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 all 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.29956056295211008.1	x^16 - 4x^15 + 5x^14 + 2x^13 - 10x^12 + 4x^11 + 5x^10 + 2x^9 - 8x^8 - 4x^7 + 13x^6 - 10x^4 + 4x^3 + 4x^2 - 4x + 1	\( 2^{16}\cdot 17^{6}\cdot 29\cdot 653 \)	16T1722	Trivial
16.2.32297047507421875.1	x^16 - 5x^15 + 13x^14 - 22x^13 + 26x^12 - 20x^11 + 4x^10 + 12x^9 - 19x^8 + 12x^7 + 4x^6 - 20x^5 + 26x^4 - 22x^3 + 13x^2 - 5x + 1	\( -\,5^{8}\cdot 29^{6}\cdot 139 \)	16T1722	Trivial
16.0.141599629101850569.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 68x^12 - 44x^11 - 5x^10 + 47x^9 - 56x^8 + 30x^7 + 4x^6 - 18x^5 + 10x^4 + x^3 - 2x^2 + 1	\( 3^{12}\cdot 13^{6}\cdot 55201 \)	16T1722	Trivial
16.6.3745595669067333632.1	x^16 - 6x^15 + 15x^14 - 22x^13 + 20x^12 - 4x^11 - 21x^10 + 44x^9 - 53x^8 + 44x^7 - 21x^6 - 4x^5 + 20x^4 - 22x^3 + 15x^2 - 6x + 1	\( -\,2^{24}\cdot 41^{6}\cdot 47 \)	16T1722	Trivial (GRH)
16.8.5817627315785433088.1	x^16 - 2x^15 - 3x^14 + 2x^13 + x^12 + 14x^11 - 6x^10 + 4x^9 - 23x^8 + 4x^7 - 6x^6 + 14x^5 + x^4 + 2x^3 - 3x^2 - 2x + 1	\( 2^{24}\cdot 41^{6}\cdot 73 \)	16T1722	Trivial
16.8.7092723713765801984.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 203x^12 - 308x^11 + 331x^10 - 214x^9 + 9x^8 + 148x^7 - 159x^6 + 64x^5 + 16x^4 - 30x^3 + 9x^2 + 2x - 1	\( 2^{24}\cdot 41^{6}\cdot 89 \)	16T1722	Trivial
16.6.8208433061998624768.1	x^16 - 2x^15 - 3x^14 + 12x^13 - 8x^12 - 20x^11 + 40x^10 - 4x^9 - 49x^8 + 48x^7 + 5x^6 - 56x^5 + 23x^4 + 20x^3 - 9x^2 + 2x + 1	\( -\,2^{24}\cdot 41^{6}\cdot 103 \)	16T1722	Trivial
16.4.9005368310736355328.1	x^16 - 4x^15 + 4x^14 + 4x^13 - 17x^12 + 24x^11 - 18x^10 + 4x^9 + 3x^8 + 4x^7 - 18x^6 + 24x^5 - 17x^4 + 4x^3 + 4x^2 - 4x + 1	\( 2^{24}\cdot 41^{6}\cdot 113 \)	16T1722	Trivial
16.8.9005368310736355328.1	x^16 - 4x^15 + 2x^14 + 12x^13 - 21x^12 + 52x^10 - 116x^9 + 160x^8 - 140x^7 + 38x^6 + 100x^5 - 170x^4 + 108x^3 - 18x^2 - 4x + 1	\( 2^{24}\cdot 41^{6}\cdot 113 \)	16T1722	Trivial
16.8.10918012907706908672.1	x^16 - 2x^15 - 3x^14 + 8x^13 - 6x^12 + 2x^11 + 4x^10 - 2x^9 + 32x^8 - 62x^7 + 23x^6 - 8x^5 + 8x^4 + 6x^3 - 3x^2 + 2x + 1	\( 2^{24}\cdot 41^{6}\cdot 137 \)	16T1722	Trivial
16.6.12033722255939731456.1	x^16 - 2x^15 - 3x^14 + 14x^13 - 21x^12 + 10x^11 + 22x^10 - 60x^9 + 77x^8 - 60x^7 + 22x^6 + 10x^5 - 21x^4 + 14x^3 - 3x^2 - 2x + 1	\( -\,2^{24}\cdot 41^{6}\cdot 151 \)	16T1722	Trivial
16.4.12584463237766015625.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 265x^12 - 498x^11 + 757x^10 - 936x^9 + 927x^8 - 710x^7 + 376x^6 - 81x^5 - 75x^4 + 95x^3 - 52x^2 + 15x - 1	\( 5^{8}\cdot 29^{6}\cdot 41\cdot 1321 \)	16T1722	Trivial
