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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.254652744902639616.2	x^16 - 2x^14 - x^12 - 2x^10 + 37x^8 - 88x^6 + 104x^4 - 64x^2 + 16	\( 2^{24}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial
16.0.4074443918442233856.1	x^16 - 2x^15 + 4x^14 + 4x^13 - 28x^12 - 2x^11 + 64x^10 + 2x^9 - 77x^8 - 18x^7 + 40x^6 + 18x^5 + 4x^4 + 16x^3 + 16x^2 + 6x + 1	\( 2^{28}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$
16.0.4635236761600000000.2	x^16 - 8x^15 + 36x^14 - 106x^13 + 231x^12 - 386x^11 + 518x^10 - 582x^9 + 580x^8 - 516x^7 + 402x^6 - 250x^5 + 111x^4 - 30x^3 + 4x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial
16.0.16710207732203913216.1	x^16 - 10x^14 + 49x^12 - 142x^10 + 280x^8 - 430x^6 + 469x^4 - 322x^2 + 169	\( 2^{24}\cdot 3^{12}\cdot 37^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial
16.8.2393397489569403764736.4	x^16 - 8x^14 + 26x^12 - 68x^10 + 136x^8 - 148x^6 + 74x^4 - 16x^2 + 1	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.4.2393397489569403764736.5	x^16 - 4x^14 - 2x^12 + 8x^10 - 8x^8 + 8x^6 - 2x^4 - 4x^2 + 1	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.8.2393397489569403764736.5	x^16 - 2x^12 - 12x^8 - 12x^6 + 34x^4 - 12x^2 + 1	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.4.2393397489569403764736.6	x^16 - 4x^14 - 16x^12 - 16x^10 - 8x^8 + 40x^6 + 32x^4 + 16x^2 + 4	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial
16.0.2393397489569403764736.8	x^16 - 2x^12 - 12x^8 + 12x^6 + 34x^4 + 12x^2 + 1	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$
16.0.2393397489569403764736.9	x^16 + 8x^14 + 26x^12 + 68x^10 + 136x^8 + 148x^6 + 74x^4 + 16x^2 + 1	\( 2^{52}\cdot 3^{12} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$
16.8.27583540507977079969140625.1	x^16 - 2x^15 - 2x^14 - 59x^13 + 100x^12 + 371x^11 - 213x^10 - 1392x^9 + 1447x^8 + 1279x^7 - 3004x^6 + 1293x^5 + 860x^4 - 902x^3 + 171x^2 + 52x - 16	\( 5^{8}\cdot 29^{8}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$ (GRH)
16.0.27583540507977079969140625.2	x^16 - 4x^15 + 21x^14 - 76x^13 + 236x^12 - 586x^11 + 1771x^10 - 3310x^9 + 6160x^8 - 11358x^7 + 19208x^6 - 12266x^5 + 10932x^4 - 17850x^3 + 4931x^2 + 7110x + 2180	\( 5^{8}\cdot 29^{8}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 48]$ (GRH)
16.0.96313927189328563031640625.2	x^16 - 3x^15 + 31x^14 - 66x^13 + 344x^12 - 735x^11 + 3011x^10 - 7340x^9 + 16213x^8 - 32331x^7 + 58931x^6 - 85970x^5 + 93776x^4 - 76722x^3 + 52696x^2 - 26460x + 7025	\( 5^{8}\cdot 29^{8}\cdot 149^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 96]$ (GRH)
16.0.96313927189328563031640625.3	x^16 - 4x^15 + 26x^14 - 48x^13 + 193x^12 - 238x^11 + 961x^10 - 976x^9 + 1127x^8 - 534x^7 + 2696x^6 + 4262x^5 + 8049x^4 + 4200x^3 + 22260x^2 + 2400x + 400	\( 5^{8}\cdot 29^{8}\cdot 149^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 48]$ (GRH)
16.8.117487395465924089674203136.1	x^16 - 2x^15 - x^14 + 2x^13 - 40x^12 + 66x^11 + 145x^10 - 474x^9 + 558x^8 - 2022x^7 - 3455x^6 + 7110x^5 + 7544x^4 + 1094x^3 - 145x^2 - 14x + 1	\( 2^{28}\cdot 17^{8}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.0.584793659653495312365912064.1	x^16 - 2x^15 + 7x^14 - 44x^13 + 181x^12 - 634x^11 + 2437x^10 - 6040x^9 + 11558x^8 - 28496x^7 + 70840x^6 - 125696x^5 + 149968x^4 - 119808x^3 + 62944x^2 - 19968x + 3008	\( 2^{34}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 20]$ (GRH)
