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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.11193507750390625.1	x^16 - x^15 + 4x^14 - 4x^13 + 8x^12 - 10x^11 + 15x^10 - 14x^9 + 21x^8 - 12x^7 + 20x^6 - 10x^5 + 13x^4 - 7x^3 + 6x^2 - 2x + 1	\( 5^{8}\cdot 11^{4}\cdot 1399^{2} \)	16T1648	Trivial
16.0.35834253375390625.1	x^16 - x^15 + x^14 - 5x^13 + 8x^12 - 8x^11 + 13x^10 - 16x^9 + 15x^8 - 16x^7 + 13x^6 - 8x^5 + 8x^4 - 5x^3 + x^2 - x + 1	\( 5^{8}\cdot 19^{4}\cdot 839^{2} \)	16T1648	Trivial
16.0.81228918797265625.1	x^16 - 4x^15 + 6x^14 - 6x^13 + 4x^12 + x^11 + 10x^10 - 22x^9 - 2x^8 + 4x^7 + 21x^6 - 7x^5 - 3x^4 - 6x^3 + 3x^2 + 1	\( 5^{8}\cdot 59^{4}\cdot 131^{2} \)	16T1648	Trivial
16.0.123319929937890625.1	x^16 + 2x^14 - 4x^13 + 3x^12 - 3x^11 + 13x^10 + 7x^9 + 23x^8 + 7x^7 + 13x^6 - 3x^5 + 3x^4 - 4x^3 + 2x^2 + 1	\( 5^{8}\cdot 61^{4}\cdot 151^{2} \)	16T1648	Trivial
16.0.147253287764593521.1	x^16 - 5x^15 + 12x^14 - 18x^13 + 20x^12 - 20x^11 + 28x^10 - 47x^9 + 59x^8 - 47x^7 + 28x^6 - 20x^5 + 20x^4 - 18x^3 + 12x^2 - 5x + 1	\( 3^{8}\cdot 7^{2}\cdot 73^{4}\cdot 127^{2} \)	16T1648	Trivial
16.0.179850251761352704.1	x^16 - 2x^15 - x^14 + 4x^13 - x^12 - 2x^11 + 5x^10 - 4x^9 - 7x^8 + 4x^7 + 5x^6 + 2x^5 - x^4 - 4x^3 - x^2 + 2x + 1	\( 2^{24}\cdot 7^{4}\cdot 2113^{2} \)	16T1648	Trivial
16.0.195640900547265625.1	x^16 - 3x^15 + 6x^14 - 8x^13 + 8x^12 - 7x^11 + 8x^10 - 12x^9 + 15x^8 - 12x^7 + 8x^6 - 7x^5 + 8x^4 - 8x^3 + 6x^2 - 3x + 1	\( 5^{8}\cdot 41^{4}\cdot 421^{2} \)	16T1648	Trivial
16.0.222529782562890625.1	x^16 - x^15 + 2x^14 - 2x^13 - 2x^10 + 3x^9 - x^8 + 3x^7 - 2x^6 - 2x^3 + 2x^2 - x + 1	\( 5^{8}\cdot 41^{4}\cdot 449^{2} \)	16T1648	Trivial
16.4.266190858984765625.2	x^16 - 5x^15 + 10x^14 - 13x^13 + 19x^12 - 24x^11 + 16x^10 - 3x^9 - 11x^8 + 27x^7 - 28x^6 + 15x^5 - 3x^4 - 8x^3 + 11x^2 - 4x - 1	\( 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1648	Trivial
16.4.337785448547265625.1	x^16 - 2x^15 + x^14 + 4x^13 - 5x^12 + 3x^11 + 2x^10 + 7x^9 + 13x^8 - 5x^7 + 14x^6 + 26x^5 + 7x^4 - 11x^3 - 16x^2 - 7x - 1	\( 5^{8}\cdot 79^{4}\cdot 149^{2} \)	16T1648	Trivial
16.0.351620091844140625.1	x^16 - x^15 - x^13 + 2x^12 + x^11 - 2x^10 + x^9 - x^8 + x^7 - 2x^6 + x^5 + 2x^4 - x^3 - x + 1	\( 5^{8}\cdot 11^{4}\cdot 7841^{2} \)	16T1648	Trivial
