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
16.0.2467585431025000000.1	x^16 + x^14 - x^12 - 3x^10 + 8x^8 + 26x^6 + 21x^4 + 2x^2 + 1	\( 2^{6}\cdot 5^{8}\cdot 11^{2}\cdot 13^{8} \)	16T1656	$[2]$
16.0.4024987638464249856.1	x^16 - 6x^15 + 18x^14 - 30x^13 + 20x^12 + 32x^11 - 86x^10 + 62x^9 + 39x^8 - 88x^7 + 50x^6 - 2x^5 - 6x^4 + 6x^3 + 1	\( 2^{28}\cdot 3^{2}\cdot 7^{8}\cdot 17^{2} \)	16T1656	Trivial
16.0.114488537271871995904.1	x^16 - 4x^14 + 10x^12 - 24x^10 + 31x^8 - 24x^6 + 22x^4 - 4x^2 + 1	\( 2^{36}\cdot 7^{8}\cdot 17^{2} \)	16T1656	Trivial
16.0.1831816596349951934464.1	x^16 + 6x^14 + 14x^12 + 8x^10 - 3x^8 - 12x^6 + 6x^4 + 6x^2 + 1	\( 2^{40}\cdot 7^{8}\cdot 17^{2} \)	16T1656	Trivial
16.8.29060018988008511449664.1	x^16 - 2x^15 - 7x^14 + 4x^13 - 5x^12 - 5x^11 + 10x^10 + 3x^9 + 6x^8 + 3x^7 + 10x^6 - 5x^5 - 5x^4 + 4x^3 - 7x^2 - 2x + 1	\( 2^{6}\cdot 3^{8}\cdot 19^{2}\cdot 61^{8} \)	16T1656	Trivial (GRH)
16.4.82430635578173727768576.1	x^16 - 7x^14 + 30x^12 + 13x^10 - 58x^8 - 14x^6 + 51x^4 - 28x^2 + 4	\( 2^{16}\cdot 3^{8}\cdot 61^{8} \)	16T1656	Trivial
16.0.82430635578173727768576.2	x^16 + 7x^14 + 30x^12 - 13x^10 - 58x^8 + 14x^6 + 51x^4 + 28x^2 + 4	\( 2^{16}\cdot 3^{8}\cdot 61^{8} \)	16T1656	$[2]$ (GRH)
16.8.116240075952034045798656.1	x^16 - 3x^15 - 11x^14 + 59x^13 - 46x^12 - 166x^11 + 300x^10 + 121x^9 - 599x^8 + 265x^7 + 306x^6 - 272x^5 - 3x^4 + 64x^3 - 17x^2 - 2x + 1	\( 2^{8}\cdot 3^{8}\cdot 19^{2}\cdot 61^{8} \)	16T1656	Trivial (GRH)
16.0.179493816530169719947264.2	x^16 + 14x^14 + 73x^12 + 196x^10 + 294x^8 + 238x^6 + 84x^4 + 4x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	$[2]$ (GRH)
16.4.179493816530169719947264.2	x^16 + 2x^14 - 11x^12 - 76x^10 - 218x^8 - 254x^6 - 4x^4 + 128x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.8.179493816530169719947264.2	x^16 - 12x^14 + 16x^12 + 94x^10 - 74x^8 + 304x^6 - 1107x^4 - 1782x^2 + 729	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.0.179493816530169719947264.3	x^16 - 6x^14 + 17x^12 - 20x^10 + 70x^8 + 266x^6 + 212x^4 + 36x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	$[2]$ (GRH)
16.4.179493816530169719947264.3	x^16 - 14x^14 + 73x^12 - 196x^10 + 294x^8 - 238x^6 + 84x^4 - 4x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.8.179493816530169719947264.3	x^16 - 2x^14 - 11x^12 + 76x^10 - 218x^8 + 254x^6 - 4x^4 - 128x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.4.179493816530169719947264.4	x^16 + 12x^14 + 16x^12 - 94x^10 - 74x^8 - 304x^6 - 1107x^4 + 1782x^2 + 729	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.4.179493816530169719947264.5	x^16 + 6x^14 + 17x^12 + 20x^10 + 70x^8 - 266x^6 + 212x^4 - 36x^2 + 1	\( 2^{32}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.0.5275560677003118577188864.1	x^16 + 13x^14 + 63x^12 + 139x^10 + 144x^8 + 112x^6 + 149x^4 + 84x^2 + 1	\( 2^{22}\cdot 3^{8}\cdot 61^{8} \)	16T1656	$[2]$ (GRH)