16.2.15227477017600000000.1	x^16 + x^14 - 8x^10 - 10x^8 - 11x^6 - 14x^4 - 7x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1722	Trivial
16.6.15227477017600000000.1	x^16 - x^14 + 8x^10 - 10x^8 + 11x^6 - 14x^4 + 7x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1722	Trivial (GRH)
16.6.15227477017600000000.2	x^16 - 4x^14 + 11x^12 - 19x^10 + 15x^8 - 3x^6 - 6x^4 + 5x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T1722	Trivial (GRH)
16.4.15380850300638199808.1	x^16 - 2x^15 + x^14 + 2x^13 - 8x^12 + 16x^11 - 25x^10 + 32x^9 - 35x^8 + 32x^7 - 25x^6 + 16x^5 - 8x^4 + 2x^3 + x^2 - 2x + 1	\( 2^{24}\cdot 41^{6}\cdot 193 \)	16T1722	Trivial (GRH)
16.4.91302786715585015625.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 9x^12 + 54x^11 - 38x^10 - 19x^9 + 31x^8 + 12x^7 - 31x^6 - 4x^5 + 20x^4 + x^3 - 5x^2 - x + 1	\( 5^{6}\cdot 29^{8}\cdot 11681 \)	16T1722	Trivial
16.8.192771317751691015625.1	x^16 - 8x^15 + 20x^14 - 71x^12 + 62x^11 + 97x^10 - 100x^9 - 125x^8 + 66x^7 + 164x^6 - 5x^5 - 129x^4 - 37x^3 + 42x^2 + 23x + 1	\( 5^{8}\cdot 29^{6}\cdot 359\cdot 2311 \)	16T1722	Trivial (GRH)
16.4.522265071481486515625.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 159x^12 - 226x^11 + 244x^10 - 197x^9 + 107x^8 - 16x^7 - 43x^6 + 60x^5 - 46x^4 + 23x^3 - 7x^2 + x + 1	\( 5^{6}\cdot 29^{8}\cdot 109\cdot 613 \)	16T1722	Trivial (GRH)
16.10.1085199152125296484375.1	x^16 - 10x^14 - 10x^13 + 40x^12 + 84x^11 - 104x^10 - 194x^9 + 194x^8 + 50x^7 - 176x^6 + 172x^5 + 56x^4 - 94x^3 - 4x^2 + 7x - 1	\( -\,5^{8}\cdot 11^{5}\cdot 29^{7} \)	16T1722	Trivial (GRH)
16.10.4803208437667175858176.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 14x^12 + 84x^11 - 98x^10 + 6x^9 + 105x^8 - 104x^7 + 10x^6 + 54x^5 - 37x^4 - 2x^3 + 9x^2 - 2x - 1	\( -\,2^{24}\cdot 41^{6}\cdot 60271 \)	16T1722	Trivial (GRH)
16.10.5222794846127590998016.1	x^16 + 2x^14 - 17x^12 - 28x^10 + 54x^8 + 30x^6 - 60x^4 + 20x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.14.5222794846127590998016.1	x^16 - 10x^14 + 35x^12 - 40x^10 - 39x^8 + 128x^6 - 93x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.2.5222794846127590998016.1	x^16 + 10x^14 + 35x^12 + 40x^10 - 39x^8 - 128x^6 - 93x^4 - 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial
16.6.5222794846127590998016.1	x^16 - 2x^14 - 19x^12 + 12x^10 + 97x^8 + 56x^6 - 33x^4 - 22x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial
16.10.5222794846127590998016.2	x^16 + 2x^14 - 19x^12 - 12x^10 + 97x^8 - 56x^6 - 33x^4 + 22x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.14.5222794846127590998016.2	x^16 - 12x^14 + 56x^12 - 126x^10 + 132x^8 - 36x^6 - 33x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.2.5222794846127590998016.2	x^16 + 12x^14 + 56x^12 + 126x^10 + 132x^8 + 36x^6 - 33x^4 - 18x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial
16.6.5222794846127590998016.2	x^16 - 2x^14 - 17x^12 + 28x^10 + 54x^8 - 30x^6 - 60x^4 - 20x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.10.5222794846127590998016.3	x^16 - 2x^14 - 7x^12 + 16x^10 + 6x^8 - 22x^6 + 8x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.6.5222794846127590998016.3	x^16 - 2x^14 - 17x^12 - 4x^10 + 53x^8 + 56x^6 + 9x^4 - 6x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.10.5222794846127590998016.4	x^16 + 2x^14 - 17x^12 + 4x^10 + 53x^8 - 56x^6 + 9x^4 + 6x^2 - 1	\( -\,2^{40}\cdot 41^{6} \)	16T1722	Trivial (GRH)
16.0.5466664249318400000000.1	x^16 + 16x^14 + 111x^12 + 442x^10 + 1120x^8 + 1869x^6 + 2015x^4 + 1278x^2 + 359	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 359 \)	16T1722	Trivial
16.8.5466664249318400000000.1	x^16 - 16x^14 + 111x^12 - 442x^10 + 1120x^8 - 1869x^6 + 2015x^4 - 1278x^2 + 359	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 359 \)	16T1722	Trivial (GRH)
16.0.19019118794982400000000.1	x^16 - 8x^15 + 50x^14 - 210x^13 + 703x^12 - 1852x^11 + 3987x^10 - 7010x^9 + 10160x^8 - 12088x^7 + 11767x^6 - 9252x^5 + 5782x^4 - 2784x^3 + 986x^2 - 232x + 29	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 1249 \)	16T1722	$[2]$
16.12.29982902247654400000000.1	x^16 - 8x^15 + 20x^14 - 81x^12 + 122x^11 + 13x^10 - 230x^9 + 245x^8 + 26x^7 - 259x^6 + 198x^5 + 2x^4 - 94x^3 + 59x^2 - 14x + 1	\( 2^{16}\cdot 5^{8}\cdot 11\cdot 29^{6}\cdot 179 \)	16T1722	Trivial (GRH)
16.4.29982902247654400000000.1	x^16 - 8x^15 + 31x^14 - 66x^13 + 77x^12 - 42x^11 + 18x^10 - 6x^9 - 147x^8 + 366x^7 - 226x^6 - 208x^5 + 306x^4 - 42x^3 - 70x^2 + 6x + 11	\( 2^{16}\cdot 5^{8}\cdot 11\cdot 29^{6}\cdot 179 \)	16T1722	Trivial (GRH)
16.12.36906976806919566015625.1	x^16 - 8x^15 + 16x^14 + 28x^13 - 131x^12 + 58x^11 + 285x^10 - 336x^9 - 161x^8 + 438x^7 - 126x^6 - 183x^5 + 141x^4 - 3x^3 - 30x^2 + 11x - 1	\( 5^{8}\cdot 11^{4}\cdot 19\cdot 29^{6}\cdot 571 \)	16T1722	Trivial (GRH)
16.4.114989547959792521183232.1	x^16 - 6x^15 + 19x^14 - 42x^13 + 74x^12 - 60x^11 - 195x^10 + 788x^9 - 1383x^8 + 1732x^7 - 915x^6 - 2452x^5 + 6664x^4 - 8502x^3 + 6319x^2 - 2810x + 631	\( 2^{24}\cdot 41^{6}\cdot 113^{3} \)	16T1722	Trivial (GRH)