16.0.512376694949085184.1	x^16 - x^14 + 3x^12 - x^10 - 2x^9 + 5x^8 - 2x^7 + 3x^6 - 6x^5 + 7x^4 - 4x^3 + 3x^2 - 2x + 1	\( 2^{16}\cdot 89^{4}\cdot 353^{2} \)	16T1648	Trivial
16.4.540738703312890625.1	x^16 - 3x^15 + 5x^14 - 7x^13 + 2x^12 + 10x^11 - 24x^10 + 36x^9 - 35x^8 + 17x^7 + 4x^6 - 20x^5 + 27x^4 - 19x^3 + 10x^2 - 4x + 1	\( 5^{8}\cdot 29^{4}\cdot 1399^{2} \)	16T1648	Trivial
16.4.755661844266015625.1	x^16 - 4x^15 + 2x^14 + 15x^13 - 29x^12 + 2x^11 + 44x^10 - 29x^9 - 25x^8 + 7x^7 + 32x^6 + 16x^5 - 55x^4 + 9x^3 + 20x^2 - 6x + 1	\( 5^{8}\cdot 61^{2}\cdot 151^{4} \)	16T1648	Trivial
16.0.766764017062890625.1	x^16 - 3x^15 + 6x^14 - 8x^13 + 8x^12 - 2x^11 - 7x^10 + 13x^9 - 15x^8 + 13x^7 - 7x^6 - 2x^5 + 8x^4 - 8x^3 + 6x^2 - 3x + 1	\( 5^{8}\cdot 19^{4}\cdot 3881^{2} \)	16T1648	Trivial
16.4.816401473062890625.1	x^16 - x^15 - 5x^14 + 3x^13 + 4x^12 - 2x^11 + 7x^10 - 6x^9 - 15x^8 + 6x^7 + 7x^6 + 2x^5 + 4x^4 - 3x^3 - 5x^2 + x + 1	\( 3^{4}\cdot 5^{8}\cdot 29^{4}\cdot 191^{2} \)	16T1648	Trivial
16.4.823636792594140625.1	x^16 - 2x^15 - 3x^14 + 6x^13 + 3x^12 - 8x^11 + 3x^10 + 4x^9 - 7x^8 + 4x^7 + 3x^6 - 8x^5 + 3x^4 + 6x^3 - 3x^2 - 2x + 1	\( 5^{8}\cdot 31^{4}\cdot 1511^{2} \)	16T1648	Trivial
16.4.945584854641015625.1	x^16 - x^15 - x^14 - x^13 + 3x^12 + 2x^11 - 2x^10 - 2x^9 - 3x^8 + 4x^7 - 3x^6 + 9x^5 - 2x^4 - 3x^3 + x^2 - 2x + 1	\( 5^{8}\cdot 31^{4}\cdot 1619^{2} \)	16T1648	Trivial
16.0.1201598260406640625.1	x^16 - 4x^15 + 5x^14 + 5x^13 - 22x^12 + 25x^11 - 7x^10 - 20x^9 + 47x^8 - 54x^7 + 29x^6 - 5x^5 + 13x^4 - 28x^3 + 23x^2 - 8x + 1	\( 5^{8}\cdot 79^{2}\cdot 149^{4} \)	16T1648	Trivial
16.0.2160383693344140625.1	x^16 - 2x^15 + x^14 + x^13 - 2x^10 + x^9 + x^8 + x^7 - 2x^6 + x^3 + x^2 - 2x + 1	\( 5^{8}\cdot 41^{4}\cdot 1399^{2} \)	16T1648	Trivial
16.4.2545159570219140625.1	x^16 - 3x^15 + x^14 + 6x^13 - 6x^12 - 10x^11 + 6x^10 + 15x^9 - 5x^8 - 15x^7 + 4x^6 + 20x^5 + 14x^4 + 2x^3 - x^2 + x + 1	\( 5^{8}\cdot 79^{4}\cdot 409^{2} \)	16T1648	Trivial
16.0.4161398552437890625.1	x^16 - 2x^15 - x^13 + 9x^12 - 8x^11 + 4x^10 - 10x^9 + 5x^8 + 11x^6 - 6x^5 - 6x^4 + 2x^3 + x + 1	\( 5^{8}\cdot 29^{4}\cdot 3881^{2} \)	16T1648	Trivial
16.0.4161398552437890625.2	x^16 - 3x^15 + 3x^14 - x^13 + 6x^12 - 12x^11 - x^10 + 16x^9 + x^8 - 16x^7 - x^6 + 12x^5 + 6x^4 + x^3 + 3x^2 + 3x + 1	\( 5^{8}\cdot 29^{4}\cdot 3881^{2} \)	16T1648	Trivial
