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 3622)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.229345007.1	x^10 - x^9 + 6x^8 - 3x^7 + 11x^6 - 3x^5 + 11x^4 - 3x^3 + 6x^2 - x + 1	\( -\,47^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.3077056399.1	x^10 - 2x^9 + 3x^8 - 7x^7 + x^6 + 2x^5 + 19x^4 - 25x^3 + 21x^2 - 5x + 1	\( -\,79^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.11592740743.1	x^10 - 2x^9 + 3x^8 + x^7 - 15x^6 + 22x^5 + 9x^4 - 65x^3 + 77x^2 - 39x + 9	\( -\,103^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.23863536599.2	x^10 - x^9 + 6x^8 + 3x^7 - x^6 + 37x^5 - 2x^4 + 12x^3 + 48x^2 - 16x + 32	\( -\,7^{5}\cdot 17^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.33038369407.1	x^10 - 5x^9 + 18x^8 - 42x^7 + 76x^6 - 102x^5 + 99x^4 - 67x^3 + 22x^2 + 9	\( -\,127^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.38579489651.1	x^10 - 4x^9 + 4x^8 - 4x^7 + 9x^6 - 6x^5 + 12x^4 - 2x^3 + 41x^2 - 2x + 4	\( -\,131^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.59797108943.2	x^10 + 6x^8 - x^7 + 12x^6 - 13x^5 + 45x^4 + 40x^3 + 43x^2 - 15x + 25	\( -\,11^{5}\cdot 13^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.101621504799.2	x^10 - 5x^9 + 22x^8 - 58x^7 + 119x^6 - 175x^5 + 181x^4 - 128x^3 + 37x^2 + 6x + 9	\( -\,3^{5}\cdot 53^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.183765996899.1	x^10 - x^9 + 11x^8 + 4x^7 + 45x^6 + 49x^5 + 131x^4 + 148x^3 + 156x^2 + 144x + 64	\( -\,179^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.296630859375.1	x^10 + 5x^8 + 15x^6 + 20x^4 + 25x^2 + 15	\( -\,3^{5}\cdot 5^{13} \)	$D_5$ (as 10T2)	$[2]$
10.0.602738989907.1	x^10 - 2x^9 + 5x^8 - 4x^7 - 9x^6 + 28x^5 - 41x^4 + 30x^3 + 99x^2 + 16x + 113	\( -\,227^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.779811265199.1	x^10 - 2x^8 - 15x^7 - 30x^6 + x^5 + 147x^4 + 366x^3 + 405x^2 + 217x + 49	\( -\,239^{5} \)	$D_5$ (as 10T2)	$[3]$
10.0.1250000000000.1	x^10 + 5x^8 - 10x^7 + 5x^6 - 28x^5 + 15x^4 - 10x^3 + 30x^2 + 40x + 16	\( -\,2^{10}\cdot 5^{13} \)	$D_5$ (as 10T2)	$[2]$
10.0.2272262782976.1	x^10 - 2x^9 - 5x^8 + 16x^7 - x^6 - 42x^5 + 37x^4 + 36x^3 + 236x^2 - 592x + 332	\( -\,2^{15}\cdot 37^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.2553954421743.1	x^10 - 2x^9 + 2x^8 + 13x^7 + 47x^6 + 4x^5 - 92x^4 - 114x^3 + 6x^2 + 135x + 81	\( -\,3^{5}\cdot 101^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.3303341057599.3	x^10 + 5x^8 - 10x^7 + 47x^6 - 25x^5 + 87x^4 - 124x^3 + 460x^2 - 319x + 319	\( -\,11^{5}\cdot 29^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.3602729712967.3	x^10 - 3x^8 + 19x^6 + 37x^4 - 54x^2 + 175	\( -\,7^{5}\cdot 11^{8} \)	$D_5$ (as 10T2)	$[5]$
10.0.4817172660224.1	x^10 + 2x^8 - 3x^6 - 4x^4 + 4x^2 + 1376	\( -\,2^{15}\cdot 43^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.5030919566507.1	x^10 - 2x^9 + x^8 + 6x^7 + 2x^6 + 10x^5 - 9x^4 + 24x^3 + 417x^2 - 622x + 428	\( -\,347^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.7024111812608.2	x^10 - 4x^8 + 13x^6 - 6x^4 + 64x^2 + 32	\( -\,2^{15}\cdot 11^{8} \)	$D_5$ (as 10T2)	$[5]$
10.10.10368641602001.1	x^10 - 2x^9 - 20x^8 + 2x^7 + 69x^6 - x^5 - 69x^4 + 2x^3 + 20x^2 - 2x - 1	\( 401^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.12309502009375.1	x^10 - 2x^9 - x^8 - 5x^7 - 11x^6 + 46x^5 + 115x^4 - 161x^3 - 291x^2 + 225x + 515	\( -\,5^{5}\cdot 83^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.16305067506199.1	x^10 - 4x^9 + 5x^8 + 15x^7 + 12x^6 - 79x^5 + 142x^4 - 103x^3 + 619x^2 - 128x + 443	\( -\,439^{5} \)	$D_5$ (as 10T2)	$[3]$
