10.2.34535205078125.1	x^10 + 5x^8 - 10x^7 + 10x^6 - 15x^5 + 5x^4 + 30x^3 - 45x^2 + 25x - 5	\( 5^{11}\cdot 29^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.38506593828125.1	x^10 - 5x^9 - x^8 + 34x^7 - 21x^6 - 77x^5 + 64x^4 + 50x^3 - 55x^2 + 10x - 5	\( 5^{7}\cdot 149^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.39792905551872.1	x^10 - 12x^8 + 50x^6 - 76x^4 + 81x^2 - 8	\( 2^{25}\cdot 3^{4}\cdot 11^{4} \)	$F_5$ (as 10T4)	Trivial
10.2.41702720000000.1	x^10 + 4x^8 - 8x^7 + 23x^6 - 8x^5 + 14x^4 - 100x^3 - 13x^2 - 4x - 4	\( 2^{12}\cdot 5^{7}\cdot 19^{4} \)	$F_5$ (as 10T4)	Trivial