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 90)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.21407557176262656.1	x^16 - 6x^15 + 18x^14 - 36x^13 + 67x^12 - 138x^11 + 270x^10 - 420x^9 + 489x^8 - 420x^7 + 270x^6 - 138x^5 + 67x^4 - 36x^3 + 18x^2 - 6x + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.42238838692642816.1	x^16 + 2x^12 - 5x^8 + 2x^4 + 1	\( 2^{44}\cdot 7^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.43980465111040000.1	x^16 - 4x^15 + 12x^13 + 14x^12 - 52x^11 - 28x^10 + 108x^9 + 28x^8 - 108x^7 - 28x^6 + 52x^5 + 14x^4 - 12x^3 + 4x + 1	\( 2^{46}\cdot 5^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.87500953582971201.1	x^16 - 9x^13 + 7x^12 + 21x^10 - 24x^9 + 9x^8 - 27x^7 + 24x^6 - 9x^5 + 16x^4 - 9x^3 + 3x^2 - 3x + 1	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.95951257600000000.1	x^16 - 4x^15 + 8x^14 - 14x^13 + 15x^12 - 4x^11 - 6x^10 + 16x^9 - 7x^8 - 16x^7 - 6x^6 + 4x^5 + 15x^4 + 14x^3 + 8x^2 + 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.117033789351264256.2	x^16 + 5x^12 + 4x^8 + 5x^4 + 1	\( 2^{24}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.130540626662916096.2	x^16 - 2x^14 + 13x^12 + 22x^10 + 76x^8 + 22x^6 + 13x^4 - 2x^2 + 1	\( 2^{24}\cdot 3^{12}\cdot 11^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.200779471797682176.1	x^16 - 9x^14 + 37x^12 - 90x^10 + 135x^8 - 120x^6 + 58x^4 - 12x^2 + 1	\( 2^{16}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.232218265089212416.1	x^16 - 3x^12 + 20x^8 - 3x^4 + 1	\( 2^{24}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.350749278894882816.3	x^16 - x^14 + 2x^12 + 3x^10 - x^8 + 3x^6 + 2x^4 - x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.429496729600000000.4	x^16 - 2x^14 - 4x^12 + 8x^10 + 19x^8 + 8x^6 - 4x^4 - 2x^2 + 1	\( 2^{40}\cdot 5^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.584325558976905216.2	x^16 - 6x^14 + 16x^12 - 24x^10 + 27x^8 - 24x^6 + 16x^4 - 6x^2 + 1	\( 2^{40}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.675821419082285056.1	x^16 - 4x^14 + 8x^12 - 8x^10 + 7x^8 - 8x^6 + 8x^4 - 4x^2 + 1	\( 2^{48}\cdot 7^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.1040864112987605361.1	x^16 - x^15 + 8x^14 + 4x^13 + 8x^12 + 25x^11 + 39x^10 + 88x^8 + 39x^6 + 25x^5 + 8x^4 + 4x^3 + 8x^2 - x + 1	\( 3^{12}\cdot 7^{4}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.1108540930828271616.1	x^16 - 2x^15 + 2x^14 - 2x^13 + 9x^12 - 10x^11 + 4x^10 + 8x^9 + 18x^8 - 32x^7 + 26x^6 + 16x^5 + 4x^4 - 6x^3 + 18x^2 + 18x + 9	\( 2^{24}\cdot 3^{4}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.1459166279268040704.1	x^16 - 12x^12 + 166x^8 - 12x^4 + 1	\( 2^{54}\cdot 3^{4} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.1872540629620228096.1	x^16 + 10x^14 + 26x^12 + 32x^10 + 31x^8 + 32x^6 + 26x^4 + 10x^2 + 1	\( 2^{28}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.1872540629620228096.2	x^16 - 2x^14 - 4x^12 + 12x^10 + 16x^8 + 38x^6 + 49x^4 - 20x^2 + 4	\( 2^{28}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.3715492241427398656.1	