16.12.5275560677003118577188864.1	x^16 - 13x^14 + 63x^12 - 139x^10 + 144x^8 - 112x^6 + 149x^4 - 84x^2 + 1	\( 2^{22}\cdot 3^{8}\cdot 61^{8} \)	16T1656	Trivial (GRH)
16.4.5275560677003118577188864.1	x^16 + 6x^14 + 2x^12 - 34x^10 + 75x^8 - 16x^6 - 69x^4 - 40x^2 + 16	\( 2^{22}\cdot 3^{8}\cdot 61^{8} \)	16T1656	Trivial (GRH)
16.0.5275560677003118577188864.2	x^16 + 12x^14 + 68x^12 + 220x^10 + 423x^8 + 436x^6 + 171x^4 + 22x^2 + 1	\( 2^{22}\cdot 3^{8}\cdot 61^{8} \)	16T1656	$[2]$ (GRH)
16.0.45950417031723448306499584.1	x^16 + 16x^14 + 110x^12 + 424x^10 + 987x^8 + 1368x^6 + 1022x^4 + 312x^2 + 1	\( 2^{40}\cdot 7^{2}\cdot 31^{8} \)	16T1656	$[4]$ (GRH)
16.12.45950417031723448306499584.2	x^16 - 16x^14 + 110x^12 - 424x^10 + 987x^8 - 1368x^6 + 1022x^4 - 312x^2 + 1	\( 2^{40}\cdot 7^{2}\cdot 31^{8} \)	16T1656	Trivial (GRH)
16.12.108132330654379671104199744.1	x^16 - 4x^15 - 18x^14 + 78x^13 + 82x^12 - 385x^11 - 489x^10 + 1133x^9 + 2252x^8 - 2697x^7 - 5170x^6 + 4285x^5 + 6033x^4 - 3516x^3 - 3564x^2 + 1094x + 886	\( 2^{6}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.4.108132330654379671104199744.1	x^16 - x^15 + 2x^14 + 10x^13 - 63x^12 + 198x^11 - 422x^10 + 255x^9 + 903x^8 - 2180x^7 + 1957x^6 - 306x^5 - 1199x^4 + 1566x^3 - 1110x^2 + 512x - 122	\( 2^{6}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	$[2]$ (GRH)
16.12.108132330654379671104199744.2	x^16 - 6x^15 + 4x^14 + 21x^13 - 82x^12 + 496x^11 - 705x^10 - 1759x^9 + 3169x^8 + 1631x^7 - 1468x^6 - 1888x^5 - 3969x^4 + 2171x^3 + 4091x^2 - 618x - 857	\( 2^{6}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.4.108132330654379671104199744.2	x^16 - 2x^15 - 17x^14 - 2x^13 + 67x^12 - 113x^11 - 436x^10 + 560x^9 + 39x^8 - 2168x^7 + 1721x^6 - 110x^5 + 158x^4 - 203x^3 - 948x^2 + 706x + 409	\( 2^{6}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	$[2]$ (GRH)
16.8.432529322617518684416798976.1	x^16 - 3x^15 - 15x^14 + 99x^13 - 191x^12 - 163x^11 + 1033x^10 - 659x^9 - 2086x^8 + 1030x^7 + 15045x^6 - 28593x^5 + 14911x^4 + 2490x^3 - 4047x^2 + 977x - 71	\( 2^{8}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.8.432529322617518684416798976.2	x^16 - 6x^15 + 14x^14 - 2x^13 - 82x^12 + 321x^11 - 421x^10 - 310x^9 + 3198x^8 - 3391x^7 - 6443x^6 + 4891x^5 + 3501x^4 - 2720x^3 - 548x^2 + 470x - 50	\( 2^{8}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.0.2823369678315287559234816064.1	x^16 - 3x^15 + 30x^14 - 78x^13 + 397x^12 - 692x^11 + 1985x^10 - 175x^9 - 1948x^8 + 23065x^7 - 33643x^6 + 41132x^5 + 120605x^4 - 371078x^3 + 788212x^2 - 782887x + 565529	\( 2^{6}\cdot 97^{4}\cdot 163^{8} \)	16T1656	$[4]$ (GRH)
