Global number field search results

Further refine search

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 55)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3143861048180736.1	x^16 - 4x^15 + 8x^14 - 8x^13 - 4x^12 + 30x^11 - 56x^10 + 58x^9 - 18x^8 - 48x^7 + 98x^6 - 102x^5 + 73x^4 - 40x^3 + 18x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 13^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.12210723828596736.2	x^16 - 4x^15 + 11x^14 - 22x^13 + 34x^12 - 46x^11 + 55x^10 - 60x^9 + 63x^8 - 60x^7 + 55x^6 - 46x^5 + 34x^4 - 22x^3 + 11x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 73^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.12210723828596736.3	x^16 + x^14 - 4x^13 + 2x^12 - 4x^11 + 9x^10 - 8x^9 + 7x^8 - 8x^7 + 9x^6 - 8x^5 + 6x^4 - 2x^3 + x^2 - 2x + 1	\( 2^{16}\cdot 3^{8}\cdot 73^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.50301776770891776.1	x^16 - 6x^15 + 16x^14 - 24x^13 + 24x^12 - 18x^11 + 8x^10 + 6x^9 - 13x^8 + 6x^7 + 8x^6 - 18x^5 + 24x^4 - 24x^3 + 16x^2 - 6x + 1	\( 2^{28}\cdot 3^{8}\cdot 13^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.50301776770891776.2	x^16 - 2x^15 - 4x^13 + 12x^12 - 6x^11 + 8x^10 - 18x^9 + 11x^8 - 10x^7 + 8x^6 - 2x^5 + 4x^4 - 4x^3 + 4x^2 - 2x + 1	\( 2^{28}\cdot 3^{8}\cdot 13^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.99038527051792384.2	x^16 + 2x^12 + 9x^8 - 20x^4 + 16	\( 2^{34}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.121459186643042304.1	x^16 - x^14 - 11x^12 - 5x^10 + 36x^8 + 65x^6 + 31x^4 - 8x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 7^{10} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.371968759094317056.1	x^16 - x^15 + 2x^14 + 3x^13 - 2x^12 + 6x^11 + 2x^10 + 2x^9 + x^8 - 2x^7 + 2x^6 - 6x^5 - 2x^4 - 3x^3 + 2x^2 + x + 1	\( 2^{12}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.466612625725526016.1	x^16 - 3x^15 + 8x^14 - 9x^13 + 16x^12 - 30x^11 + 26x^10 - 30x^9 + 43x^8 - 30x^7 + 26x^6 - 30x^5 + 16x^4 - 9x^3 + 8x^2 - 3x + 1	\( 2^{12}\cdot 3^{12}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.829533556845379584.1	x^16 + 4x^14 + 11x^12 + 9x^10 - 4x^8 + 3x^6 + 5x^4 - 5x^2 + 1	\( 2^{16}\cdot 3^{10}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.1305169153600000000.1	x^16 + 5x^14 + 5x^12 + 10x^10 + 22x^8 + 10x^6 + 5x^4 + 5x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 13^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.1584616432828678144.1	x^16 + x^12 + 4x^8 + x^4 + 1	\( 2^{38}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.5951500145509072896.1	x^16 - 4x^15 + 13x^14 - 8x^13 - 4x^12 + 32x^11 - 13x^10 - 14x^9 + 43x^8 - 14x^7 - 13x^6 + 32x^5 - 4x^4 - 8x^3 + 13x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.6052387225600000000.3	x^16 + 4x^14 + 27x^12 + 28x^10 + 93x^8 - 146x^6 + 128x^4 - 72x^2 + 16	\( 2^{24}\cdot 5^{8}\cdot 31^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.6338465731314712576.4	x^16 - 2x^14 + 18x^12 - 54x^10 + 106x^8 - 54x^6 + 18x^4 - 2x^2 + 1	\( 2^{40}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.6338465731314712576.5	x^16 - 6x^14 + 10x^12 + 10x^10 - 14x^8 - 10x^6 + 10x^4 + 6x^2 + 1	\( 2^{40}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.8.6871947673600000000.1	x^16 - 4x^14 - 4x^12 - 36x^10 + 118x^8 - 188x^6 + 124x^4 - 28x^2 + 1	\( 2^{44}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.6871947673600000000.10	x^16 + 4x^14 - 4x^12 + 36x^10 + 118x^8 + 188x^6 + 124x^4 + 28x^2 + 1	\( 2^{44}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.7465802011608416256.2	x^16 + 7x^14 + 42x^12 + 136x^10 + 262x^8 + 243x^6 + 174x^4 - 90x^2 + 9	\( 2^{16}\cdot 3^{12}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.9349208943630483456.1	x^16 - 4x^15 + 12x^14 - 20x^13 + 18x^12 - 24x^11 + 4x^10 + 28x^9 + 51x^8 - 64x^7 - 20x^6 + 60x^5 - 12x^4 - 28x^3 + 24x^2 - 8x + 1	\( 2^{44}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.9349208943630483456.7	x^16 - 4x^15 + 8x^14 - 12x^13 + 28x^12 - 56x^11 + 52x^10 + 4x^9 - 125x^8 + 192x^7 - 88x^6 - 76x^5 + 232x^4 - 204x^3 + 96x^2 - 24x + 3	\( 2^{44}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.8.11161211905600000000.1	x^16 - 6x^14 + x^12 + 25x^10 - 70x^8 + 75x^6 - 29x^4 + x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 17^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.16620815899787526144.1	x^16 - 16x^13 - 8x^12 + 8x^11 + 96x^10 + 72x^9 - 2x^8 - 192x^7 - 128x^6 + 16x^5 + 176x^4 + 96x^3 + 32x^2 + 16x + 4	\( 2^{48}\cdot 3^{10} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.16620815899787526144.2	x^16 - 4x^14 - 16x^13 + 6x^12 + 40x^11 + 48x^10 + 24x^9 - 15x^8 - 80x^7 - 96x^6 - 40x^5 + 50x^4 + 48x^3 + 28x^2 + 24x + 9	\( 2^{48}\cdot 3^{10} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.18518907289600000000.1	x^16 - 4x^15 + 16x^14 - 38x^13 + 91x^12 - 156x^11 + 235x^10 - 300x^9 + 276x^8 - 220x^7 + 185x^6 - 88x^5 + 61x^4 - 36x^3 + 9x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{4} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.8.18518907289600000000.1	x^16 - 4x^15 + 20x^13 - 48x^12 + 92x^11 - 110x^10 - 30x^9 + 313x^8 - 392x^7 + 40x^6 + 250x^5 - 123x^4 - 34x^3 + 23x^2 + 2x - 1	\( 2^{24}\cdot 5^{8}\cdot 41^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.18518907289600000000.2	x^16 + 6x^14 + 14x^12 - 4x^10 + 41x^8 - 146x^6 + 24x^4 + 64x^2 + 16	\( 2^{24}\cdot 5^{8}\cdot 41^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.31093551780618829824.2	x^16 - 8x^15 + 24x^14 - 28x^13 - 2x^12 + 12x^11 + 60x^10 - 124x^9 + 105x^8 - 116x^7 + 132x^6 - 24x^5 + 80x^4 - 256x^3 - 64x^2 + 208x + 172	\( 2^{24}\cdot 3^{8}\cdot 7^{10} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.8.51399544780206637056.1	x^16 - 6x^15 + 8x^14 + 26x^13 - 124x^12 + 246x^11 - 172x^10 - 522x^9 + 1678x^8 - 1788x^7 - 218x^6 + 2644x^5 - 2985x^4 + 1510x^3 - 290x^2 - 8x + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.51399544780206637056.3	x^16 - 8x^15 + 38x^14 - 126x^13 + 304x^12 - 550x^11 + 856x^10 - 1288x^9 + 1858x^8 - 2322x^7 + 2414x^6 - 2060x^5 + 1411x^4 - 738x^3 + 282x^2 - 72x + 9	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.0.89791815397090000896.10	x^16 - 6x^15 + 18x^14 - 32x^13 + 49x^12 - 110x^11 + 290x^10 - 584x^9 + 890x^8 - 1238x^7 + 1936x^6 - 3410x^5 + 5784x^4 - 8416x^3 + 9248x^2 - 6664x + 2401	\( 2^{24}\cdot 3^{8}\cdot 13^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$ (GRH)
