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 155)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.35450825752503.1	x^10 - 4x^9 + 9x^8 + 3x^7 - 21x^6 + 21x^4 - 3x^3 - 9x^2 + x + 5	\( -\,3^{16}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial
10.0.35664401793024.1	x^10 - 3x^8 + 12x^6 - 24x^5 + 12x^4 + 45x^2 - 24x + 9	\( -\,2^{26}\cdot 3^{12} \)	$\PGL(2,9)$ (as 10T30)	$[2]$
10.0.36585180721152.1	x^10 - 2x^9 + 6x^7 + 6x^6 - 24x^5 + 9x^4 + 6x^3 + 3x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{12}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$
10.2.55267035185152.1	x^10 - 2x^9 + 9x^8 - 7x^2 + 14x - 7	\( 2^{26}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial
10.2.218070794717793.1	x^10 - 3x^9 + 6x^8 - 15x^7 + 21x^6 - 3x^5 - 27x^4 + 21x^3 + 6x^2 - 13x - 3	\( 3^{12}\cdot 17^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial
10.0.245929148263683.1	x^10 - 3x^9 + x^8 + 5x^7 - 3x^6 + 2x^5 - x^4 - 5x^3 + 2x^2 + x + 1	\( -\,3^{5}\cdot 17^{4}\cdot 59^{4} \)	$\PGL(2,9)$ (as 10T30)	$[8]$
10.0.507227047723008.4	x^10 - 4x^9 + 9x^8 - 16x^7 + 22x^6 - 24x^5 + 22x^4 - 16x^3 + 45x^2 + 12x + 21	\( -\,2^{33}\cdot 3^{10} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.648731689453125.3	x^10 - 15x^6 - 9x^5 + 15x^4 + 30x^3 + 135x^2 + 200x + 84	\( 3^{12}\cdot 5^{13} \)	$\PGL(2,9)$ (as 10T30)	$[8]$
10.0.740849909603328.1	x^10 - 4x^9 + 30x^7 - 39x^6 - 108x^5 + 180x^4 + 198x^3 - 288x^2 - 178x + 226	\( -\,2^{10}\cdot 3^{16}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$
10.0.1141260857376768.7	x^10 - 24x^4 - 48x^3 + 18x^2 + 64x + 96	\( -\,2^{31}\cdot 3^{12} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.1163398544883712.1	x^10 - 2x^9 + 8x^8 + 12x^7 + 3x^6 + 30x^5 - 20x^4 - 112x^3 + 35x^2 + 102x - 46	\( 2^{24}\cdot 37^{5} \)	$\PGL(2,9)$ (as 10T30)	$[2]$
10.0.1358954496000000.2	x^10 - 4x^9 + 4x^8 + 24x^7 - 42x^6 - 8x^5 + 120x^4 - 96x^3 + 122x^2 - 104x + 120	\( -\,2^{30}\cdot 3^{4}\cdot 5^{6} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.1444408272617472.2	x^10 - 2x^9 + 3x^8 - 24x^7 - 24x^6 - 72x^5 - 72x^4 - 72x^3 - 27x^2 - 138x - 57	\( 2^{25}\cdot 3^{16} \)	$\PGL(2,9)$ (as 10T30)	$[2]$
10.0.1792673855336448.1	x^10 - 4x^9 + 6x^8 + 21x^4 + 21x^2 + 28x + 35	\( -\,2^{12}\cdot 3^{12}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.1792673855336448.2	x^10 - 2x^9 - 6x^7 + 21x^6 - 42x^4 + 48x^3 + 324x^2 - 224x + 160	\( -\,2^{12}\cdot 3^{12}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.2268852848160192.1	x^10 - x^9 - 3x^8 + 3x^7 - 21x^6 + 21x^5 + 147x^4 + 69x^3 - 48x^2 - 32x + 32	\( -\,2^{6}\cdot 3^{16}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.2446118092800000.3	x^10 - 2x^9 + 5x^8 + 12x^6 - 96x^5 + 240x^4 - 360x^3 + 297x^2 - 162x + 81	\( -\,2^{30}\cdot 3^{6}\cdot 5^{5} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.2.3049119689998336.5	x^10 - 3x^9 + 2x^8 + 12x^7 - 18x^6 + 14x^5 + 32x^4 - 52x^3 + 33x^2 + 53x - 42	\( 2^{31}\cdot 17^{5} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.2.3090719637245952.1	x^10 - 2x^9 - 3x^8 + 18x^7 - 3x^6 - 72x^5 + 72x^4 + 72x^3 - 234x^2 - 36x - 36	\( 2^{12}\cdot 3^{12}\cdot 17^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$