16.4.2823369678315287559234816064.1	x^16 - 6x^15 + x^14 + 71x^13 - 263x^12 + 509x^11 - 441x^10 + 493x^9 - 2800x^8 + 8880x^7 - 22644x^6 + 28358x^5 - 14925x^4 + 44273x^3 - 40223x^2 - 16320x - 24192	\( 2^{6}\cdot 97^{4}\cdot 163^{8} \)	16T1656	Trivial (GRH)
16.8.2823369678315287559234816064.1	x^16 - 7x^15 - 27x^14 + 258x^13 + 233x^12 - 3742x^11 - 1001x^10 + 28944x^9 + 3095x^8 - 120079x^7 - 8216x^6 + 206433x^5 + 23830x^4 + 21454x^3 - 51500x^2 - 97734x + 10711	\( 2^{6}\cdot 97^{4}\cdot 163^{8} \)	16T1656	Trivial (GRH)
16.4.2823369678315287559234816064.2	x^16 + 18x^14 - 36x^13 + 84x^12 - 656x^11 - 622x^10 - 5968x^9 - 10790x^8 - 21798x^7 - 55335x^6 + 53438x^5 - 157840x^4 + 836990x^3 - 39069x^2 + 2271962x - 1482867	\( 2^{6}\cdot 97^{4}\cdot 163^{8} \)	16T1656	Trivial (GRH)
16.0.57060464282465730530874753024.1	x^16 + 16x^14 + 156x^12 + 976x^10 + 4320x^8 + 13312x^6 + 28352x^4 + 37632x^2 + 25600	\( 2^{28}\cdot 3^{8}\cdot 13^{2}\cdot 61^{8} \)	16T1656	$[2, 2]$ (GRH)
16.0.57060464282465730530874753024.2	x^16 - 16x^14 + 156x^12 - 976x^10 + 4320x^8 - 13312x^6 + 28352x^4 - 37632x^2 + 25600	\( 2^{28}\cdot 3^{8}\cdot 13^{2}\cdot 61^{8} \)	16T1656	$[2, 2]$ (GRH)
16.8.1501116880865095877501562890625.1	x^16 - 20x^14 + 210x^12 - 1400x^10 + 5877x^8 - 15020x^6 + 20720x^4 - 9600x^2 + 256	\( 3^{8}\cdot 5^{8}\cdot 67^{8}\cdot 1201^{2} \)	16T1656	$[2]$ (GRH)
16.0.1771640105441356531371208605696.1	x^16 + 48x^14 + 835x^12 + 7059x^10 + 32040x^8 + 79971x^6 + 106201x^4 + 67344x^2 + 14884	\( 2^{20}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	$[2, 2, 2, 460]$ (GRH)
16.16.1771640105441356531371208605696.1	x^16 - 57x^14 + 1114x^12 - 10416x^10 + 52596x^8 - 147498x^6 + 218197x^4 - 139812x^2 + 14884	\( 2^{20}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.0.1771640105441356531371208605696.2	x^16 + 52x^14 + 1064x^12 + 10870x^10 + 58396x^8 + 160613x^6 + 197762x^4 + 68015x^2 + 3721	\( 2^{20}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	$[2, 2, 2, 424]$ (GRH)
16.16.1771640105441356531371208605696.2	x^16 - 57x^14 + 1037x^12 - 8434x^10 + 34815x^8 - 74359x^6 + 76128x^4 - 29890x^2 + 3721	\( 2^{20}\cdot 3^{8}\cdot 19^{2}\cdot 61^{10} \)	16T1656	Trivial (GRH)
16.0.11564522202379417842625806598144.1	x^16 - 4x^15 + 45x^14 + 66x^13 + 161x^12 + 2442x^11 + 3998x^10 + 20474x^9 + 33149x^8 + 74028x^7 + 404579x^6 - 411364x^5 + 1614500x^4 - 7900602x^3 + 12183227x^2 - 7967400x + 2173248	\( 2^{18}\cdot 97^{4}\cdot 163^{8} \)	16T1656	$[4]$ (GRH)
16.0.61968568365574294423987478237184.1	x^16 - 6x^15 + 60x^14 - 268x^13 + 2823x^12 - 5840x^11 + 57115x^10 - 110248x^9 + 961663x^8 + 741178x^7 + 16018790x^6 + 24918136x^5 + 87965021x^4 + 48668900x^3 - 29208525x^2 - 10659500x + 14667500	\( 2^{12}\cdot 3^{2}\cdot 163^{8}\cdot 241^{4} \)	16T1656	$[8]$ (GRH)
