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 636)

Label	Polynomial	Discriminant	Galois group	Class group
11.3.24963663301.1	x^11 - 2x^8 + 4x^4 - x^3 - 3x^2 + x + 1	\( 971\cdot 25709231 \)	$S_{11}$ (as 11T8)	Trivial
11.3.26176773577.1	x^11 - x^9 - x^8 - 2x^7 + 2x^5 + 3x^4 - 2x^2 + 1	\( 14851\cdot 1762627 \)	$S_{11}$ (as 11T8)	Trivial
11.3.26877166541.1	x^11 - x^9 - x^8 - 2x^7 + x^5 + 2x^4 + 2x^3 - 1	\( 1583\cdot 2731\cdot 6217 \)	$S_{11}$ (as 11T8)	Trivial
11.3.27095385033.1	x^11 - 2x^9 - x^7 - x^6 + 4x^5 + x^4 - 2x - 1	\( 3^{3}\cdot 1003532779 \)	$S_{11}$ (as 11T8)	Trivial
11.3.27252765193.1	x^11 - 2x^8 - x^7 + x^6 + x^5 - x^4 - 2x^3 + x^2 + 2x + 1	\( 1559\cdot 17480927 \)	$S_{11}$ (as 11T8)	Trivial
11.3.28208540809.1	x^11 - x^10 + x^9 - 3x^5 + x^4 - 2x^2 + x + 1	\( 28208540809 \)	$S_{11}$ (as 11T8)	Trivial
11.3.28385393161.1	x^11 - x^10 + 2x^9 - x^7 + 2x^6 - x^5 - x^4 + x^3 - x^2 - x + 1	\( 28385393161 \)	$S_{11}$ (as 11T8)	Trivial
11.3.28868429753.1	x^11 - x^9 - x^6 - x^5 + x^4 - x^3 + 2x - 1	\( 163\cdot 177106931 \)	$S_{11}$ (as 11T8)	Trivial
11.3.32252418553.1	x^11 - 4x^10 + 9x^9 - 15x^8 + 21x^7 - 21x^6 + 17x^5 - 8x^4 + 3x^2 - 3x + 1	\( 61\cdot 227\cdot 397\cdot 5867 \)	$S_{11}$ (as 11T8)	Trivial
11.3.64283038681.1	x^11 - x^10 - 5x^9 + 3x^8 + 10x^7 - 3x^6 - 11x^5 + 3x^4 + 5x^3 - 2x^2 + 1	\( 71^{2}\cdot 3571^{2} \)	$A_{11}$ (as 11T7)	Trivial
11.3.66355073541.1	x^11 - 5x^9 - x^8 + 7x^7 + 4x^6 - x^5 - 5x^4 - 2x^3 + 2x^2 - 1	\( 3^{2}\cdot 7372785949 \)	$S_{11}$ (as 11T8)	Trivial
11.3.118125032125.1	x^11 - 2x^10 + x^9 + 4x^8 - 6x^7 + 2x^6 + 5x^5 - 5x^4 + 3x^2 - 3x + 1	\( 5^{3}\cdot 73\cdot 139\cdot 93131 \)	$S_{11}$ (as 11T8)	Trivial
11.3.121321855232.1	x^11 + 2x^9 - x^8 - x^7 + 2x^6 - 4x^5 + 2x^4 - 2x^3 - 2x^2 + 2x - 1	\( 2^{8}\cdot 2927\cdot 161911 \)	$S_{11}$ (as 11T8)	Trivial
11.3.127663872125.1	x^11 - 3x^10 + x^9 + 3x^8 + 2x^7 - 3x^6 - 6x^5 - 2x^4 + 6x^3 + 4x^2 - x - 1	\( 5^{3}\cdot 131\cdot 1297\cdot 6011 \)	$S_{11}$ (as 11T8)	Trivial
11.3.133644778349.1	x^11 - 2x^10 + 2x^9 - 2x^8 + x^6 - 3x^5 + 3x^4 - x^3 + x^2 - 1	\( 401\cdot 333278749 \)	$S_{11}$ (as 11T8)	Trivial
11.3.136113034225.1	x^11 - 2x^10 + x^9 + 4x^8 - 6x^7 + 8x^5 - 7x^4 - 2x^3 + 5x^2 - 2x - 1	\( 5^{2}\cdot 7^{2}\cdot 83^{2}\cdot 127^{2} \)	$A_{11}$ (as 11T7)	Trivial
11.3.177546554301.1	x^11 + 2x^9 - 2x^8 + x^7 - 4x^6 + x^5 - x^3 + 3x^2 - 3x + 1	\( 3\cdot 34963\cdot 1692709 \)	$S_{11}$ (as 11T8)	Trivial
11.3.233856337233.1	x^11 - 4x^10 + 6x^9 - 5x^8 + 7x^6 - 9x^5 + 3x^4 + 4x^3 - 4x^2 + 3x - 1	\( 3\cdot 246941\cdot 315671 \)	$S_{11}$ (as 11T8)	Trivial
