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 52)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.234925181632512.1	x^10 - 4x^9 - 2x^8 + 16x^7 + 28x^6 - 56x^5 - 76x^4 + 41x^2 + 36x + 34	\( 2^{27}\cdot 3^{6}\cdot 7^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$
10.2.352387772448768.1	x^10 + 4x^8 - 8x^7 + 4x^6 - 8x^5 - 68x^4 + 136x^3 - 167x^2 + 120x - 32	\( 2^{26}\cdot 3^{7}\cdot 7^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$
10.2.704775544897536.1	x^10 - 2x^9 + x^8 - 16x^7 - 2x^6 - 28x^5 + 26x^4 - 24x^3 + 50x^2 - 132x + 46	\( 2^{27}\cdot 3^{7}\cdot 7^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$
10.2.28665446400000000.1	x^10 - 2x^9 - 7x^8 - 32x^7 - 77x^6 - 126x^5 - 179x^4 - 224x^3 - 169x^2 - 74x + 19	\( 2^{25}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.28665446400000000.5	x^10 - 10x^8 + 35x^6 - 100x^5 - 50x^4 + 500x^3 + 25x^2 - 500x - 2204	\( 2^{25}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.98101701371953125.1	x^10 + 9x^8 - 35x^7 + 46x^6 - 315x^5 + 119x^4 - 245x^3 + 111x^2 + 1260x - 7600	\( 3^{6}\cdot 5^{7}\cdot 7^{6}\cdot 11^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$
10.2.114661785600000000.6	x^10 - 2x^9 + 7x^8 + 24x^6 - 144x^5 - 216x^4 + 1296x^3 - 1755x^2 + 1062x - 261	\( 2^{27}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial
10.2.114661785600000000.9	x^10 - 2x^9 + 11x^8 - 8x^7 - 26x^6 + 60x^5 + 22x^4 - 296x^3 - 1102x^2 + 556x - 86	\( 2^{27}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.114661785600000000.14	x^10 - 16x^8 - 24x^7 + 92x^6 + 224x^5 + 40x^4 - 784x^3 - 671x^2 + 808x + 760	\( 2^{27}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.114661785600000000.16	x^10 - 2x^9 - 17x^8 - 32x^7 + 136x^6 + 616x^5 - 212x^4 - 2672x^3 - 392x^2 + 4176x + 3240	\( 2^{27}\cdot 3^{7}\cdot 5^{8} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.149299200000000000.41	x^10 - 5x^9 + 15x^8 - 10x^7 - 75x^6 - 87x^5 + 1005x^4 - 2390x^3 + 6585x^2 - 13975x + 10711	\( 2^{22}\cdot 3^{6}\cdot 5^{11} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.149299200000000000.61	x^10 - 5x^9 + 5x^8 - 20x^7 + 130x^6 - 126x^5 - 350x^4 + 460x^3 + 125x^2 + 715x - 1511	\( 2^{22}\cdot 3^{6}\cdot 5^{11} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.412027145762203125.1	x^10 - 10x^8 + 35x^6 - 598x^5 - 50x^4 + 2990x^3 + 25x^2 - 2990x - 2075	\( 3^{7}\cdot 5^{6}\cdot 7^{7}\cdot 11^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$
10.2.439718882080078125.1	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x - 17	\( 3^{7}\cdot 5^{12}\cdot 7^{7} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.439718882080078125.3	x^10 - 10x^8 + 35x^6 - 52x^5 - 50x^4 + 260x^3 + 25x^2 - 260x - 668	\( 3^{7}\cdot 5^{12}\cdot 7^{7} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.716636160000000000.29	x^10 - 10x^8 + 35x^6 - 28x^5 - 50x^4 + 140x^3 + 25x^2 - 140x + 100	\( 2^{25}\cdot 3^{7}\cdot 5^{10} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.716636160000000000.31	x^10 - 10x^8 + 35x^6 - 68x^5 - 50x^4 + 340x^3 + 25x^2 - 340x + 292	\( 2^{25}\cdot 3^{7}\cdot 5^{10} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.2060135728811015625.1	x^10 - 3x^9 - 26x^8 + 83x^7 + 331x^6 - 1105x^5 - 1790x^4 + 4595x^3 + 505x^2 - 3150x - 1400	\( 3^{7}\cdot 5^{7}\cdot 7^{7}\cdot 11^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[10]$ (GRH)
