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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1679616000000000000.2	x^16 - 2x^14 + 6x^12 - 61x^10 + 209x^8 - 328x^6 + 264x^4 - 104x^2 + 16	\( 2^{20}\cdot 3^{8}\cdot 5^{12} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial
16.0.6003725062500000000.1	x^16 - x^15 + 10x^14 + 10x^13 + 54x^12 + 109x^11 + 312x^10 + 580x^9 + 1186x^8 + 2089x^7 + 3262x^6 + 3838x^5 + 3419x^4 + 2108x^3 + 876x^2 + 192x + 16	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial
16.8.6879707136000000000000.1	x^16 - 10x^14 - 4x^13 + 11x^12 - 40x^11 + 46x^10 + 432x^9 + 446x^8 - 224x^7 - 562x^6 - 132x^5 + 212x^4 + 104x^3 - 24x^2 - 16x + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.8.21743271936000000000000.1	x^16 - 16x^14 - 16x^13 + 20x^12 - 8x^11 + 112x^10 + 444x^9 + 101x^8 - 768x^7 - 756x^6 + 228x^5 + 998x^4 + 576x^3 - 200x^2 - 156x + 41	\( 2^{40}\cdot 3^{4}\cdot 5^{12} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.0.30467756702686506909696.1	x^16 + 8x^14 - 16x^13 + 92x^12 - 416x^11 + 1876x^10 - 6416x^9 + 16982x^8 - 34576x^7 + 55728x^6 - 70344x^5 + 70592x^4 - 54032x^3 + 31624x^2 - 12288x + 3106	\( 2^{52}\cdot 3^{4}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2]$
16.0.30467756702686506909696.2	x^16 - 4x^14 - 16x^13 + 136x^12 + 160x^11 - 316x^10 - 496x^9 + 1174x^8 + 5104x^7 + 7652x^6 + 7040x^5 + 5336x^4 + 4720x^3 + 6172x^2 + 4608x + 2897	\( 2^{52}\cdot 3^{4}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2]$
16.0.136651472896000000000000.1	x^16 + 28x^14 - 24x^13 + 322x^12 - 464x^11 + 2076x^10 - 3352x^9 + 8090x^8 - 11072x^7 + 17748x^6 - 18172x^5 + 21047x^4 - 13424x^3 + 11388x^2 - 3272x + 2201	\( 2^{32}\cdot 5^{12}\cdot 19^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.0.136651472896000000000000.2	x^16 - 12x^14 - 16x^13 + 62x^12 + 184x^11 - 124x^10 - 1268x^9 - 1715x^8 + 2192x^7 + 11808x^6 + 22092x^5 + 25512x^4 + 20344x^3 + 11688x^2 + 4772x + 1271	\( 2^{32}\cdot 5^{12}\cdot 19^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.8.2467888292917607059685376.1	x^16 - 24x^14 - 32x^13 + 124x^12 + 288x^11 - 56x^10 - 704x^9 + 470x^8 + 3648x^7 + 376x^6 - 8544x^5 - 3652x^4 + 9504x^3 + 2968x^2 - 9152x - 2111	\( 2^{52}\cdot 3^{8}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.8.3502227787776000000000000.1	x^16 - 2x^15 - 10x^14 + 60x^13 - 96x^12 - 142x^11 + 638x^10 - 810x^9 + 2021x^8 - 8862x^7 + 20038x^6 - 19126x^5 - 4256x^4 + 23336x^3 - 10836x^2 - 6154x + 3541	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 19^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.0.43381651460325376000000000000.1	x^16 + 88x^14 - 44x^13 + 3622x^12 - 2744x^11 + 84906x^10 - 69432x^9 + 1203805x^8 - 853752x^7 + 10143918x^6 - 5250312x^5 + 47701212x^4 - 13773424x^3 + 101881698x^2 - 3534252x + 60133751	\( 2^{32}\cdot 5^{12}\cdot 11^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2, 2]$ (GRH)
16.0.43381651460325376000000000000.2	x^16 - 118x^14 - 20x^13 + 5630x^12 + 4080x^11 - 133878x^10 - 205460x^9 + 1697264x^8 + 3791040x^7 - 10234682x^6 - 28254140x^5 + 24944210x^4 + 66116880x^3 - 55097722x^2 + 51903780x + 290639471	\( 2^{32}\cdot 5^{12}\cdot 11^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2, 2]$ (GRH)
16.8.33531062442740678656000000000000.1	x^16 - 4x^15 - 14x^14 + 372x^13 - 3608x^12 + 10836x^11 + 12692x^10 - 425328x^9 + 3141706x^8 - 11880328x^7 + 33848312x^6 - 52326304x^5 - 24759608x^4 + 180554672x^3 - 626828664x^2 - 165073424x + 447410716	\( 2^{36}\cdot 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2]$ (GRH)
16.8.33531062442740678656000000000000.2	x^16 - 4x^15 - 60x^14 + 276x^13 - 580x^12 + 3640x^11 + 29412x^10 - 487616x^9 + 2400752x^8 + 2909352x^7 - 65404272x^6 + 202341208x^5 + 330768x^4 - 1951919440x^3 + 6195469544x^2 - 7573198816x + 3611349436	\( 2^{36}\cdot 5^{12}\cdot 29^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2]$ (GRH)
16.0.79688620999701608976000000000000.1	x^16 - 8x^15 + 323x^14 - 1972x^13 + 39783x^12 - 185618x^11 + 2417269x^10 - 8510506x^9 + 77623693x^8 - 201140128x^7 + 1308764896x^6 - 2362029700x^5 + 10813266968x^4 - 10291651056x^3 + 35038013272x^2 + 10096911248x + 18671230096	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 181^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2, 2, 2, 27880]$ (GRH)
16.16.79688620999701608976000000000000.1	x^16 - 6x^15 - 212x^14 + 1162x^13 + 17428x^12 - 81548x^11 - 745869x^10 + 2695196x^9 + 18559353x^8 - 44414652x^7 - 275403616x^6 + 325908724x^5 + 2293812968x^4 - 325075504x^3 - 8596723528x^2 - 5263277392x + 4182359056	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 181^{4} \)	$C_2^4.C_2^3$ (as 16T203)	Trivial (GRH)
16.0.177691244381492740096000000000000.1	x^16 - 4x^15 + 168x^14 - 352x^13 + 11378x^12 - 7312x^11 + 430056x^10 + 191104x^9 + 10154778x^8 + 11990232x^7 + 151448504x^6 + 234650416x^5 + 1339583508x^4 + 2029216704x^3 + 5894282792x^2 + 6112206352x + 6648587356	\( 2^{44}\cdot 5^{12}\cdot 11^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2, 2, 2, 2, 10892]$ (GRH)
16.16.177691244381492740096000000000000.1	x^16 - 4x^15 - 224x^14 + 876x^13 + 19944x^12 - 77544x^11 - 891496x^10 + 3540612x^9 + 20530069x^8 - 87322848x^7 - 214623836x^6 + 1089455540x^5 + 509655902x^4 - 5441325612x^3 + 2787323020x^2 + 6665735720x - 5487281519	\( 2^{44}\cdot 5^{12}\cdot 11^{4}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2]$ (GRH)