11.3.303820448000.1	x^11 - 3x^10 + 9x^8 - 6x^7 - 11x^6 + 6x^5 + 13x^4 - 4x^3 - 8x^2 + 2	\( 2^{8}\cdot 5^{3}\cdot 9494389 \)	$S_{11}$ (as 11T8)	Trivial
11.3.337570274092.1	x^11 - 3x^10 + 6x^9 - 4x^8 + 2x^7 + 4x^6 - 3x^5 + x^4 + 2x^3 + 5x^2 - 2x - 1	\( 2^{2}\cdot 89\cdot 4801\cdot 197507 \)	$S_{11}$ (as 11T8)	Trivial
11.3.836463893056.1	x^11 - x^9 + x^7 - x^6 + 2x^5 + x^4 - 2x^3 - x - 1	\( 2^{6}\cdot 11^{2}\cdot 19^{2}\cdot 547^{2} \)	$A_{11}$ (as 11T7)	Trivial
11.3.1013364643329.1	x^11 - 3x^10 + 5x^9 - 11x^8 + 11x^7 - 9x^6 + 7x^5 + x^4 - 6x^3 + 3x^2 - 4x + 1	\( 3^{4}\cdot 33829\cdot 369821 \)	$S_{11}$ (as 11T8)	Trivial
11.3.6912019581184.1	x^11 - x^9 - x^8 + 3x^5 + 2x^4 - 4x^3 - 3x^2 + x + 1	\( 2^{8}\cdot 37^{2}\cdot 4441^{2} \)	$A_{11}$ (as 11T7)	Trivial
11.3.11239665258721.1	x^11 - 2x^10 + 3x^9 + 2x^8 - 5x^7 + 16x^6 - 10x^5 + 10x^4 + 2x^3 - 3x^2 + 4x - 1	\( 1831^{4} \)	$\PSL(2,11)$ (as 11T5)	Trivial
11.3.11239665258721.2	x^11 - 2x^10 + x^9 - 5x^8 + 13x^7 - 9x^6 + x^5 - 8x^4 + 9x^3 - 3x^2 - 2x + 1	\( 1831^{4} \)	$\PSL(2,11)$ (as 11T5)	Trivial
11.3.31421675094016.1	x^11 - 3x^10 + 3x^9 - x^8 - x^5 - x^4 + 2x^2 - x - 1	\( 2^{14}\cdot 43793^{2} \)	$A_{11}$ (as 11T7)	Trivial
11.3.377913600000000.1	x^11 - x^10 + 7x^9 - 3x^8 + 3x^7 - 3x^6 - 7x^5 + x^4 - 4x^3 + 4x^2 + 2x - 2	\( 2^{14}\cdot 3^{10}\cdot 5^{8} \)	$A_{11}$ (as 11T7)	Trivial
11.3.590490000000000.1	x^11 - x^10 + x^9 - 5x^8 - 7x^7 + 7x^6 - 7x^5 + 31x^4 - 40x^3 + 8x^2 + 16x - 16	\( 2^{10}\cdot 3^{10}\cdot 5^{10} \)	$A_{11}$ (as 11T7)	Trivial
11.3.1771184688329389.1	x^11 - 3x - 1	\( 1771184688329389 \)	$S_{11}$ (as 11T8)	Trivial
11.3.3188646000000000.1	x^11 - 2x^10 + 4x^9 + 6x^8 - 18x^7 + 18x^6 - 42x^4 + 12x^3 + 44x^2 + 32x + 8	\( 2^{10}\cdot 3^{13}\cdot 5^{9} \)	$S_{11}$ (as 11T8)	Trivial
11.3.11337408000000000.1	x^11 - 2x^10 + x^9 + 6x^8 - 21x^7 + 42x^6 - 60x^5 + 12x^4 + 12x^3 + 8x^2 + 20x + 8	\( 2^{15}\cdot 3^{11}\cdot 5^{9} \)	$S_{11}$ (as 11T8)	Trivial
11.3.12754584000000000.1	x^11 - 6x^9 + 27x^7 - 36x^6 - 18x^5 + 36x^4 - 72x^2 + 108	\( 2^{12}\cdot 3^{13}\cdot 5^{9} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.14946778125000000.1	x^11 - 5x^10 + 10x^9 - 60x^7 + 159x^6 - 170x^5 - 5x^4 + 175x^3 - 95x^2 - 86x + 130	\( 2^{6}\cdot 3^{14}\cdot 5^{11} \)	$S_{11}$ (as 11T8)	Trivial
11.3.22674816000000000.1	x^11 - 3x^10 - 6x^9 + 12x^8 + 18x^7 - 54x^6 - 96x^5 + 72x^4 + 126x^3 - 206x^2 - 336x - 96	\( 2^{16}\cdot 3^{11}\cdot 5^{9} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.29393280000000000.1	x^11 - 4x^10 + 20x^9 - 40x^8 + 90x^7 - 48x^6 - 8x^5 + 300x^4 - 360x^3 + 240x^2 + 128x - 592	\( 2^{16}\cdot 3^{8}\cdot 5^{10}\cdot 7 \)	$S_{11}$ (as 11T8)	Trivial