16.0.91376968498145132544.1	x^16 + 8x^14 + 38x^12 + 116x^10 + 227x^8 + 284x^6 + 214x^4 + 84x^2 + 9	\( 2^{28}\cdot 3^{10}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.8.91376968498145132544.1	x^16 - 8x^14 + 8x^12 + 24x^10 - 34x^8 + 24x^6 + 8x^4 - 8x^2 + 1	\( 2^{28}\cdot 3^{10}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.95224002328145166336.4	x^16 - x^14 + 5x^12 - 2x^10 + 10x^8 + 6x^6 + 45x^4 + 27x^2 + 81	\( 2^{20}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.0.101415451701035401216.2	x^16 - 8x^15 + 32x^14 - 84x^13 + 150x^12 - 164x^11 + 60x^10 + 124x^9 - 217x^8 + 108x^7 + 120x^6 - 304x^5 + 346x^4 - 272x^3 + 132x^2 - 24x + 2	\( 2^{44}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.101415451701035401216.3	x^16 - 8x^15 + 40x^14 - 140x^13 + 362x^12 - 716x^11 + 1096x^10 - 1300x^9 + 1207x^8 - 900x^7 + 588x^6 - 384x^5 + 254x^4 - 144x^3 + 60x^2 - 16x + 2	\( 2^{44}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.8.109951162777600000000.1	x^16 - 12x^14 - 8x^13 + 26x^12 - 16x^10 + 104x^9 + 33x^8 - 208x^7 - 72x^6 + 152x^5 + 22x^4 - 72x^3 + 20x^2 + 32x - 1	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.8.109951162777600000000.2	x^16 - 8x^14 + 36x^12 - 56x^10 + 2x^8 - 72x^6 + 124x^4 - 24x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.109951162777600000000.11	x^16 + 16x^12 + 48x^10 + 76x^8 + 64x^6 + 32x^4 - 32x^2 + 36	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.109951162777600000000.12	x^16 - 8x^14 + 40x^12 - 32x^11 - 48x^10 + 72x^9 - 40x^8 + 160x^6 - 240x^5 + 28x^4 + 48x^3 + 136x^2 - 184x + 71	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.119452832185734660096.4	x^16 + 11x^14 + 33x^12 - 22x^10 - 158x^8 + 66x^6 + 297x^4 - 297x^2 + 81	\( 2^{20}\cdot 3^{12}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.0.149587343098087735296.8	x^16 + 4x^12 - 24x^11 + 48x^10 - 24x^9 + 18x^8 - 96x^7 + 288x^6 - 576x^5 + 760x^4 - 576x^3 + 240x^2 - 48x + 4	\( 2^{48}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.149587343098087735296.10	x^16 - 4x^14 + 18x^12 - 24x^11 + 32x^10 - 47x^8 - 48x^7 + 240x^6 - 288x^5 + 150x^4 - 36x^2 + 9	\( 2^{48}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial
16.0.212360590552417173504.2	x^16 - 2x^15 - 16x^13 + 19x^12 + 56x^11 + 4x^10 - 130x^9 - 71x^8 + 128x^7 + 112x^6 - 28x^5 - 60x^4 - 8x^3 - 8x^2 + 12	\( 2^{24}\cdot 3^{10}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2]$
16.8.225371421906094140625.1	x^16 - 2x^15 - 9x^14 - x^13 + 83x^12 + 51x^11 - 445x^10 + 6x^9 + 890x^8 - 218x^7 - 673x^6 + 140x^5 + 127x^4 + 23x^3 + 27x^2 + 17x - 1	\( 5^{8}\cdot 13^{8}\cdot 29^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.822392716483306192896.1	x^16 - 2x^15 - 4x^14 - 8x^12 + 38x^11 + 76x^10 + 134x^9 + 163x^8 + 18x^7 + 128x^6 - 38x^5 + 40x^4 - 48x^3 + 12x^2 - 18x + 9	\( 2^{28}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2, 2]$
16.8.822392716483306192896.1	x^16 - 2x^15 - 6x^14 + 20x^13 + 18x^12 - 60x^11 - 56x^10 + 20x^9 + 150x^8 + 172x^7 - 248x^6 - 240x^5 + 204x^4 + 88x^3 - 48x^2 - 16x + 4	\( 2^{28}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.0.1436669046353440014336.2	x^16 - 2x^15 - 6x^14 - 4x^13 + 54x^12 + 24x^11 - 148x^10 - 72x^9 + 290x^8 + 140x^7 - 1600x^6 + 880x^5 + 2788x^4 - 1600x^3 + 424x^2 - 320x + 100	\( 2^{28}\cdot 3^{8}\cdot 13^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2, 2]$
16.0.1436669046353440014336.4	x^16 - 6x^15 + 10x^14 + 12x^13 - 42x^12 - 132x^11 + 860x^10 - 2064x^9 + 2750x^8 - 1860x^7 + 56x^6 + 384x^5 + 1548x^4 - 3840x^3 + 3952x^2 - 2112x + 484	\( 2^{28}\cdot 3^{8}\cdot 13^{8} \)	$C_2\wr C_2^2$ (as 16T149)	$[2, 2]$
16.0.1523584037250322661376.1	x^16 - 6x^15 + 10x^14 + 12x^13 - 30x^12 - 90x^11 + 416x^10 - 786x^9 + 947x^8 - 786x^7 + 416x^6 - 90x^5 - 30x^4 + 12x^3 + 10x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T149)	$[2, 2]$