10.2.2617374298095703125.1	x^10 + 20x^8 + 70x^6 - 42x^5 - 425x^4 - 420x^3 + 275x^2 + 630x + 436	\( 3^{6}\cdot 5^{15}\cdot 7^{6} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.17915904000000000000.19	x^10 - 10x^8 + 35x^6 - 28x^5 - 50x^4 + 140x^3 + 25x^2 - 140x - 188	\( 2^{25}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.17915904000000000000.26	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x - 92	\( 2^{25}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.17915904000000000000.68	x^10 - 4x^9 - 26x^8 + 136x^7 - 11x^6 - 872x^5 + 1766x^4 - 4596x^3 + 17681x^2 - 32256x + 18472	\( 2^{25}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.23887872000000000000.79	x^10 - 20x^8 - 40x^7 + 160x^6 + 176x^5 - 200x^4 + 1040x^3 - 1820x^2 - 9600x + 12256	\( 2^{27}\cdot 3^{6}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.23887872000000000000.81	x^10 - 120x^7 - 270x^6 - 1512x^5 + 1800x^4 + 1800x^3 + 17505x^2 - 46440x + 26568	\( 2^{27}\cdot 3^{6}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.35831808000000000000.19	x^10 - 90x^6 - 72x^5 + 5040x^3 + 11025x^2 - 7560x - 19872	\( 2^{26}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.35831808000000000000.22	x^10 - 20x^8 + 210x^6 - 144x^5 - 2300x^4 + 9240x^3 - 20210x^2 + 26400x - 18048	\( 2^{26}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.35831808000000000000.24	x^10 + 20x^8 - 120x^7 + 320x^6 - 5024x^5 + 3400x^4 - 6320x^3 + 25060x^2 - 10720x - 10688	\( 2^{26}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.35831808000000000000.28	x^10 - 40x^8 + 620x^6 - 176x^5 - 4400x^4 + 3520x^3 + 12100x^2 - 19360x + 2944	\( 2^{26}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.35831808000000000000.29	x^10 + 20x^8 + 20x^6 - 272x^5 - 800x^4 + 1600x^3 + 4600x^2 - 8320x + 2944	\( 2^{26}\cdot 3^{7}\cdot 5^{12} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.54964860260009765625.1	x^10 - 10x^8 + 35x^6 - 17x^5 - 50x^4 + 85x^3 + 25x^2 - 85x + 46	\( 3^{7}\cdot 5^{15}\cdot 7^{7} \)	$C_5^2 : Q_8$ (as 10T20)	$[2]$ (GRH)
10.2.93312000000000000000.67	x^10 + 30x^8 - 80x^7 + 295x^6 - 2196x^5 + 650x^4 - 17540x^3 - 6885x^2 - 16860x - 10576	\( 2^{22}\cdot 3^{6}\cdot 5^{15} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.93312000000000000000.74	x^10 + 20x^8 + 70x^6 - 192x^5 - 2300x^4 - 1920x^3 + 1025x^2 + 2880x + 9136	\( 2^{22}\cdot 3^{6}\cdot 5^{15} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.10.225013362437548828125.1	x^10 - 5x^9 - 75x^8 + 250x^7 + 2045x^6 - 3495x^5 - 24665x^4 + 8590x^3 + 115395x^2 + 64975x - 63445	\( 3^{6}\cdot 5^{11}\cdot 43^{6} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.10.232213790035550390625.1	x^10 - 40x^8 + 560x^6 - x^5 - 3200x^4 + 20x^3 + 6400x^2 - 80x - 32	\( 3^{7}\cdot 5^{8}\cdot 43^{7} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.10.320870687440896000000.1	x^10 - 4x^9 - 68x^8 + 304x^7 + 943x^6 - 5216x^5 - 280x^4 + 17700x^3 - 2305x^2 - 18480x - 2450	\( 2^{25}\cdot 3^{7}\cdot 5^{6}\cdot 23^{4} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial
