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 148)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.292820000000.1	x^10 - x^9 + 3x^8 + x^6 + 5x^5 - 3x^4 + 8x^3 + x^2 + 5x + 5	\( 2^{8}\cdot 5^{7}\cdot 11^{4} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.714892578125.1	x^10 - 9x^5 - 11	\( 5^{11}\cdot 11^{4} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.7812500000000.1	x^10 - 6x^5 + 4	\( 2^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.7812500000000.4	x^10 - 2x^5 - 4	\( 2^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.19073486328125.1	x^10 - 5x^5 + 5	\( 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.19073486328125.2	x^10 - 5x^5 - 5	\( 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.91511767578125.1	x^10 + 5x^8 + 10x^6 - 23x^5 + 45x^4 - 100x^3 + 85x^2 - 25x + 1	\( 5^{11}\cdot 37^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.91511767578125.3	x^10 - 5x^9 + 15x^8 - 20x^7 - 15x^6 + 137x^5 - 330x^4 + 490x^3 - 475x^2 + 300x - 99	\( 5^{11}\cdot 37^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.125000000000000.1	x^10 + 5x^8 - 10x^6 - 2x^5 - 25x^4 + 20x^3 + 25x^2 + 10x - 4	\( 2^{12}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.125000000000000.2	x^10 - 5x^8 - 10x^6 - 10x^5 + 25x^4 + 25x^2 - 50x + 20	\( 2^{12}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.157809620000000.1	x^10 - 4x^9 - 3x^8 + 24x^7 - 32x^6 - 32x^5 - 16x^4 + 188x^3 - 369x^2 + 172x - 29	\( 2^{8}\cdot 5^{7}\cdot 53^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.157809620000000.3	x^10 - 4x^9 - 4x^8 + 46x^7 - 54x^6 - 80x^5 + 180x^4 + 40x^3 - 80x^2 - 100x + 100	\( 2^{8}\cdot 5^{7}\cdot 53^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.200225830078125.4	x^10 - 3x^5 - 9	\( 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.200225830078125.5	x^10 - 9x^5 + 9	\( 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.357012500000000.1	x^10 + 5x^8 - 10x^7 + 10x^6 - 4x^5 + 40x^4 + 10x^3 - 15x^2 - 1	\( 2^{8}\cdot 5^{11}\cdot 13^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.357012500000000.2	x^10 + 5x^8 - 30x^7 - 66x^5 + 300x^4 - 110x^3 + 215x^2 - 1010x + 739	\( 2^{8}\cdot 5^{11}\cdot 13^{4} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.632812500000000.1	x^10 + 10x^8 + 35x^6 - 6x^5 + 50x^4 - 30x^3 + 25x^2 - 30x + 4	\( 2^{8}\cdot 3^{4}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.632812500000000.2	x^10 + 10x^8 + 35x^6 - 18x^5 + 50x^4 - 90x^3 + 25x^2 - 90x - 44	\( 2^{8}\cdot 3^{4}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.1312200000000000.12	x^10 - 5x^9 + 20x^8 - 35x^7 + 60x^6 - 65x^5 + 135x^4 - 50x^3 + 70x^2 + 100x + 20	\( 2^{12}\cdot 3^{8}\cdot 5^{11} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.1312200000000000.32	x^10 - 10x^8 - 30x^7 - 5x^6 + 144x^5 + 115x^4 - 390x^3 - 1120x^2 - 1380x - 461	\( 2^{12}\cdot 3^{8}\cdot 5^{11} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.1638400000000000.9	x^10 - 20x^8 - 20x^7 + 105x^6 + 228x^5 + 150x^4 + 80x^3 + 130x^2 + 120x + 36	\( 2^{25}\cdot 5^{11} \)	$C_5^2 : C_4$ (as 10T10)	$[10]$ (GRH)
10.2.1638400000000000.12	x^10 - 10x^8 + 10x^6 - 96x^5 - 100x^4 + 80x^3 - 175x^2 - 880x - 746	\( 2^{25}\cdot 5^{11} \)	$C_5^2 : C_4$ (as 10T10)	$[10]$
10.2.4287177620000000.2	x^10 - 5x^9 + 11x^8 + 8x^7 - 81x^6 + 249x^5 - 289x^4 + 340x^3 - 605x^2 + 305x + 155	\( 2^{8}\cdot 5^{7}\cdot 11^{8} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.4882812500000000.3	x^10 - 10x^5 - 20	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.6	x^10 - 10x^5 + 20	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.9	x^10 - 10x^5 - 100	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.10	x^10 - 20x^5 - 80	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.12	x^10 - 20x^5 + 80	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.13	x^10 - 30x^5 + 100	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.15	x^10 - 80x^5 + 1280	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.4882812500000000.16	x^10 - 40x^5 - 1600	\( 2^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.8192000000000000.5	x^10 + 10x^8 - 20x^7 + 45x^6 - 124x^5 + 200x^4 - 320x^3 + 290x^2 - 520x - 248	\( 2^{25}\cdot 5^{12} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.8192000000000000.8	x^10 - 10x^8 - 20x^7 + 35x^6 + 188x^5 + 100x^4 - 440x^3 - 430x^2 + 840x + 136	\( 2^{25}\cdot 5^{12} \)	$C_5^2 : C_4$ (as 10T10)	Trivial
10.2.10125000000000000.6	x^10 + 10x^8 + 35x^6 - 48x^5 + 50x^4 - 240x^3 + 25x^2 - 240x + 76	\( 2^{12}\cdot 3^{4}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.10125000000000000.7	x^10 - 15x^8 + 60x^6 - 10x^5 - 75x^4 - 200x^3 + 25x^2 + 650x - 580	\( 2^{12}\cdot 3^{4}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.10466742236328125.2	x^10 - 99x^5 - 1331	\( 5^{11}\cdot 11^{8} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.18757812500000000.1	x^10 + 10x^8 + 35x^6 - 14x^5 + 50x^4 - 70x^3 + 25x^2 - 70x + 4	\( 2^{8}\cdot 5^{15}\cdot 7^{4} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.18757812500000000.3	x^10 + 15x^8 + 60x^6 - 128x^5 + 75x^4 - 410x^3 + 25x^2 - 590x + 1676	\( 2^{8}\cdot 5^{15}\cdot 7^{4} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.4	x^10 - 6x^5 - 36	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.7	x^10 - 18x^5 + 36	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.8	x^10 - 18x^5 - 324	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.51257812500000000.11	x^10 - 12x^5 - 144	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.13	x^10 - 36x^5 + 144	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.20	x^10 - 54x^5 + 324	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	$[5]$
10.2.51257812500000000.26	x^10 - 144x^5 + 2304	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.51257812500000000.29	x^10 - 48x^5 - 2304	\( 2^{8}\cdot 3^{8}\cdot 5^{15} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.125141143798828125.2	x^10 - 15x^5 - 45	\( 3^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.125141143798828125.6	x^10 - 15x^5 - 225	\( 3^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.125141143798828125.8	x^10 - 15x^5 + 45	\( 3^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)
10.2.125141143798828125.12	x^10 - 45x^5 + 225	\( 3^{8}\cdot 5^{19} \)	$C_5^2 : C_4$ (as 10T10)	Trivial (GRH)