x^16 + 2x^14 + 2x^12 - 32x^10 + 55x^8 - 32x^6 + 2x^4 + 2x^2 + 1	\( 2^{28}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.3715492241427398656.3	x^16 + 6x^14 + 12x^12 + 12x^10 + 24x^8 + 62x^6 + 73x^4 + 20x^2 + 4	\( 2^{28}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.4597392194616650625.1	x^16 - 5x^15 + 17x^14 - 47x^13 + 112x^12 - 223x^11 + 374x^10 - 511x^9 + 571x^8 - 540x^7 + 459x^6 - 360x^5 + 261x^4 - 189x^3 + 162x^2 - 162x + 81	\( 3^{12}\cdot 5^{4}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.5487587353600000000.2	x^16 - x^14 + 14x^12 + x^10 + 29x^8 - x^6 + 14x^4 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.6338465731314712576.3	x^16 - 6x^14 + 27x^12 - 74x^10 + 108x^8 - 74x^6 + 27x^4 - 6x^2 + 1	\( 2^{40}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.6871947673600000000.13	x^16 - 8x^14 + 38x^12 - 116x^10 + 203x^8 - 188x^6 + 106x^4 - 60x^2 + 25	\( 2^{44}\cdot 5^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.9349208943630483456.6	x^16 - 8x^15 + 36x^14 - 112x^13 + 264x^12 - 456x^11 + 532x^10 - 280x^9 - 222x^8 + 568x^7 - 380x^6 - 48x^5 + 264x^4 - 104x^3 - 12x^2 + 8x + 1	\( 2^{44}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.18809679472226205696.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 38x^12 + 46x^11 + 42x^10 - 12x^9 - 165x^8 + 94x^7 + 190x^6 - 236x^5 + 254x^4 - 346x^3 + 248x^2 - 78x + 9	\( 2^{24}\cdot 3^{4}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.27487790694400000000.1	x^16 - 4x^14 - 24x^13 + 72x^12 - 24x^11 + 40x^10 - 280x^9 + 240x^8 + 144x^7 - 88x^6 - 192x^5 + 80x^4 + 48x^3 - 16x + 4	\( 2^{46}\cdot 5^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.0.27487790694400000000.2	x^16 + 8x^14 - 24x^13 - 4x^12 - 48x^11 + 88x^10 + 104x^9 + 110x^8 - 80x^7 - 168x^6 - 104x^5 + 132x^4 + 64x^3 - 24x^2 - 40x + 25	\( 2^{46}\cdot 5^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.0.27487790694400000000.3	x^16 - 4x^15 - 8x^14 + 68x^13 - 94x^12 - 196x^11 + 856x^10 - 1156x^9 + 296x^8 + 932x^7 - 844x^6 - 140x^5 + 246x^4 + 244x^3 - 180x^2 - 156x + 169	\( 2^{46}\cdot 5^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.29548117155177824256.1	x^16 - 4x^14 + 2x^12 - 48x^10 + 179x^8 - 48x^6 + 2x^4 - 4x^2 + 1	\( 2^{52}\cdot 3^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.29548117155177824256.3	x^16 + 4x^14 + 2x^12 + 48x^10 + 179x^8 + 48x^6 + 2x^4 + 4x^2 + 1	\( 2^{52}\cdot 3^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial
16.0.29960650073923649536.1	x^16 + 9x^12 - 16x^8 + 9x^4 + 1	\( 2^{32}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.8.29960650073923649536.1	x^16 - 10x^14 + 26x^12 - 32x^10 + 31x^8 - 32x^6 + 26x^4 - 10x^2 + 1	\( 2^{32}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.29960650073923649536.5	x^16 + 2x^14 - 4x^12 - 12x^10 + 16x^8 - 38x^6 + 49x^4 + 20x^2 + 4	\( 2^{32}\cdot 17^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.0.37396835774521933824.1	x^16 - 4x^15 + 12x^14 - 12x^13 - 6x^12 + 36x^11 - 16x^10 - 140x^9 + 264x^8 - 140x^7 - 16x^6 + 36x^5 - 6x^4 - 12x^3 + 12x^2 - 4x + 1	\( 2^{46}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.8.37396835774521933824.1	x^16 - 12x^14 + 52x^12 - 144x^10 + 300x^8 - 408x^6 + 304x^4 - 96x^2 + 4	\( 2^{46}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.37396835774521933824.2	x^16 + 12x^14 + 52x^12 + 144x^10 + 300x^8 + 408x^6 + 304x^4 + 96x^2 + 4	\( 2^{46}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.37396835774521933824.3	x^16 - 4x^15 + 8x^14 - 4x^13 - 2x^12 - 20x^11 + 32x^10 + 52x^9 - 92x^8 - 84x^7 + 132x^6 + 132x^5 - 30x^4 - 36x^3 + 36x^2 + 36x + 9	\( 2^{46}\cdot 3^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.51399544780206637056.2	x^16 - 2x^15 + 2x^14 - 4x^13 - 25x^12 - 34x^11 + 126x^10 + 408x^9 + 577x^8 + 408x^7 + 126x^6 - 34x^5 - 25x^4 - 4x^3 + 2x^2 - 2x + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.51399544780206637056.4	x^16 - 8x^15 + 40x^14 - 140x^13 + 406x^12 - 980x^11 + 1972x^10 - 3260x^9 + 4411x^8 - 4860x^7 + 4356x^6 - 3156x^5 + 1866x^4 - 900x^3 + 324x^2 - 72x + 9	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.51399544780206637056.7	x^16 - 8x^15 + 44x^14 - 168x^13 + 502x^12 - 1192x^11 + 2302x^10 - 3634x^9 + 4876x^8 - 5664x^7 + 5834x^6 - 5216x^5 + 3955x^4 - 2394x^3 + 1128x^2 - 366x + 93	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.0.51399544780206637056.8	x^16 - 4x^15 + 16x^14 - 40x^13 + 75x^12 - 118x^11 + 166x^10 - 96x^9 - 32x^8 + 378x^7 - 850x^6 + 888x^5 - 82x^4 - 338x^3 + 974x^2 - 630x + 133	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.0.59447875862838378496.1	x^16 - 2x^14 + 2x^12 + 32x^10 + 55x^8 + 32x^6 + 2x^4 - 2x^2 + 1	\( 2^{32}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.59447875862838378496.2	x^16 - 6x^14 + 12x^12 - 12x^10 + 24x^8 - 62x^6 + 73x^4 - 20x^2 + 4	\( 2^{32}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.59447875862838378496.5	x^16 - 5x^12 + 19x^8 + 25x^4 + 256	\( 2^{32}\cdot 7^{12} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.8.89791815397090000896.1	x^16 - 4x^15 + 30x^13 - 64x^12 - 76x^11 + 240x^10 + 142x^9 - 306x^8 - 190x^7 + 144x^6 + 70x^5 - 43x^4 + 18x^3 + 36x^2 + 10x + 1	\( 2^{24}\cdot 3^{8}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)
16.0.89791815397090000896.2	x^16 - 6x^15 + 18x^14 - 36x^13 + 59x^12 - 114x^11 + 270x^10 - 492x^9 + 609x^8 - 492x^7 + 270x^6 - 114x^5 + 59x^4 - 36x^3 + 18x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.89791815397090000896.3	x^16 - 4x^15 - 8x^14 + 52x^13 - 15x^12 - 202x^11 + 228x^10 + 180x^9 - 320x^8 - 50x^7 + 170x^6 + 6x^5 - 11x^4 - 48x^3 + 6x^2 + 18x + 9	\( 2^{24}\cdot 3^{8}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$
16.0.89791815397090000896.9	x^16 - 4x^15 + 8x^14 - 26x^13 + 82x^12 - 176x^11 + 352x^10 - 652x^9 + 936x^8 - 1158x^7 + 1438x^6 - 1758x^5 + 2199x^4 - 2736x^3 + 2826x^2 - 1944x + 621	\( 2^{24}\cdot 3^{8}\cdot 13^{8} \)	$C_2^2\wr C_2$ (as 16T39)	$[2]$ (GRH)
16.8.101415451701035401216.1	x^16 - 12x^14 + 32x^12 - 68x^8 + 128x^4 - 96x^2 + 16	\( 2^{44}\cdot 7^{8} \)	$C_2^2\wr C_2$ (as 16T39)	Trivial (GRH)