16.0.6256256925181149184.1	x^16 - 2x^15 + x^14 + 4x^13 - 12x^12 + 16x^11 - 6x^10 - 18x^9 + 50x^8 - 30x^7 - 10x^6 + 16x^5 + 12x^4 - 8x^3 - x^2 + 2x + 1	\( 2^{24}\cdot 17^{4}\cdot 2113^{2} \)	16T1648	Trivial
16.0.12348332167875390625.1	x^16 - x^15 + 2x^13 - 2x^12 - 2x^11 + 3x^10 + x^9 - 3x^8 + x^7 + 3x^6 - 2x^5 - 2x^4 + 2x^3 - x + 1	\( 5^{8}\cdot 61^{4}\cdot 1511^{2} \)	16T1648	Trivial
16.8.16519860494484765625.1	x^16 - 3x^15 + 3x^14 - 6x^13 + x^12 + 18x^11 - 6x^10 - 9x^9 + x^8 + 9x^7 - 6x^6 - 18x^5 + x^4 + 6x^3 + 3x^2 + 3x + 1	\( 5^{8}\cdot 89^{4}\cdot 821^{2} \)	16T1648	Trivial
16.0.16625807472469140625.1	x^16 - 2x^15 + 3x^14 - x^13 - 2x^12 + 6x^11 - 8x^10 + 10x^9 - x^8 - 10x^7 + 18x^6 - 13x^5 + 13x^4 - 3x^3 + 7x^2 + x + 1	\( 5^{8}\cdot 41^{4}\cdot 3881^{2} \)	16T1648	Trivial
16.8.65183814230437890625.1	x^16 - 4x^15 + 4x^14 - 4x^13 - 8x^12 + 13x^11 + 19x^10 + 68x^9 - 62x^8 - 154x^7 + 73x^6 + 104x^5 - 27x^4 - 17x^3 + x^2 - 5x - 1	\( 5^{8}\cdot 11^{4}\cdot 106759^{2} \)	16T1648	Trivial (GRH)
16.8.73811466649600000000.1	x^16 - 2x^15 - 2x^14 + 2x^13 - 8x^12 + 56x^11 - 50x^10 - 110x^9 + 203x^8 - 80x^7 - 10x^6 + 2x^5 - 38x^4 + 46x^3 - 8x^2 - 4x + 1	\( 2^{28}\cdot 5^{8}\cdot 839^{2} \)	16T1648	Trivial (GRH)
16.8.135737193960187890625.1	x^16 - x^15 - 3x^14 + 5x^13 - 2x^12 - 10x^11 + 5x^10 + 4x^9 - 3x^8 - 4x^7 + 5x^6 + 10x^5 - 2x^4 - 5x^3 - 3x^2 + x + 1	\( 5^{8}\cdot 181^{4}\cdot 569^{2} \)	16T1648	Trivial (GRH)
16.8.140853221785600000000.1	x^16 - 4x^15 - 6x^14 + 44x^13 - 20x^12 - 148x^11 + 154x^10 + 232x^9 - 340x^8 - 184x^7 + 366x^6 + 64x^5 - 188x^4 + 38x^2 - 4x - 1	\( 2^{28}\cdot 5^{8}\cdot 19^{2}\cdot 61^{2} \)	16T1648	Trivial (GRH)
16.0.332523453594656640625.1	x^16 - x^15 + 6x^14 - 7x^13 + 36x^12 - 31x^11 + 60x^10 + 5x^9 + 69x^8 - 5x^7 + 60x^6 + 31x^5 + 36x^4 + 7x^3 + 6x^2 + x + 1	\( 5^{8}\cdot 61^{4}\cdot 7841^{2} \)	16T1648	Trivial
16.8.607506927808594140625.1	x^16 - 2x^15 - 6x^14 + 17x^13 - 9x^12 - 20x^11 + 37x^10 + 37x^9 - 169x^8 + 239x^7 - 297x^6 + 355x^5 - 274x^4 + 99x^3 - 4x^2 - 6x + 1	\( 5^{8}\cdot 59^{4}\cdot 11329^{2} \)	16T1648	Trivial (GRH)
16.8.610290117282562890625.1	x^16 - 2x^15 - 7x^14 + 11x^13 + 10x^12 - 16x^11 + 12x^10 + 7x^9 - 31x^8 + 7x^7 + 12x^6 - 16x^5 + 10x^4 + 11x^3 - 7x^2 - 2x + 1	\( 5^{8}\cdot 71^{4}\cdot 7841^{2} \)	16T1648	Trivial (GRH)