11.3.41650880849294336.1	x^11 - 4x - 2	\( 2^{10}\cdot 181\cdot 224722034969 \)	$S_{11}$ (as 11T8)	Trivial
11.3.41942754688329389.1	x^11 - 4x - 1	\( 79\cdot 137\cdot 1583\cdot 2448095621 \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.72862986240000000.1	x^11 - 2x^10 + 4x^9 - 20x^8 - 31x^7 - 58x^6 - 148x^5 - 8x^4 - 92x^3 + 120x^2 - 24x + 48	\( 2^{18}\cdot 3^{5}\cdot 5^{7}\cdot 11^{4} \)	$S_{11}$ (as 11T8)	Trivial
11.3.83593920849294336.1	x^11 - 8x - 4	\( 2^{10}\cdot 3\cdot 13\cdot 919\cdot 6323\cdot 360223 \)	$S_{11}$ (as 11T8)	Trivial
11.3.89671040138808576.1	x^11 - 2x^10 + 2x^9 + 20x^8 - 40x^7 + 28x^6 + 126x^5 - 324x^4 + 39x^3 + 374x^2 - 544x - 32	\( 2^{8}\cdot 3^{11}\cdot 7^{11} \)	$S_{11}$ (as 11T8)	Trivial
11.3.89671040138808576.2	x^11 - 3x^10 - 6x^9 + 43x^8 - 24x^7 - 126x^6 + 266x^5 - 69x^4 - 339x^3 + 533x^2 - 342x + 102	\( 2^{8}\cdot 3^{11}\cdot 7^{11} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.95234227200000000.1	x^11 - 3x^10 + 18x^9 - 44x^8 + 117x^7 - 147x^6 + 201x^5 + 3x^4 - 234x^3 + 182x^2 - 63x + 9	\( 2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 7 \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.153055008000000000.1	x^11 - x^10 + x^9 + 5x^8 - 17x^7 + 17x^6 + 3x^5 - 39x^4 + 120x^3 - 72x^2 - 144x + 144	\( 2^{14}\cdot 3^{14}\cdot 5^{9} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.226748160000000000.1	x^11 - x^10 - 20x^9 + 25x^8 + 170x^7 - 219x^6 - 651x^5 + 930x^4 + 900x^3 - 1530x^2 - 198x + 648	\( 2^{17}\cdot 3^{11}\cdot 5^{10} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.306163501093434961.1	x^11 - 9x - 4	\( 1823\cdot 7177\cdot 23400427991 \)	$S_{11}$ (as 11T8)	Trivial
11.3.327680000000000000.1	x^11 - 60x^7 - 64x^6 - 320x^4 - 380x^3 - 512x - 640	\( 2^{28}\cdot 5^{13} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.356874190848000000.1	x^11 - 5x^10 + 3x^9 + 13x^8 - 44x^7 + 128x^6 - 60x^5 - 116x^4 + 44x^3 + 108x^2 - 500x + 180	\( 2^{24}\cdot 3^{4}\cdot 5^{6}\cdot 7^{5} \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.471433881162091061.1	x^11 - 5x - 3	\( 628638793\cdot 749928077 \)	$S_{11}$ (as 11T8)	Trivial
11.3.487989090849294336.1	x^11 - 5x - 2	\( 2^{11}\cdot 3\cdot 4391\cdot 18088204909 \)	$S_{11}$ (as 11T8)	Trivial (GRH)
11.3.488280964688329389.1	x^11 - 5x - 1	\( 3\cdot 73\cdot 2229593446065431 \)	$S_{11}$ (as 11T8)	Trivial (GRH)