16.8.584793659653495312365912064.1	x^16 - 8x^15 + 24x^14 + 16x^13 - 249x^12 + 336x^11 + 842x^10 - 2224x^9 - 2404x^8 + 3016x^7 - 984x^6 - 9896x^5 - 5550x^4 + 2552x^3 + 2308x^2 + 48x - 144	\( 2^{34}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.0.584793659653495312365912064.2	x^16 - 14x^14 + 95x^12 - 20x^10 + 791x^8 + 4594x^6 + 20057x^4 + 3136x^2 + 1024	\( 2^{34}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 2, 20]$ (GRH)
16.8.584793659653495312365912064.2	x^16 - 10x^14 - 277x^12 - 1168x^10 - 253x^8 + 1118x^6 - 163x^4 - 52x^2 + 4	\( 2^{34}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T373)	Trivial (GRH)
16.0.669770746878591518927486976.1	x^16 + 12x^14 + 82x^12 + 228x^10 + 396x^8 + 408x^6 + 622x^4 - 600x^2 + 625	\( 2^{52}\cdot 3^{12}\cdot 23^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 2, 2, 10]$ (GRH)
16.8.1062004354962295536520003584.1	x^16 - 8x^15 + 80x^13 + 204x^12 - 840x^11 - 3296x^10 + 5984x^9 + 22038x^8 + 472x^7 - 133856x^6 - 67536x^5 + 381732x^4 + 82648x^3 - 55776x^2 + 1472x + 529	\( 2^{46}\cdot 3^{12}\cdot 73^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$ (GRH)
16.0.1062004354962295536520003584.2	x^16 - 8x^15 + 20x^14 - 32x^13 + 316x^12 - 1336x^11 + 2840x^10 - 6688x^9 + 17656x^8 - 60864x^7 + 171600x^6 - 107184x^5 + 310344x^4 - 144000x^3 + 326736x^2 - 38016x + 160632	\( 2^{46}\cdot 3^{12}\cdot 73^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 8, 8]$ (GRH)
16.0.1879798327454785434787250176.1	x^16 - 8x^15 + 60x^14 - 280x^13 + 1164x^12 - 3708x^11 + 10174x^10 - 22600x^9 + 43061x^8 - 67708x^7 + 107994x^6 - 151328x^5 + 269360x^4 - 335548x^3 + 372830x^2 - 223464x + 407601	\( 2^{32}\cdot 17^{8}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 2, 8]$ (GRH)
16.16.4248017419849182146080014336.2	x^16 - 8x^15 - 8x^14 + 176x^13 - 136x^12 - 1376x^11 + 1940x^10 + 4544x^9 - 8624x^8 - 5152x^7 + 15392x^6 - 2000x^5 - 8980x^4 + 5096x^3 - 764x^2 - 8x + 1	\( 2^{48}\cdot 3^{12}\cdot 73^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$ (GRH)
16.16.4248017419849182146080014336.3	x^16 - 8x^15 - 8x^14 + 192x^13 - 168x^12 - 1712x^11 + 2436x^10 + 7224x^9 - 11288x^8 - 15488x^7 + 21400x^6 + 17360x^5 - 15780x^4 - 7704x^3 + 4172x^2 + 832x - 263	\( 2^{48}\cdot 3^{12}\cdot 73^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$ (GRH)
16.8.9356698554455924997854593024.1	x^16 + 36x^14 + 282x^12 - 712x^10 - 5415x^8 + 6436x^6 + 692x^4 - 736x^2 + 64	\( 2^{38}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T373)	$[2]$ (GRH)
16.0.15155900128400657740323618816.1	x^16 + 6x^14 - 42x^12 - 594x^10 - 54x^8 + 13770x^6 + 102006x^4 + 490050x^2 + 1185921	\( 2^{40}\cdot 3^{12}\cdot 11^{10} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 4, 4, 4]$ (GRH)
16.0.28654123680257493540299341824.1	x^16 + 58x^14 + 1207x^12 + 11284x^10 + 52027x^8 + 116938x^6 + 112537x^4 + 35800x^2 + 2500	\( 2^{34}\cdot 3^{12}\cdot 11^{12} \)	$C_2^4.C_2^3$ (as 16T373)	$[2, 4, 4, 8]$ (GRH)