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 338)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.11284439629824.1	x^10 - 2x^9 - 3x^8 + 12x^7 - 15x^6 + 6x^5 + 9x^4 + 6x^2 + 8x + 2	\( 2^{18}\cdot 3^{16} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.15542770074624.1	x^10 + 3x^8 + 18x^6 - 12x^5 - 18x^4 - 27x^2 + 12x - 9	\( 2^{10}\cdot 3^{12}\cdot 13^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.38806720086016.1	x^10 - 4x^9 + 7x^8 - 15x^6 + 13x^4 + 8x^3 + 32x^2 - 64x + 20	\( 2^{18}\cdot 23^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial
10.2.45579633110361.1	x^10 - 3x^9 + 18x^7 - 18x^6 - 18x^5 + 9x^4 - 9x^3 - 36x^2 + 16x - 3	\( 3^{18}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial
10.2.57987356893249.1	x^10 - 3x^8 - 3x^7 + 13x^6 - 15x^5 - 9x^4 + 20x^3 + 16x^2 - 32x + 16	\( 7^{6}\cdot 149^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.227081481823729.1	x^10 - 5x^9 + 2x^8 + 20x^7 - 8x^6 - 50x^5 - 3x^4 + 95x^3 + 57x^2 - 95x - 76	\( 13^{6}\cdot 19^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial
10.2.256096265048064.1	x^10 - 9x^8 + 15x^6 - 24x^5 + 9x^4 + 144x^3 + 180x^2 + 96x + 36	\( 2^{12}\cdot 3^{12}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.316113500535561.1	x^10 - x^9 + 3x^8 - 6x^7 + 3x^6 - 3x^5 - 3x^3 - 6x^2 - 8x - 1	\( 3^{12}\cdot 29^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.334493080879104.1	x^10 - 2x^9 + 6x^8 - 12x^7 + 27x^6 - 42x^5 + 54x^4 - 84x^3 + 60x^2 + 4x - 14	\( 2^{18}\cdot 3^{12}\cdot 7^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.357790957421769.1	x^10 - 3x^9 + 12x^7 - 9x^6 - 9x^5 + 39x^4 + 18x^3 - 99x^2 + 42x + 9	\( 3^{18}\cdot 31^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.370517533364224.1	x^10 - 2x^9 + 12x^8 - 28x^7 + 42x^6 - 38x^5 + 33x^4 - 10x^3 - 5x^2 - 6x - 1	\( 2^{12}\cdot 67^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.471655843734321.1	x^10 - 3x^9 + 9x^8 - 9x^7 - 6x^6 + 57x^5 - 117x^4 + 144x^3 - 117x^2 + 51x - 9	\( 3^{12}\cdot 31^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.688747536000000.1	x^10 - 4x^9 + 6x^7 - 6x^6 + 18x^5 - 42x^4 + 60x^3 - 72x^2 + 32x - 20	\( 2^{10}\cdot 3^{16}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.1393140695040000.8	x^10 - 2x^9 - 9x^8 + 24x^7 + 21x^6 - 66x^5 - 51x^4 + 108x^3 + 144x^2 + 60x + 6	\( 2^{22}\cdot 3^{12}\cdot 5^{4} \)	$\PSL(2,9)$ (as 10T26)	Trivial
10.2.1624959306694656.1	x^10 - 2x^9 - 9x^8 + 12x^7 + 48x^6 - 36x^5 - 30x^4 - 48x^3 + 64x + 16	\( 2^{22}\cdot 3^{18} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.1624959306694656.2	x^10 - 12x^7 + 27x^6 - 168x^4 + 216x^3 + 162x^2 - 712x + 648	\( 2^{22}\cdot 3^{18} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.1763193692160000.1	x^10 + 3x^8 + 3x^6 - 6x^5 + 6x^4 - 24x^3 - 6x^2 - 4x + 12	\( 2^{16}\cdot 3^{16}\cdot 5^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.1870004703089601.1	