10.0.17061555810443.1	x^10 - 4x^9 + 4x^8 + 14x^7 - 70x^6 + 96x^5 + 25x^4 - 294x^3 + 968x^2 - 2024x + 1808	\( -\,443^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.17391168553984.1	x^10 + 16x^8 + 110x^6 + 352x^4 + 529x^2 + 144	\( -\,2^{10}\cdot 19^{8} \)	$D_5$ (as 10T2)	Trivial (GRH)
10.0.19501004534375.1	x^10 - 4x^9 + 4x^8 - 5x^7 - 22x^6 + 43x^5 + 162x^4 + 80x^3 + 536x^2 + 336x + 224	\( -\,5^{5}\cdot 7^{5}\cdot 13^{5} \)	$D_5$ (as 10T2)	$[2, 2]$
10.0.20516357421875.1	x^10 - 5x^9 + 15x^8 - 30x^7 + 45x^6 - 51x^5 + 85x^4 - 110x^3 + 295x^2 - 245x + 329	\( -\,5^{13}\cdot 7^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.25216079618399.1	x^10 + 18x^8 + 145x^6 + 576x^4 + 1024x^2 + 479	\( -\,479^{5} \)	$D_5$ (as 10T2)	$[5]$
10.0.27675731591168.1	x^10 - 10x^8 - 8x^7 - 3x^6 + 156x^4 + 312x^3 + 844x^2 + 560x + 400	\( -\,2^{15}\cdot 61^{5} \)	$D_5$ (as 10T2)	$[2]$ (GRH)
10.0.37078857421875.2	x^10 - 5x^8 + 10x^6 - 168x^5 + 225x^4 + 450x^3 + 405x^2 + 270x + 108	\( -\,3^{5}\cdot 5^{16} \)	$D_5$ (as 10T2)	Trivial (GRH)
10.0.39129873538843.1	x^10 + 14x^8 - 15x^6 + 75x^4 - 22x^2 + 523	\( -\,523^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.40000000000000.4	x^10 - 35x^6 + 130x^4 + 160	\( -\,2^{15}\cdot 5^{13} \)	$D_5$ (as 10T2)	$[2]$ (GRH)
10.0.60698860931851.1	x^10 - 2x^8 - 13x^6 + 14x^4 + 49x^2 + 2284	\( -\,571^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.77114156402999.1	x^10 + 14x^8 - 17x^6 + 137x^4 - 109x^2 + 599	\( -\,599^{5} \)	$D_5$ (as 10T2)	$[5]$
10.0.85154195684051.1	x^10 + 14x^8 - 31x^6 + 51x^4 + 378x^2 + 611	\( -\,13^{5}\cdot 47^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.87978302634375.1	x^10 - x^8 - 6x^7 + 99x^6 - 27x^5 - 271x^4 + 180x^3 + 1000x^2 + 825x + 225	\( -\,3^{5}\cdot 5^{5}\cdot 41^{5} \)	$D_5$ (as 10T2)	$[2, 2]$
10.0.90876845839099.1	x^10 + 14x^8 - 15x^6 + 171x^4 - 214x^2 + 619	\( -\,619^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.103244904396875.1	x^10 + 10x^8 - 67x^6 + 175x^4 + 846x^2 + 635	\( -\,5^{5}\cdot 127^{5} \)	$D_5$ (as 10T2)	$[2]$
10.0.121559878349523.1	x^10 - 11x^8 + 31x^6 + 303x^4 - 1908x^2 + 3888	\( -\,3^{5}\cdot 29^{8} \)	$D_5$ (as 10T2)	Trivial (GRH)
10.0.129074483789824.1	x^10 + 12x^8 - 4x^7 - 34x^6 - 28x^5 + 248x^4 + 116x^3 - 95x^2 + 140x + 668	\( -\,2^{15}\cdot 83^{5} \)	$D_5$ (as 10T2)	$[2]$ (GRH)
10.0.136023078872351.1	x^10 - 2x^8 + 99x^6 + 573x^4 + 1059x^2 + 671	\( -\,11^{5}\cdot 61^{5} \)	$D_5$ (as 10T2)	$[6]$
10.0.148628987203643.1	x^10 - 4x^9 - 8x^8 + 2x^7 + 66x^6 + 144x^5 + 237x^4 + 250x^3 + 908x^2 + 112x + 64	\( -\,683^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.156250000000000.3	x^10 - 10x^7 - 55x^6 - 106x^5 + 50x^4 + 680x^3 + 1600x^2 + 2240x + 1568	\( -\,2^{10}\cdot 5^{16} \)	$D_5$ (as 10T2)	$[5]$ (GRH)
10.0.157539780804451.1	x^10 + 2x^8 - 99x^6 + 591x^4 + 1118x^2 + 691	\( -\,691^{5} \)	$D_5$ (as 10T2)	Trivial (GRH)
10.0.166872925103499.1	x^10 - 10x^8 + 129x^6 + 179x^4 + 1306x^2 + 699	\( -\,3^{5}\cdot 233^{5} \)	$D_5$ (as 10T2)	$[2]$ (GRH)
10.0.196595458984375.1	x^10 - 5x^9 - 5x^8 + 40x^7 - 45x^6 + 67x^5 + 530x^4 + 85x^3 + 575x^2 + 495x + 121	\( -\,5^{13}\cdot 11^{5} \)	$D_5$ (as 10T2)	$[4]$
10.0.198926586778624.1	x^10 - 4x^8 + 102x^6 + 528x^4 + 953x^2 + 724	\( -\,2^{10}\cdot 181^{5} \)	$D_5$ (as 10T2)	$[2]$ (GRH)
10.0.207252522098163.3	x^10 - 4x^9 + 14x^8 - 22x^7 + 65x^6 + 164x^5 + 508x^4 + 888x^3 + 1671x^2 + 1890x + 900	\( -\,3^{5}\cdot 31^{8} \)	$D_5$ (as 10T2)	$[5]$ (GRH)
10.0.220405380367699.1	x^10 - 14x^8 + 109x^6 + 319x^4 - 578x^2 + 739	\( -\,739^{5} \)	$D_5$ (as 10T2)	Trivial (GRH)
10.0.238890943128751.1	x^10 + 6x^8 - 19x^6 - 84x^4 + 196x^2 + 6759	\( -\,751^{5} \)	$D_5$ (as 10T2)	$[3]$