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 54)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.69678188720703125.1	x^16 - x^15 + 2x^14 - 7x^13 + 12x^12 - 15x^11 + 28x^10 - 39x^9 + 45x^8 - 51x^7 + 48x^6 - 40x^5 + 27x^4 - 13x^3 + 7x^2 - 4x + 1	\( 5^{12}\cdot 41^{4}\cdot 101 \)	16T1726	Trivial
16.0.611840141845703125.1	x^16 - 2x^15 + 4x^14 + 3x^12 + 10x^11 + 11x^10 + 17x^9 + 28x^8 + 27x^7 + 31x^6 + 30x^5 + 23x^4 + 15x^3 + 9x^2 + 3x + 1	\( 5^{12}\cdot 61^{4}\cdot 181 \)	16T1726	Trivial
16.4.6989586621679009792.1	x^16 + 12x^12 - 32x^10 - 16x^9 + 32x^8 + 32x^7 + 8x^6 - 16x^5 - 24x^4 + 8x^2 - 1	\( 2^{56}\cdot 97 \)	16T1726	Trivial
16.4.13907115649320091648.1	x^16 + 4x^14 - 8x^13 - 6x^12 - 16x^11 + 4x^10 + 16x^9 + 15x^8 + 16x^7 - 16x^6 - 8x^5 - 4x^4 + 8x^2 - 2	\( 2^{56}\cdot 193 \)	16T1726	Trivial
16.2.62880624000000000000.1	x^16 - 2x^15 - 2x^14 + 12x^13 + 3x^12 - 12x^11 - x^10 + 26x^9 + 18x^8 - 22x^7 + 21x^6 + 30x^5 + 28x^4 + 46x^3 + 2x^2 + 2x + 1	\( -\,2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 599 \)	16T1726	Trivial
16.8.141192720000000000000.1	x^16 - 2x^15 - 10x^14 + 12x^13 + 50x^12 - 30x^11 - 132x^10 + 58x^9 + 217x^8 - 94x^7 - 278x^6 - 4x^5 + 123x^4 + 20x^3 - 19x^2 - 2x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{13}\cdot 269 \)	16T1726	Trivial (GRH)
16.4.166032817679570567168.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 12x^12 + 72x^11 - 62x^10 - 64x^9 + 184x^8 - 132x^7 - 12x^6 + 56x^5 - 23x^4 + 8x^3 - 4x^2 + 2	\( 2^{44}\cdot 17^{4}\cdot 113 \)	16T1726	Trivial
16.2.376145144477611196416.1	x^16 + 8x^14 + 20x^12 + 40x^10 + 36x^8 + 16x^6 + 16x^4 - 1	\( -\,2^{52}\cdot 17^{4} \)	16T1726	$[2]$
16.6.376145144477611196416.1	x^16 - 12x^14 + 46x^12 - 84x^10 + 75x^8 - 16x^6 - 20x^4 + 16x^2 - 4	\( -\,2^{52}\cdot 17^{4} \)	16T1726	Trivial
16.2.1450147075312500000000.1	x^16 + 4x^14 + 16x^12 + 74x^10 + 51x^8 - 20x^6 - 35x^4 - 25x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 29^{4} \)	16T1726	Trivial
16.6.1450147075312500000000.1	x^16 - 6x^14 + 26x^12 - 111x^10 + 266x^8 - 210x^6 - 200x^4 + 375x^2 - 125	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 29^{4} \)	16T1726	Trivial (GRH)
16.0.1554138188210029723648.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 28x^12 + 72x^11 + 8x^10 - 168x^9 + 354x^8 - 584x^7 + 472x^6 + 216x^5 - 516x^4 - 264x^3 + 1016x^2 - 792x + 223	\( 2^{62}\cdot 337 \)	16T1726	Trivial
16.4.1554138188210029723648.1	x^16 - 16x^13 - 16x^12 + 16x^11 + 80x^10 + 16x^9 - 44x^8 - 160x^7 + 96x^6 - 48x^4 + 160x^3 - 96x^2 + 32x - 4	\( 2^{62}\cdot 337 \)	16T1726	Trivial
16.8.1554138188210029723648.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 52x^12 + 216x^11 - 232x^10 - 264x^9 + 846x^8 - 440x^7 - 680x^6 + 1096x^5 - 428x^4 - 424x^3 + 568x^2 - 232x + 31	\( 2^{62}\cdot 337 \)	16T1726	Trivial (GRH)
16.0.1554138188210029723648.2	x^16 - 8x^15 + 32x^14 - 80x^13 + 144x^12 - 208x^11 + 272x^10 - 320x^9 + 324x^8 - 272x^7 + 224x^6 - 160x^5 + 96x^4 - 32x^3 + 32x^2 + 2	\( 2^{62}\cdot 337 \)	16T1726	Trivial
16.4.1554138188210029723648.2	x^16 - 8x^14 - 16x^13 + 4x^12 + 80x^11 + 104x^10 - 80x^9 - 310x^8 - 192x^7 + 312x^6 + 816x^5 + 956x^4 + 720x^3 + 360x^2 + 112x + 17	\( 2^{62}\cdot 337 \)	16T1726	Trivial