16.0.830526151346062890625.1	x^16 - 2x^15 - 6x^14 + 14x^13 + 29x^12 - 41x^11 - 78x^10 + 68x^9 + 150x^8 - 26x^7 - 112x^6 + 13x^5 + 54x^4 - 8x^3 - 9x^2 + x + 1	\( 5^{8}\cdot 109^{4}\cdot 3881^{2} \)	16T1648	Trivial
16.8.1506825527144812890625.1	x^16 - 4x^15 - 3x^14 + 37x^13 - 53x^12 - 48x^11 + 213x^10 - 123x^9 - 262x^8 + 266x^7 + 157x^6 - 131x^5 - 78x^4 + 6x^3 + 18x^2 + 7x + 1	\( 5^{8}\cdot 89^{4}\cdot 7841^{2} \)	16T1648	Trivial (GRH)
16.8.1577360656000000000000.2	x^16 - 13x^14 + 70x^12 - 198x^10 + 314x^8 - 282x^6 + 140x^4 - 32x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 9929^{2} \)	16T1648	Trivial (GRH)
16.0.1681397159705859765625.1	x^16 - 3x^15 + 8x^14 - 19x^13 + 27x^12 - 64x^11 + 77x^10 - 120x^9 + 218x^8 - 112x^7 + 517x^6 - 168x^5 + 250x^4 - 355x^3 + 428x^2 - 215x + 59	\( 5^{8}\cdot 31^{2}\cdot 41^{4}\cdot 1259^{2} \)	16T1648	Trivial
16.8.2428242994208531640625.1	x^16 - 4x^15 + 23x^13 - 37x^12 - 28x^11 + 111x^10 + 30x^9 - 153x^8 - 90x^7 + 84x^6 + 106x^5 + 8x^4 - 34x^3 - 10x^2 + 3x + 1	\( 5^{8}\cdot 59^{2}\cdot 101^{4}\cdot 131^{2} \)	16T1648	Trivial (GRH)
16.12.17953987376400100000000.1	x^16 - 2x^15 - 10x^14 + 5x^13 + 47x^12 + 24x^11 - 109x^10 - 72x^9 + 137x^8 + 41x^7 - 126x^6 - 3x^5 + 72x^4 + 5x^3 - 15x^2 - x + 1	\( 2^{8}\cdot 5^{8}\cdot 181^{4}\cdot 409^{2} \)	16T1648	Trivial (GRH)
16.12.18239950264729600000000.1	x^16 - 2x^15 - 14x^14 + 18x^13 + 66x^12 - 34x^11 - 102x^10 - 90x^9 - 92x^8 + 318x^7 + 378x^6 - 278x^5 - 294x^4 + 86x^3 + 74x^2 - 10x - 5	\( 2^{28}\cdot 5^{8}\cdot 11^{4}\cdot 109^{2} \)	16T1648	Trivial (GRH)
16.16.309510571750932234765625.1	x^16 - 2x^15 - 23x^14 + 36x^13 + 184x^12 - 194x^11 - 668x^10 + 397x^9 + 1185x^8 - 250x^7 - 995x^6 - 55x^5 + 334x^4 + 63x^3 - 29x^2 - 4x + 1	\( 5^{8}\cdot 29^{4}\cdot 439^{2}\cdot 2411^{2} \)	16T1648	Trivial (GRH)
16.16.309510571750932234765625.2	x^16 - 2x^15 - 24x^14 + 42x^13 + 207x^12 - 320x^11 - 792x^10 + 1076x^9 + 1357x^8 - 1618x^7 - 926x^6 + 935x^5 + 249x^4 - 172x^3 - 23x^2 + 8x + 1	\( 5^{8}\cdot 29^{4}\cdot 439^{2}\cdot 2411^{2} \)	16T1648	Trivial (GRH)
16.0.1236570617253236016015625.2	x^16 - 6x^15 + 15x^14 - 20x^13 + 54x^12 - 196x^11 + 498x^10 - 910x^9 + 1851x^8 - 3296x^7 + 5624x^6 - 6916x^5 + 10488x^4 - 11073x^3 + 14051x^2 - 7613x + 10109	\( 5^{8}\cdot 41^{4}\cdot 439^{2}\cdot 2411^{2} \)	16T1648	$[36]$ (GRH)