10.2.3820118932979712.1	x^10 - 4x^9 + 2x^8 + 8x^7 - 10x^6 + 40x^5 + 36x^4 - 32x^3 + 22x^2 - 24x - 68	\( 2^{30}\cdot 3^{5}\cdot 11^{4} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.4565043429507072.12	x^10 - 4x^9 + 24x^7 - 42x^6 + 84x^4 - 120x^3 - 81x^2 + 188x - 212	\( 2^{33}\cdot 3^{12} \)	$\PGL(2,9)$ (as 10T30)	Trivial
10.2.8153726976000000.7	x^10 + 4x^8 - 8x^7 - 8x^6 + 40x^4 - 400x^3 + 350x^2 + 400	\( 2^{31}\cdot 3^{5}\cdot 5^{6} \)	$\PGL(2,9)$ (as 10T30)	Trivial
10.0.10554638336000000.1	x^10 - 3x^9 + 4x^8 + 18x^7 - 29x^6 - 97x^5 + 96x^4 + 122x^3 - 151x^2 + 153x + 430	\( -\,2^{22}\cdot 5^{6}\cdot 11^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.2.11694053485707264.1	x^10 - 4x^9 + 13x^8 + 16x^7 - 108x^6 + 176x^5 + 100x^4 - 224x^3 + 238x^2 + 408x + 270	\( 2^{33}\cdot 3^{4}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.13956530861938752.1	x^10 - 5x^9 - 3x^8 + 33x^7 + 3x^6 - 27x^5 - 99x^4 - 57x^3 - 60x^2 - 44x - 14	\( 2^{6}\cdot 3^{12}\cdot 17^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.20480000000000000.11	x^10 - 20x^8 + 150x^6 - 48x^5 - 360x^4 + 240x^3 + 140x^2 - 640x - 64	\( 2^{24}\cdot 5^{13} \)	$\PGL(2,9)$ (as 10T30)	$[2]$
10.0.22290251120640000.1	x^10 - 4x^9 + 9x^8 - 12x^6 + 24x^5 + 36x^4 - 3x^2 + 4x + 5	\( -\,2^{26}\cdot 3^{12}\cdot 5^{4} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.0.28682781685383168.1	x^10 + 3x^8 - 36x^7 + 84x^6 - 84x^5 - 42x^4 + 144x^3 - 16x + 24	\( -\,2^{16}\cdot 3^{12}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.32780321926152192.1	x^10 - 18x^8 + 123x^6 - 132x^5 - 96x^4 + 156x^3 + 66x^2 - 128x + 60	\( 2^{19}\cdot 3^{12}\cdot 7^{6} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.0.36301645570563072.1	x^10 - 4x^9 - 9x^8 + 66x^7 - 21x^6 - 378x^5 + 819x^4 - 90x^3 - 4176x^2 + 3638x + 9082	\( -\,2^{10}\cdot 3^{16}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.83599920451289088.1	x^10 - 4x^9 + 28x^8 - 64x^7 + 316x^6 - 428x^5 + 1838x^4 - 1208x^3 + 3995x^2 - 224x + 834	\( -\,2^{22}\cdot 3^{4}\cdot 7^{5}\cdot 11^{4} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.0.92389579776000000.1	x^10 - 4x^9 - 3x^8 + 24x^7 + 49x^6 - 166x^5 - 358x^4 + 384x^3 + 2210x^2 + 2348x + 820	\( -\,2^{16}\cdot 3^{5}\cdot 5^{6}\cdot 13^{5} \)	$\PGL(2,9)$ (as 10T30)	$[2, 4]$