x^10 - 2x^9 - 3x^7 + 15x^6 + 18x^5 - 18x^4 - 18x^3 - 9x - 9	\( 3^{18}\cdot 13^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.2176782336000000.10	x^10 - 4x^9 + 12x^8 + 12x^7 + 18x^6 + 24x^5 + 24x^4 - 48x^3 - 96x^2 + 64x + 32	\( 2^{18}\cdot 3^{12}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.2754990144000000.1	x^10 - 2x^9 - 15x^8 + 72x^6 + 138x^5 + 105x^4 + 96x^3 + 120x^2 + 80x + 20	\( 2^{12}\cdot 3^{16}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.3722460239233024.7	x^10 - 4x^9 + 14x^8 - 8x^7 - 56x^6 + 36x^5 + 158x^4 - 432x^3 + 935x^2 - 1152x + 512	\( 2^{22}\cdot 31^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.4097540240769024.1	x^10 - 2x^9 - 12x^8 + 24x^7 + 45x^6 - 102x^5 - 12x^4 + 180x^3 - 216x^2 + 120x - 24	\( 2^{16}\cdot 3^{12}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.5351889294065664.1	x^10 - 2x^9 - 9x^8 + 24x^7 + 15x^6 - 90x^5 + 69x^4 + 36x^3 - 90x^2 + 84x - 42	\( 2^{22}\cdot 3^{12}\cdot 7^{4} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.6499837226778624.3	x^10 - 2x^9 + 9x^8 - 24x^7 - 6x^6 + 36x^5 + 66x^4 + 264x^3 + 117x^2 + 78x - 219	\( 2^{24}\cdot 3^{18} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.8303765625000000.3	x^10 - 5x^9 + 15x^8 - 15x^7 + 60x^4 - 60x^3 - 60x^2 - 20x + 64	\( 2^{6}\cdot 3^{12}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	$[4]$ (GRH)
10.2.11664000000000000.20	x^10 + 5x^8 - 20x^7 + 5x^6 + 82x^5 - 130x^4 + 40x^3 + 140x^2 - 280x + 152	\( 2^{16}\cdot 3^{6}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.12744293212890625.1	x^10 - 5x^9 + 20x^8 - 20x^7 - 50x^6 + 238x^5 - 855x^4 + 1575x^3 - 1900x^2 + 1800x - 355	\( 5^{16}\cdot 17^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.16390160963076096.1	x^10 - 4x^9 + 12x^7 - 24x^6 + 36x^4 - 48x^3 + 64x + 32	\( 2^{18}\cdot 3^{12}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.20743797468893184.1	x^10 - 3x^9 - 3x^8 + 15x^7 + 6x^6 - 42x^5 - 9x^4 + 57x^3 + 33x^2 - 47x - 24	\( 2^{12}\cdot 3^{16}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$ (GRH)
10.2.20743797468893184.2	x^10 - 2x^9 + 9x^8 - 12x^7 + 24x^6 - 18x^5 + 3x^4 - 24x^3 - 72x^2 - 64x - 16	\( 2^{12}\cdot 3^{16}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.24794911296000000.1	x^10 - 2x^9 + 36x^5 + 33x^4 - 210x^3 + 45x^2 - 160x - 265	\( 2^{12}\cdot 3^{18}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.33215062500000000.8	x^10 - 5x^9 + 30x^7 + 15x^6 - 153x^5 + 110x^4 - 160x^3 + 135x^2 + 125x + 20	\( 2^{8}\cdot 3^{12}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	$[4]$ (GRH)