16.6.1585557504000000000000.1	x^16 - 2x^15 - 2x^14 + 24x^13 - 45x^12 + 8x^11 + 92x^10 - 124x^9 + 230x^8 - 224x^7 + 166x^6 - 206x^5 + 34x^4 + 38x^3 + 4x^2 + 6x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1726	Trivial (GRH)
16.2.1585557504000000000000.2	x^16 - 2x^15 + 2x^14 - 2x^13 + 30x^12 - 110x^11 + 186x^10 - 214x^9 + 136x^8 - 6x^7 - 114x^6 + 74x^5 - 62x^4 - 42x^3 + 6x^2 - 18x - 9	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1726	Trivial
16.6.1585557504000000000000.2	x^16 - 2x^15 - 16x^13 + 37x^12 + 18x^11 - 100x^10 + 28x^9 + 121x^8 + 12x^7 - 6x^6 + 26x^5 - 29x^4 - 48x^3 - 14x^2 + 2x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59 \)	16T1726	Trivial (GRH)
16.12.9082871696000000000000.1	x^16 - 6x^15 + 7x^14 + 26x^13 - 84x^12 + 50x^11 + 178x^10 - 280x^9 - 283x^8 + 660x^7 + 328x^6 - 980x^5 + 56x^4 + 576x^3 - 248x^2 - 16x + 16	\( 2^{16}\cdot 5^{12}\cdot 41\cdot 61^{4} \)	16T1726	Trivial (GRH)
16.4.9082871696000000000000.1	x^16 - 6x^15 + 7x^14 + 6x^13 - 4x^12 + 13x^10 + 10x^9 - 13x^8 + 10x^7 + 13x^6 - 4x^4 + 6x^3 + 7x^2 - 6x + 1	\( 2^{16}\cdot 5^{12}\cdot 41\cdot 61^{4} \)	16T1726	Trivial (GRH)
16.8.9082871696000000000000.1	x^16 - 7x^14 - 12x^13 + 26x^12 + 38x^11 - 22x^10 - 22x^9 - 110x^8 + 104x^7 + 7x^6 + 38x^5 - 17x^4 - 42x^3 + 22x^2 - 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 41\cdot 61^{4} \)	16T1726	Trivial (GRH)
16.8.9082871696000000000000.2	x^16 - 8x^15 + 28x^14 - 56x^13 + 43x^12 + 106x^11 - 387x^10 + 582x^9 - 375x^8 - 254x^7 + 767x^6 - 716x^5 + 176x^4 + 256x^3 - 283x^2 + 120x - 19	\( 2^{16}\cdot 5^{12}\cdot 41\cdot 61^{4} \)	16T1726	Trivial (GRH)
16.4.47983484309395893911552.1	x^16 - 4x^15 + 10x^14 - 16x^13 + 15x^12 + 40x^11 - 138x^10 + 124x^9 - 321x^8 + 1256x^7 - 2420x^6 + 2608x^5 - 1714x^4 + 1040x^3 - 688x^2 + 192x + 32	\( 2^{44}\cdot 17^{6}\cdot 113 \)	16T1726	Trivial
16.8.61196206578187500000000.1	x^16 - 17x^14 + 127x^12 - 540x^10 + 1411x^8 - 2290x^6 + 2208x^4 - 1116x^2 + 211	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 211 \)	16T1726	Trivial (GRH)
16.10.914371047424000000000000.1	x^16 - 8x^15 + 16x^14 + 28x^13 - 142x^12 + 124x^11 + 196x^10 - 496x^9 + 311x^8 + 236x^7 - 524x^6 + 320x^5 - 10x^4 - 92x^3 + 52x^2 - 12x + 1	\( -\,2^{24}\cdot 5^{12}\cdot 41^{4}\cdot 79 \)	16T1726	Trivial (GRH)
16.10.1010567048425312500000000.1	x^16 - 12x^14 - 6x^12 + 322x^10 + 61x^8 - 1860x^6 - 155x^4 + 2495x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.14.1010567048425312500000000.1	x^16 - 2x^15 - 21x^14 + 27x^13 + 176x^12 - 130x^11 - 725x^10 + 325x^9 + 1615x^8 - 565x^7 - 2175x^6 + 485x^5 + 1620x^4 - 75x^3 - 425x^2 + 25x + 25	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.2.1010567048425312500000000.1	x^16 + 16x^14 + 41x^12 - 224x^10 - 1029x^8 - 1350x^6 - 645x^4 - 110x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.1	x^16 + 6x^14 - 9x^12 - 94x^10 - 44x^8 + 300x^6 + 250x^4 + 40x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.10.1010567048425312500000000.2	x^16 - 8x^14 - 56x^12 + 348x^10 - 479x^8 + 80x^6 + 105x^4 - 15x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.14.1010567048425312500000000.2	x^16 - 23x^14 + 174x^12 - 477x^10 + 51x^8 + 1825x^6 - 2800x^4 + 1375x^2 - 125	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.2.1010567048425312500000000.2	x^16 + 17x^14 + 109x^12 + 318x^10 + 361x^8 - 80x^6 - 360x^4 - 