10.0.114731126741532672.1	x^10 - 9x^8 - 24x^7 + 63x^6 + 252x^5 + 651x^4 + 828x^3 + 504x^2 + 136x + 36	\( -\,2^{18}\cdot 3^{12}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.145206582282252288.1	x^10 - 2x^9 + 15x^8 - 42x^7 + 147x^6 - 126x^5 + 1071x^4 - 1386x^3 + 5166x^2 - 4704x + 6132	\( -\,2^{12}\cdot 3^{16}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.145206582282252288.2	x^10 - 2x^9 + 9x^8 + 42x^7 - 84x^6 + 378x^5 + 525x^4 - 1302x^3 + 5985x^2 - 3556x + 7364	\( -\,2^{12}\cdot 3^{16}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.166075312500000000.7	x^10 - 30x^6 - 456x^5 + 840x^4 + 720x^3 - 315x^2 + 120x + 144	\( 2^{8}\cdot 3^{12}\cdot 5^{13} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.2.223304493791020032.1	x^10 - 4x^9 + 12x^8 - 6x^7 + 72x^6 + 330x^5 - 318x^4 - 636x^3 + 288x^2 - 160x + 16	\( 2^{10}\cdot 3^{12}\cdot 17^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.326714810135067648.1	x^10 + 9x^8 - 24x^7 - 63x^6 + 126x^5 + 21x^4 + 2862x^3 - 1575x^2 - 4846x - 4239	\( 2^{10}\cdot 3^{18}\cdot 7^{7} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.369768517790072832.1	x^10 - 4x^9 + 9x^8 - 48x^7 + 138x^6 + 216x^5 - 78x^4 - 912x^3 - 153x^2 + 3764x + 5311	\( -\,2^{33}\cdot 3^{16} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.524288000000000000.29	x^10 - 5x^8 - 10x^6 - 256x^5 + 850x^4 - 2240x^3 + 3435x^2 - 7600x + 6321	\( 2^{31}\cdot 5^{12} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.557256278016000000.6	x^10 - 4x^9 + 9x^8 - 24x^7 + 66x^6 - 144x^5 + 234x^4 - 360x^3 + 630x^2 - 720x + 450	\( -\,2^{26}\cdot 3^{12}\cdot 5^{6} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.0.557256278016000000.7	x^10 - 2x^9 - 6x^8 + 24x^7 - 30x^6 + 12x^5 + 144x^4 - 384x^3 + 594x^2 - 692x + 460	\( -\,2^{26}\cdot 3^{12}\cdot 5^{6} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.2.599411600935354368.1	x^10 - 4x^9 + 48x^7 - 132x^6 + 576x^4 - 1056x^3 + 648x^2 - 224x + 32	\( 2^{26}\cdot 3^{12}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.2.599411600935354368.2	x^10 - 4x^9 - 3x^8 + 72x^7 - 144x^6 - 240x^5 + 1104x^4 - 168x^3 - 1479x^2 - 1316x + 2213	\( 2^{26}\cdot 3^{12}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	$[4]$ (GRH)
10.0.831979165027663872.2	x^10 - 2x^9 + 9x^8 - 36x^6 + 216x^5 - 324x^4 + 864x^3 + 972x^2 - 6264x + 12204	\( -\,2^{31}\cdot 3^{18} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.831979165027663872.3	x^10 - 4x^9 + 24x^7 + 138x^6 - 720x^5 - 348x^4 + 4344x^3 - 495x^2 - 13964x + 13052	\( -\,2^{31}\cdot 3^{18} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.831979165027663872.4	x^10 - 2x^9 + 9x^8 + 48x^7 - 96x^6 + 576x^5 + 192x^4 - 528x^3 + 10026x^2 - 13332x + 29490	\( -\,2^{31}\cdot 3^{18} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.0.995328000000000000.13	x^10 - 5x^8 - 20x^7 + 255x^6 - 764x^5 + 1475x^4 - 1540x^3 + 965x^2 + 1040x + 199	\( -\,2^{24}\cdot 3^{5}\cdot 5^{12} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)
10.2.1065620623885074432.1	x^10 - 2x^9 - 3x^8 + 48x^7 - 54x^6 - 204x^5 + 726x^4 + 288x^3 - 2118x^2 + 1372x + 3490	\( 2^{30}\cdot 3^{10}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	Trivial (GRH)
10.2.1070622572544000000.1	x^10 - 4x^9 - 31x^8 + 136x^7 + 326x^6 - 1624x^5 - 666x^4 + 4880x^3 + 1420x^2 - 880x - 4100	\( 2^{24}\cdot 3^{5}\cdot 5^{6}\cdot 7^{5} \)	$\PGL(2,9)$ (as 10T30)	$[2]$ (GRH)