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 77)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.594823321.1	x^8 - 3x^7 + 9x^6 - 15x^5 + 23x^4 - 21x^3 + 18x^2 - 7x + 2	\( 29^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial
8.0.2081951752609.1	x^8 - x^7 + 3x^6 - 7x^5 + 6x^4 + 11x^3 + 65x^2 - 145x + 108	\( 113^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial
8.8.9745585291264.1	x^8 - 20x^6 - 8x^5 + 100x^4 + 88x^3 - 96x^2 - 112x - 20	\( 2^{14}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial
8.0.15177592680649.1	x^8 - 3x^7 + 9x^6 - 26x^5 + 14x^4 - 18x^3 + 92x^2 - 46x + 135	\( 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$
8.8.15177592680649.1	x^8 - 2x^7 - 21x^6 + 62x^5 + 57x^4 - 311x^3 + 125x^2 + 360x - 283	\( 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial
8.0.49680238593241.2	x^8 - 2x^7 + 16x^6 - 9x^5 + 39x^4 - 33x^3 + 50x^2 - 497x + 484	\( 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$
8.0.58451728309129.1	x^8 - 2x^7 + 17x^6 - 37x^5 + 99x^4 - 158x^3 + 158x^2 - 75x + 74	\( 197^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial
8.0.80062677450625.1	x^8 - 2x^7 + 3x^6 + 11x^5 + 13x^4 + 143x^3 + 751x^2 + 755x + 225	\( 5^{4}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$
8.0.80062677450625.2	x^8 - 3x^7 + 22x^6 - 32x^5 + 118x^4 - 62x^3 + 287x^2 - 38x + 561	\( 5^{4}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$
8.0.103569212194816.1	x^8 + 16x^6 - 36x^5 + 214x^4 - 352x^3 + 672x^2 - 508x + 385	\( 2^{14}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.103569212194816.5	x^8 - 4x^7 + 4x^6 - 28x^5 + 164x^4 + 224x^3 + 736x^2 - 368x + 104	\( 2^{14}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.186374892382561.1	x^8 - 3x^7 + 20x^6 + 4x^5 + 39x^4 + 106x^3 + 304x^2 + 434x + 187	\( 239^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.226775649501184.4	x^8 - 2x^7 + 14x^6 - 14x^5 - 126x^4 + 630x^3 + 658x^2 - 5130x + 10267	\( 2^{14}\cdot 7^{12} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.226775649501184.5	x^8 - 2x^7 + 14x^6 + 84x^4 - 112x^3 + 28x^2 + 188x + 310	\( 2^{14}\cdot 7^{12} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.1680828542372281.2	x^8 - 2x^7 + 4x^6 + 33x^5 - 30x^4 - 124x^3 + 58x^2 + 47x + 90	\( 29^{6}\cdot 41^{4} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.0.1803810389321521.1	x^8 - 2x^7 - 28x^6 + 154x^5 + 189x^4 - 2016x^3 + 5278x^2 + 2701x + 2949	\( 7^{12}\cdot 19^{4} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.1803810389321521.2	x^8 - 4x^7 + 35x^6 - 42x^5 + 329x^4 - 14x^3 + 2611x^2 - 6607x + 3692	\( 7^{12}\cdot 19^{4} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$
8.0.2098795051761664.5	x^8 - 4x^7 + 8x^6 + 8x^5 + 44x^4 - 528x^3 + 2264x^2 - 3680x + 3100	\( 2^{14}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.2098795051761664.9	x^8 - 2x^7 - 32x^5 + 750x^4 - 4284x^3 + 13640x^2 - 22336x + 20334	\( 2^{14}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.7207688911775881.3	x^8 - 2x^7 + 34x^6 - 35x^5 + 166x^4 - 264x^3 - 1350x^2 - 1411x + 25450	\( 29^{6}\cdot 59^{4} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.0.9851127637605409.1	x^8 - x^7 + 37x^6 - 131x^5 + 327x^4 - 453x^3 + 515x^2 - 350x + 223	\( 463^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.10699063813365841.1	x^8 - x^7 + 41x^6 - 98x^5 + 411x^4 - 2087x^3 + 7263x^2 - 8915x + 6934	\( 17^{4}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.10699063813365841.2	x^8 - x^7 + 39x^6 - 8x^5 + 532x^4 - 683x^3 + 886x^2 - 8177x + 12648	\( 17^{4}\cdot 71^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.11847252093276889.1	x^8 - x^7 - 2x^6 - 143x^5 + 516x^4 - 733x^3 + 2136x^2 - 3095x + 1542	\( 37^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.11847252093276889.2	x^8 + 11x^6 - 9x^5 + 211x^4 + 1079x^3 + 4127x^2 + 7877x + 9987	\( 37^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$