90x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.2	x^16 - 9x^14 - 39x^12 + 76x^10 + 451x^8 + 570x^6 + 190x^4 - 40x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.10.1010567048425312500000000.3	x^16 - 6x^14 - 9x^12 + 44x^10 + 31x^8 - 90x^6 - 35x^4 + 40x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.3	x^16 - 4x^15 + 3x^14 + 5x^13 - 19x^12 + 50x^11 - 88x^10 + 12x^9 - 29x^8 - 700x^7 + 770x^6 + 10x^5 - 1590x^4 + 545x^3 + 70x^2 - 80x - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.10.1010567048425312500000000.4	x^16 - 4x^14 - 29x^12 + 51x^10 + 226x^8 - 35x^6 - 105x^4 + 45x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.4	x^16 + 7x^14 - 71x^12 - 297x^10 + 1456x^8 + 2045x^6 - 3075x^4 - 330x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.10.1010567048425312500000000.5	x^16 - 11x^14 - 4x^12 + 334x^10 - 1134x^8 + 1215x^6 - 90x^4 - 290x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.5	x^16 - 4x^15 - 2x^14 + 14x^13 - 22x^12 + 6x^11 - 45x^10 + 45x^9 + 51x^8 - 260x^7 + 85x^6 + 89x^5 - 152x^4 + 46x^3 + 3x^2 - 11x + 1	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.6.1010567048425312500000000.6	x^16 + 2x^14 - 106x^12 - 532x^10 - 489x^8 + 150x^6 + 165x^4 + 5x^2 - 5	\( -\,2^{8}\cdot 3^{8}\cdot 5^{13}\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.12.1757726260143877120851968.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 170x^12 - 72x^11 + 644x^10 - 272x^9 - 1013x^8 + 888x^7 + 556x^6 - 904x^5 + 138x^4 + 280x^3 - 168x^2 + 32x - 1	\( 2^{52}\cdot 17^{4}\cdot 4673 \)	16T1726	Trivial (GRH)
16.0.1809943292753764892578125.1	x^16 - 3x^15 + 4x^14 - 5x^13 + 13x^12 - 110x^11 + 276x^10 - 277x^9 + 1113x^8 + 1023x^7 + 2501x^6 + 3205x^5 + 2858x^4 + 2495x^3 + 1289x^2 + 1757x + 1231	\( 3^{10}\cdot 5^{12}\cdot 29^{5}\cdot 6121 \)	16T1726	$[2]$ (GRH)
16.8.1809943292753764892578125.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 111x^12 + 29x^11 + 264x^10 - 132x^9 - 407x^8 + 165x^7 + 440x^6 - 50x^5 - 308x^4 - 61x^3 + 99x^2 + 41x + 1	\( 3^{10}\cdot 5^{12}\cdot 29^{5}\cdot 6121 \)	16T1726	Trivial (GRH)
16.8.6265515700236937500000000.1	x^16 + x^14 - 17x^12 - 10x^10 + 81x^8 + 40x^6 - 128x^4 - 58x^2 + 31	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31\cdot 149^{4} \)	16T1726	Trivial (GRH)
16.4.15268307320976000000000000.1	x^16 - 4x^15 + 14x^14 - 26x^13 - 68x^12 + 180x^11 - 195x^10 + 100x^9 + 2868x^8 - 2512x^7 - 15061x^6 - 5186x^5 + 21634x^4 + 23016x^3 + 177x^2 - 13038x - 7339	\( 2^{16}\cdot 5^{12}\cdot 41^{3}\cdot 61^{4} \)	16T1726	$[2]$ (GRH)
16.0.15666228884016000000000000.1	x^16 + 17x^14 + 127x^12 + 540x^10 + 1411x^8 + 2290x^6 + 2208x^4 + 1116x^2 + 211	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 211 \)	16T1726	$[2]$ (GRH)
16.8.66561157991406937500000000.1	x^16 + 11x^14 + 29x^12 - 33x^10 - 136x^8 + 69x^6 + 161x^4 - 142x^2 + 31	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31\cdot 269^{4} \)	16T1726	Trivial (GRH)
16.0.1466360073814016000000000000.1	x^16 + 20x^14 + 163x^12 + 700x^10 + 1714x^8 + 2420x^6 + 1892x^4 + 730x^2 + 101	\( 2^{32}\cdot 5^{12}\cdot 61^{4}\cdot 101 \)	16T1726	$[2, 142]$ (GRH)
16.16.1466360073814016000000000000.1	x^16 - 20x^14 + 163x^12 - 700x^10 + 1714x^8 - 2420x^6 + 1892x^4 - 730x^2 + 101	\( 2^{32}\cdot 5^{12}\cdot 61^{4}\cdot 101 \)	16T1726	Trivial (GRH)