10.2.1349292851200000000000.1	x^10 - 10x^8 - 980x^6 - 3952x^5 - 13840x^4 - 51080x^3 - 156285x^2 - 170120x - 190354	\( 2^{25}\cdot 5^{11}\cdot 7^{7} \)	$C_5^2 : Q_8$ (as 10T20)	$[10]$ (GRH)
10.2.2239488000000000000000.43	x^10 - 10x^8 + 35x^6 - 92x^5 - 50x^4 + 460x^3 + 25x^2 - 460x + 196	\( 2^{25}\cdot 3^{7}\cdot 5^{15} \)	$C_5^2 : Q_8$ (as 10T20)	$[2]$ (GRH)
10.10.8603217100800000000000.1	x^10 - 80x^8 + 2115x^6 - 372x^5 - 22400x^4 + 6180x^3 + 93175x^2 - 15540x - 129054	\( 2^{25}\cdot 3^{7}\cdot 5^{11}\cdot 7^{4} \)	$C_5^2 : Q_8$ (as 10T20)	$[2]$ (GRH)
10.2.11197440000000000000000.51	x^10 + 50x^8 + 875x^6 - 700x^5 + 6250x^4 - 17500x^3 + 15625x^2 - 87500x - 12500	\( 2^{25}\cdot 3^{7}\cdot 5^{16} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.11197440000000000000000.52	x^10 + 50x^8 + 875x^6 - 100x^5 + 6250x^4 - 2500x^3 + 15625x^2 - 12500x - 12500	\( 2^{25}\cdot 3^{7}\cdot 5^{16} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.10.29026723754443798828125.1	x^10 - 40x^8 + 560x^6 - x^5 - 3200x^4 + 20x^3 + 6400x^2 - 80x - 4031	\( 3^{7}\cdot 5^{11}\cdot 43^{7} \)	$C_5^2 : Q_8$ (as 10T20)	$[10]$ (GRH)
10.2.58320000000000000000000.36	x^10 - 100x^8 + 3850x^6 - 960x^5 - 69500x^4 + 72000x^3 + 274025x^2 + 9600x - 1271120	\( 2^{22}\cdot 3^{6}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.58320000000000000000000.171	x^10 - 400x^7 + 2650x^6 + 4320x^5 - 10000x^4 - 678400x^3 + 4100625x^2 - 8946000x + 6894320	\( 2^{22}\cdot 3^{6}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	$[3]$ (GRH)
10.10.860680177459200000000000.1	x^10 - 210x^8 - 280x^7 + 14455x^6 + 29988x^5 - 373870x^4 - 892780x^3 + 2921625x^2 + 7782180x + 4138736	\( 2^{22}\cdot 3^{6}\cdot 5^{11}\cdot 7^{8} \)	$C_5^2 : Q_8$ (as 10T20)	$[5]$ (GRH)
10.2.1399680000000000000000000.71	x^10 + 50x^8 + 425x^6 - 5300x^5 - 1250x^4 + 18700x^3 + 625x^2 + 54500x - 597980	\( 2^{25}\cdot 3^{7}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	$[2, 30]$ (GRH)
10.2.1399680000000000000000000.78	x^10 + 50x^8 + 425x^6 - 700x^5 - 1250x^4 + 1700x^3 + 625x^2 - 500x - 380	\( 2^{25}\cdot 3^{7}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	$[10]$ (GRH)
10.2.1399680000000000000000000.102	x^10 + 50x^8 + 425x^6 - 220x^5 - 1250x^4 + 500x^3 + 625x^2 - 500x + 100	\( 2^{25}\cdot 3^{7}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	$[2]$ (GRH)
10.2.1399680000000000000000000.113	x^10 + 50x^8 + 425x^6 - 940x^5 - 1250x^4 - 10300x^3 + 625x^2 - 126500x + 162820	\( 2^{25}\cdot 3^{7}\cdot 5^{19} \)	$C_5^2 : Q_8$ (as 10T20)	$[2]$ (GRH)
10.2.4216540160000000000000000.2	x^10 + 50x^8 + 875x^6 - 300x^5 + 6250x^4 - 7500x^3 + 15625x^2 - 37500x - 12500	\( 2^{25}\cdot 5^{16}\cdot 7^{7} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)
10.2.9411920000000000000000000.1	x^10 + 100x^8 - 600x^7 + 1750x^6 - 29400x^5 + 52500x^4 + 255000x^3 - 39375x^2 - 225000x - 6182000	\( 2^{22}\cdot 5^{19}\cdot 7^{6} \)	$C_5^2 : Q_8$ (as 10T20)	Trivial (GRH)