16.8.114989547959792521183232.1	x^16 - 14x^14 - 6x^13 - 20x^12 - 176x^11 - 161x^10 - 346x^9 - 613x^8 - 748x^7 - 932x^6 - 552x^5 - 624x^4 - 608x^3 + 8x^2 + 96x + 16	\( 2^{24}\cdot 41^{6}\cdot 113^{3} \)	16T1722	Trivial (GRH)
16.8.204920184264750968864768.1	x^16 - 2x^15 - 13x^14 + 4x^13 + 69x^12 + 146x^11 - 261x^10 - 332x^9 + 162x^8 - 46x^7 + 336x^6 - 226x^5 + 701x^4 - 526x^3 - 789x^2 + 538x - 73	\( 2^{24}\cdot 41^{6}\cdot 137^{3} \)	16T1722	Trivial (GRH)
16.0.458465832550497280000000.1	x^16 + 20x^14 + 173x^12 + 845x^10 + 2543x^8 + 4805x^6 + 5520x^4 + 3475x^2 + 895	\( 2^{16}\cdot 5^{7}\cdot 29^{8}\cdot 179 \)	16T1722	Trivial (GRH)
16.12.572921292848472304648192.1	x^16 - 16x^14 - 14x^13 + 28x^12 + 140x^11 + 649x^10 + 70x^9 - 3184x^8 - 3908x^7 + 1448x^6 + 11310x^5 + 11594x^4 - 9136x^3 - 11481x^2 + 2626x + 1297	\( 2^{24}\cdot 41^{6}\cdot 193^{3} \)	16T1722	Trivial (GRH)
16.0.1624289197145680800382976.1	x^16 + 20x^14 + 168x^12 + 770x^10 + 2092x^8 + 3420x^6 + 3247x^4 + 1610x^2 + 311	\( 2^{40}\cdot 41^{6}\cdot 311 \)	16T1722	$[66]$ (GRH)
16.16.1624289197145680800382976.1	x^16 - 20x^14 + 168x^12 - 770x^10 + 2092x^8 - 3420x^6 + 3247x^4 - 1610x^2 + 311	\( 2^{40}\cdot 41^{6}\cdot 311 \)	16T1722	Trivial (GRH)
16.16.4868894411515494400000000.1	x^16 - 2x^15 - 36x^14 + 28x^13 + 497x^12 + 66x^11 - 3180x^10 - 2478x^9 + 8976x^8 + 11376x^7 - 8290x^6 - 15518x^5 + 1562x^4 + 7776x^3 + 588x^2 - 1178x - 79	\( 2^{24}\cdot 5^{8}\cdot 29^{6}\cdot 1249 \)	16T1722	Trivial (GRH)
16.4.8900751743270385297265625.1	x^16 - 2x^15 + 6x^14 - 17x^13 - 139x^12 + 390x^11 - 312x^10 - 165x^9 + 1931x^8 - 21989x^7 - 5874x^6 - 44174x^5 - 133249x^4 + 194942x^3 - 252667x^2 - 130350x + 1222489	\( 5^{8}\cdot 29^{10}\cdot 41\cdot 1321 \)	16T1722	$[2]$ (GRH)
16.0.12517949420193642250390625.1	x^16 - 2x^15 - 13x^14 + 72x^13 + 8x^12 - 674x^11 + 1392x^10 + 312x^9 - 6134x^8 + 13160x^7 - 13159x^6 - 6434x^5 + 50809x^4 - 96082x^3 + 101920x^2 - 61896x + 16976	\( 5^{8}\cdot 89^{6}\cdot 401^{3} \)	16T1722	$[2]$ (GRH)
16.0.12517949420193642250390625.2	x^16 - 3x^15 + 19x^14 - 54x^13 + 159x^12 - 331x^11 + 656x^10 - 1611x^9 + 304x^8 - 1845x^7 + 12807x^6 + 2112x^5 - 9491x^4 - 11557x^3 + 6235x^2 + 2944x + 2624	\( 5^{8}\cdot 89^{6}\cdot 401^{3} \)	16T1722	$[2]$ (GRH)
16.12.26103603462974877571097265625.1	x^16 - 5x^15 - 23x^14 + 160x^13 - 329x^12 - 171x^11 + 7911x^10 - 22020x^9 - 1725x^8 + 71146x^7 - 378007x^6 + 638197x^5 + 852831x^4 - 1953614x^3 + 532701x^2 + 114347x - 32741	\( 5^{8}\cdot 11^{4}\cdot 19\cdot 29^{10}\cdot 571 \)	16T1722	$[2]$ (GRH)