16.0.61968568365574294423987478237184.2	x^16 - 7x^15 + 170x^13 - 354x^12 - 5294x^11 + 1056x^10 + 63304x^9 - 24703x^8 - 419579x^7 + 3571512x^6 + 26681182x^5 + 74132680x^4 + 107736616x^3 + 83665008x^2 + 33038264x + 8200912	\( 2^{12}\cdot 3^{2}\cdot 163^{8}\cdot 241^{4} \)	16T1656	$[8]$ (GRH)
16.0.61968568365574294423987478237184.3	x^16 + 46x^14 - 152x^13 + 547x^12 - 7352x^11 + 19793x^10 - 111402x^9 + 606339x^8 - 1728796x^7 + 7540184x^6 - 24654776x^5 + 57489965x^4 - 155776620x^3 + 322183713x^2 - 331101126x + 126306612	\( 2^{12}\cdot 3^{2}\cdot 163^{8}\cdot 241^{4} \)	16T1656	$[8]$ (GRH)
16.0.61968568365574294423987478237184.4	x^16 - 5x^15 + 39x^14 + 149x^13 - 722x^12 + 5322x^11 + 5473x^10 - 47437x^9 + 272746x^8 - 361042x^7 - 1271180x^6 + 6730392x^5 - 22431976x^4 + 36983096x^3 + 139967056x^2 - 582314496x + 527088896	\( 2^{12}\cdot 3^{2}\cdot 163^{8}\cdot 241^{4} \)	16T1656	$[8]$ (GRH)
16.8.67129786029648929079511980455641.1	x^16 - 22x^14 + 135x^12 - 213x^10 + 551x^8 - 797x^6 + 443x^4 - 86x^2 + 1	\( 7^{2}\cdot 29^{8}\cdot 37^{8}\cdot 883^{2} \)	16T1656	$[2]$ (GRH)
16.0.75014108983158875161309828004416.1	x^16 - 6x^15 + 35x^14 - 116x^13 + 1126x^12 - 13197x^11 + 96370x^10 - 508867x^9 + 2005178x^8 - 5807296x^7 + 17488201x^6 - 40970949x^5 + 169319518x^4 - 399717697x^3 + 1309829567x^2 - 1677911242x + 3011146922	\( 2^{6}\cdot 97^{4}\cdot 163^{10} \)	16T1656	$[2, 4]$ (GRH)
16.4.75014108983158875161309828004416.1	x^16 - x^15 + 133x^14 - 176x^13 + 6360x^12 - 11770x^11 + 141519x^10 - 318503x^9 + 1555186x^8 - 3095661x^7 + 7622467x^6 - 7707622x^5 - 28643128x^4 - 7357000x^3 - 67021671x^2 + 59114093x + 153465661	\( 2^{6}\cdot 97^{4}\cdot 163^{10} \)	16T1656	$[2]$ (GRH)
16.8.75014108983158875161309828004416.1	x^16 - 5x^15 + 133x^13 - 1552x^12 + 2435x^11 + 6074x^10 - 91824x^9 + 319644x^8 + 423462x^7 - 698031x^6 - 1557794x^5 + 3195899x^4 - 2805495x^3 - 102434227x^2 + 36273710x + 187710922	\( 2^{6}\cdot 97^{4}\cdot 163^{10} \)	16T1656	Trivial (GRH)
16.0.75014108983158875161309828004416.2	x^16 - 5x^15 + 62x^14 - 109x^13 + 228x^12 + 2572x^11 - 2929x^10 + 71807x^9 + 45097x^8 - 423717x^7 + 6930709x^6 - 15527525x^5 + 82210004x^4 - 119126639x^3 + 303331671x^2 + 55592455x + 71056989	\( 2^{6}\cdot 97^{4}\cdot 163^{10} \)	16T1656	$[4, 4]$ (GRH)
16.4.75014108983158875161309828004416.2	x^16 - 6x^15 + 126x^14 - 864x^13 + 8110x^12 - 51028x^11 + 303009x^10 - 1469674x^9 + 5842000x^8 - 18700892x^7 + 42387793x^6 - 57723124x^5 + 3046308x^4 + 154537970x^3 - 298518503x^2 + 262329408x - 46704256	\( 2^{6}\cdot 97^{4}\cdot 163^{10} \)	16T1656	$[2]$ (GRH)