10.2.34828517376000000.11	x^10 - 2x^9 - 9x^8 + 48x^7 + 27x^6 - 234x^5 + 93x^4 + 444x^3 - 180x^2 - 400x + 20	\( 2^{22}\cdot 3^{12}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.34828517376000000.23	x^10 - 4x^9 + 15x^8 - 24x^7 + 96x^6 + 12x^4 + 72x^3 + 855x^2 - 492x - 147	\( 2^{22}\cdot 3^{12}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.34828517376000000.40	x^10 - 2x^9 - 3x^8 + 78x^6 - 156x^5 + 30x^4 - 384x^3 + 576x^2 + 208x - 440	\( 2^{22}\cdot 3^{12}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.46656000000000000.33	x^10 + 10x^8 - 64x^5 - 160x^4 + 240x^2 + 480	\( 2^{18}\cdot 3^{6}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.46673544305009664.1	x^10 - 2x^9 - 9x^8 + 30x^7 + 3x^6 - 54x^5 + 21x^4 + 66x^3 + 72x^2 + 32x + 8	\( 2^{10}\cdot 3^{18}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.46673544305009664.2	x^10 - 4x^9 + 9x^8 - 81x^6 + 144x^5 + 81x^4 - 432x^3 + 180x^2 + 178x - 118	\( 2^{10}\cdot 3^{18}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial
10.2.57352136505929721.1	x^10 - x^9 - 9x^8 + 9x^7 - 36x^6 + 204x^4 - 195x^3 - 477x^2 + 1267x - 907	\( 3^{18}\cdot 23^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.63474972917760000.1	x^10 - 2x^9 - 9x^8 + 12x^7 + 48x^6 - 108x^5 + 144x^4 - 180x^3 + 63x^2 - 58x + 17	\( 2^{18}\cdot 3^{18}\cdot 5^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.82944000000000000.10	x^10 + 10x^8 + 20x^6 - 40x^5 - 60x^4 - 240x^3 + 180x^2 - 720x + 1296	\( 2^{22}\cdot 3^{4}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.116552255737430016.1	x^10 - 4x^9 - 9x^8 + 32x^7 + 25x^6 + 36x^5 - 225x^4 + 216x^3 - 378x^2 + 216x - 54	\( 2^{24}\cdot 3^{10}\cdot 7^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.132860250000000000.2	x^10 + 15x^8 - 30x^7 + 90x^6 - 240x^5 + 510x^4 - 630x^3 + 405x^2 - 100x - 9	\( 2^{10}\cdot 3^{12}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.132860250000000000.14	x^10 - 15x^8 - 75x^6 - 6x^5 - 165x^4 - 30x^3 - 180x^2 - 50x - 90	\( 2^{10}\cdot 3^{12}\cdot 5^{12} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.139314069504000000.44	x^10 - 4x^9 + 36x^8 - 96x^7 + 348x^6 - 648x^5 + 1188x^4 - 1608x^3 + 1215x^2 - 1340x - 964	\( 2^{24}\cdot 3^{12}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	Trivial (GRH)
10.2.176319369216000000.1	x^10 - 2x^9 - 12x^8 + 18x^6 + 360x^5 + 90x^4 - 1080x^3 - 1800x^2 - 1200x - 300	\( 2^{18}\cdot 3^{16}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$
10.2.176319369216000000.2	x^10 - 4x^9 - 21x^8 + 72x^7 + 180x^6 - 612x^5 + 306x^4 - 576x^3 + 927x^2 - 1680x + 1707	\( 2^{18}\cdot 3^{16}\cdot 5^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.230446741890423969.1	x^10 - 3x^7 - 45x^6 - 108x^5 - 78x^4 + 36x^3 + 108x^2 + 53x + 9	\( 3^{18}\cdot 29^{6} \)	$\PSL(2,9)$ (as 10T26)	$[4]$
10.2.243845455960866816.1	x^10 - 4x^9 + 9x^8 - 48x^7 + 21x^6 + 540x^5 - 741x^4 - 1464x^3 + 1746x^2 + 2060x - 2318	\( 2^{18}\cdot 3^{18}\cdot 7^{4} \)	$\PSL(2,9)$ (as 10T26)	$[2]$ (GRH)
10.2.246803372284575744.1	x^10 - 2x^9 + 9x^8 - 24x^7 - 57x^6 + 30x^5 + 207x^4 + 156x^3 - 96x^2 - 32x + 100	\( 2^{18}\cdot 3^{12}\cdot 11^{6} \)	$\PSL(2,9)$ (as 10T26)	$[2]$