8.0.12782719397154721.1	x^8 - 3x^7 - 56x^6 + 28x^5 + 1043x^4 - 567x^3 + 4704x^2 + 46853x + 57555	\( 7^{12}\cdot 31^{4} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.8.12782719397154721.1	x^8 - x^7 - 42x^6 + 77x^5 + 420x^4 - 854x^3 - 987x^2 + 1577x + 733	\( 7^{12}\cdot 31^{4} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.8.34110697514745856.1	x^8 - 2x^7 - 26x^6 + 58x^5 + 150x^4 - 402x^3 + 130x^2 + 162x - 61	\( 2^{14}\cdot 113^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.68745181834264576.1	x^8 - 2x^7 - 4x^6 - 84x^5 + 518x^4 - 792x^3 + 144x^2 + 344x + 378	\( 2^{14}\cdot 127^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.68745181834264576.13	x^8 - 48x^6 - 28x^5 + 1306x^4 - 3144x^3 - 104x^2 + 21788x + 310673	\( 2^{14}\cdot 127^{6} \)	$C_2^3:C_7$ (as 8T25)	Trivial (GRH)
8.0.248669678479753216.1	x^8 - 4x^7 + 60x^6 - 44x^5 + 1050x^4 + 1828x^3 + 4964x^2 + 396x + 641	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.8.248669678479753216.1	x^8 - 2x^7 - 102x^6 + 244x^5 + 2188x^4 - 3496x^3 - 10508x^2 + 18916x - 3958	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2]$
8.0.248669678479753216.4	x^8 - 2x^7 + 58x^6 + 360x^5 + 888x^4 + 428x^3 + 7960x^2 - 13984x + 7226	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.0.248669678479753216.5	x^8 - 12x^6 - 104x^5 + 674x^4 - 2792x^3 + 9628x^2 - 15424x + 9025	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 4]$ (GRH)
8.0.248669678479753216.6	x^8 - 2x^7 - 46x^6 - 126x^5 + 506x^4 + 4150x^3 + 13066x^2 + 21486x + 16867	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 8]$ (GRH)
8.0.248669678479753216.7	x^8 - 2x^7 - 60x^6 + 96x^5 + 1422x^4 - 56x^3 - 8876x^2 - 1764x + 18914	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.248669678479753216.8	x^8 - 2x^7 + 34x^6 + 26x^5 - 250x^4 - 1498x^3 + 11550x^2 - 21078x + 20479	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 4]$ (GRH)
8.0.248669678479753216.10	x^8 - 2x^7 + 38x^6 - 92x^5 + 192x^4 - 352x^3 + 3400x^2 - 11160x + 27598	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 4]$ (GRH)
8.0.248669678479753216.12	x^8 - 2x^7 + 44x^6 + 4x^5 + 318x^4 + 2212x^3 + 8152x^2 + 39964x + 60622	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.248669678479753216.14	x^8 - 4x^7 + 48x^6 + 24x^5 - 628x^4 + 1664x^3 + 7848x^2 - 48608x + 100732	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.0.248669678479753216.15	x^8 - 4x^7 + 774x^4 + 860x^3 + 21328x^2 + 74992x + 104189	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.248669678479753216.18	x^8 - 4x^7 + 20x^6 + 356x^5 - 1550x^4 + 3268x^3 + 55516x^2 - 237444x + 738641	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.0.248669678479753216.21	x^8 - 2x^7 + 34x^6 + 26x^5 + 954x^4 + 4522x^3 + 22386x^2 + 49958x + 37335	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.248669678479753216.22	x^8 - 2x^7 + 8x^6 - 200x^5 + 110x^4 + 4164x^3 + 23916x^2 + 58952x + 47966	\( 2^{14}\cdot 7^{4}\cdot 43^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)
8.0.813961029111660544.1	x^8 - 2x^7 - 4x^6 - 106x^5 + 702x^4 - 1986x^3 + 3720x^2 - 3254x + 995	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 2]$ (GRH)
8.8.813961029111660544.1	x^8 - 152x^6 - 72x^5 + 6472x^4 + 1936x^3 - 80160x^2 - 17984x - 480	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2]$ (GRH)
8.0.813961029111660544.2	x^8 - 2x^7 - 14x^6 + 418x^5 + 1542x^4 - 7270x^3 + 10922x^2 - 7274x + 2083	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 8]$ (GRH)
8.0.813961029111660544.3	x^8 - 4x^7 + 40x^6 + 100x^5 + 788x^4 + 1208x^3 + 1880x^2 + 3800x + 2668	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 4]$ (GRH)
8.0.813961029111660544.4	x^8 - 2x^7 + 8x^6 - 80x^5 + 2146x^4 - 2788x^3 + 1084x^2 + 9092x + 4470	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 2, 4]$ (GRH)
8.0.813961029111660544.5	x^8 - 2x^7 + 116x^6 - 156x^5 + 3646x^4 - 2176x^3 + 37652x^2 + 920x + 67182	\( 2^{14}\cdot 17^{4}\cdot 29^{6} \)	$C_2^3:C_7$ (as 8T25)	$[2, 4]$ (GRH)