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 matches 1-50 of 56)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.32681998468583424.2	x^16 + 3x^14 + 2x^12 - 3x^10 - 4x^8 + x^4 + 1	\( 2^{12}\cdot 3^{8}\cdot 43^{2}\cdot 811^{2} \)	16T1884	Trivial
16.0.38303011586248704.1	x^16 - 5x^14 + 11x^12 - 11x^10 + 3x^8 + 3x^6 - 3x^4 + x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 19^{2}\cdot 1987^{2} \)	16T1884	Trivial
16.4.266190858984765625.1	x^16 - 4x^14 + 2x^12 - 7x^11 + x^10 + 6x^9 - 20x^8 - 22x^7 - 7x^6 - 14x^5 - 9x^4 + 14x^3 + 19x^2 + 8x + 1	\( 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial
16.0.311829406284765625.1	x^16 + 2x^14 - 3x^13 + 3x^12 - x^11 + 6x^10 + 13x^9 + 8x^8 + 19x^7 + 4x^5 + 12x^4 - 17x^3 + 12x^2 - x + 1	\( 5^{8}\cdot 61^{2}\cdot 97^{2}\cdot 151^{2} \)	16T1884	Trivial
16.4.1201598260406640625.1	x^16 - 3x^15 - 2x^14 + 11x^13 - 5x^12 - 6x^11 + x^10 - 19x^9 + 54x^8 - 14x^7 - 69x^6 + 71x^5 - 19x^4 - 6x^3 + 7x^2 - 4x + 1	\( 5^{8}\cdot 79^{2}\cdot 149^{4} \)	16T1884	Trivial
16.0.6407213906256250000.1	x^16 - x^15 - 2x^14 + 8x^13 - 6x^12 + 8x^10 - 5x^9 + 36x^8 - 118x^7 + 204x^6 - 160x^5 + 146x^4 - 74x^3 + 47x^2 + 4x + 1	\( 2^{4}\cdot 5^{8}\cdot 59^{2}\cdot 131^{4} \)	16T1884	Trivial
16.4.18153053209600000000.3	x^16 + 2x^14 - x^12 - 9x^10 - 4x^8 + 14x^6 + 4x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 31^{2}\cdot 859^{2} \)	16T1884	Trivial
16.4.21442705255472265625.1	x^16 - 5x^15 + 9x^14 - 8x^13 + 5x^12 - 4x^11 + 2x^10 + 5x^9 - 9x^8 + 5x^7 + 2x^6 - 4x^5 + 5x^4 - 8x^3 + 9x^2 - 5x + 1	\( 5^{8}\cdot 7^{2}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial
16.0.22889717862400000000.1	x^16 + 7x^14 + 31x^12 + 98x^10 + 232x^8 + 384x^6 + 416x^4 + 256x^2 + 64	\( 2^{18}\cdot 5^{8}\cdot 14951^{2} \)	16T1884	Trivial
16.4.22889717862400000000.1	x^16 - 8x^14 + 26x^12 - 48x^10 + 58x^8 - 49x^6 + 31x^4 - 14x^2 + 4	\( 2^{18}\cdot 5^{8}\cdot 14951^{2} \)	16T1884	Trivial
16.4.367725112345600000000.4	x^16 + 5x^14 + 10x^12 + 9x^10 - 7x^8 - 30x^6 - 26x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1884	Trivial
16.8.367725112345600000000.4	x^16 - x^14 - 11x^12 + 17x^10 + 22x^8 - 54x^6 + 31x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1884	Trivial
16.4.367725112345600000000.5	x^16 + 6x^14 + 4x^12 - 17x^10 - 3x^8 + 19x^6 - 4x^4 - 8x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1884	Trivial
16.8.367725112345600000000.5	x^16 - 5x^14 + 5x^12 + 12x^10 - 27x^8 + 10x^6 + 11x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 119851^{2} \)	16T1884	Trivial
16.0.764282896963472265625.1	x^16 - 2x^15 + 6x^14 - 4x^13 + 40x^12 - 38x^11 + 118x^10 - 13x^9 + 321x^8 - 29x^7 + 375x^6 + 93x^5 + 917x^4 + 362x^3 - 352x^2 - 553x + 449	\( 5^{8}\cdot 59^{4}\cdot 97^{2}\cdot 131^{2} \)	16T1884	Trivial
16.8.961227049659328515625.1	x^16 - 3x^15 - 8x^14 + 36x^13 - 2x^12 - 128x^11 + 112x^10 + 158x^9 - 276x^8 + 54x^7 + 171x^6 - 223x^5 + 93x^4 + 90x^3 - 77x^2 + 12x + 1	\( 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial
16.8.4117437015280378515625.1	x^16 - 6x^15 + 12x^14 - x^13 - 36x^12 + 63x^11 - 59x^10 + 42x^9 + 28x^8 - 177x^7 + 167x^6 + 91x^5 + 8x^4 + 82x^3 - 37x^2 - 40x + 1	\( 5^{8}\cdot 97^{2}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial
16.0.5661539616510009765625.1	x^16 - 2x^15 + x^14 + 7x^13 - 19x^12 + 24x^11 + 39x^10 - 149x^9 + 287x^8 - 404x^7 + 519x^6 - 736x^5 + 1166x^4 - 1278x^3 + 1071x^2 - 562x + 316	\( 5^{14}\cdot 97^{2}\cdot 9929^{2} \)	16T1884	$[2]$
16.8.5661539616510009765625.1	x^16 - 6x^15 + 11x^14 - 4x^13 - 22x^12 + 114x^11 - 126x^10 - 332x^9 + 368x^8 + 594x^7 - 189x^6 - 502x^5 - 142x^4 + 83x^3 + 59x^2 + 13x + 1	\( 5^{14}\cdot 97^{2}\cdot 9929^{2} \)	16T1884	Trivial
16.0.17445084134425600000000.1	x^16 + 13x^14 + 60x^12 + 90x^10 - 122x^8 - 420x^6 + 155x^4 + 1271x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial
16.4.17445084134425600000000.1	x^16 + 6x^14 - 7x^12 - 103x^10 - 349x^8 - 644x^6 - 31x^4 + 1395x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial (GRH)
16.8.17445084134425600000000.1	x^16 - 3x^14 - 27x^12 + 32x^10 + 263x^8 + 57x^6 - 403x^4 - 1240x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial (GRH)
16.0.17445084134425600000000.2	x^16 + 6x^14 + 47x^12 + 52x^10 - 32x^8 + 1331x^6 + 4123x^4 + 3782x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial
16.4.17445084134425600000000.2	x^16 - 5x^14 + 8x^12 + 64x^10 - 232x^8 + 521x^6 - 1798x^4 + 1829x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial (GRH)
16.8.17445084134425600000000.2	x^16 - 6x^14 + 47x^12 - 52x^10 - 32x^8 - 1331x^6 + 4123x^4 - 3782x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{2} \)	16T1884	Trivial (GRH)
16.4.25716105547803375390625.1	x^16 - x^15 - 11x^14 + 21x^13 + 12x^12 - 71x^11 + 40x^10 + 114x^9 - x^8 - 409x^7 + 818x^6 - 1041x^5 + 117x^4 + 504x^3 - 370x^2 - 161x + 49	\( 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial
16.8.25716105547803375390625.1	x^16 - x^15 + 2x^14 + 3x^13 - 80x^12 + 119x^11 + 3x^10 - 33x^9 + 155x^8 - 202x^7 - 11x^6 - 87x^5 - 116x^4 + 94x^3 + 86x^2 + 17x + 1	\( 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.8.28678961869849600000000.1	x^16 + 2x^14 - 14x^12 - 16x^10 + 47x^8 + 23x^6 - 51x^4 + 6x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial
16.12.28678961869849600000000.3	x^16 - 9x^14 + 23x^12 - 3x^10 - 49x^8 + 46x^6 - 6x^4 - 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial (GRH)
16.4.28678961869849600000000.3	x^16 + 6x^14 + 4x^12 - 39x^10 - 100x^8 - 89x^6 - 26x^4 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial
16.12.28678961869849600000000.4	x^16 - 11x^14 + 43x^12 - 67x^10 + 21x^8 + 34x^6 - 21x^4 + 1	\( 2^{16}\cdot 5^{8}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial (GRH)
16.0.142063500028134400000000.1	x^16 + 17x^14 + 124x^12 + 511x^10 + 1310x^8 + 2143x^6 + 2170x^4 + 1224x^2 + 289	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 138571^{2} \)	16T1884	Trivial
16.12.142063500028134400000000.1	x^16 - 17x^14 + 124x^12 - 511x^10 + 1310x^8 - 2143x^6 + 2170x^4 - 1224x^2 + 289	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 138571^{2} \)	16T1884	Trivial (GRH)
16.8.2573398134550236572265625.1	x^16 - 4x^15 - 2x^14 - 5x^13 + 33x^12 - 61x^11 - 259x^10 + 1089x^9 - 1233x^8 - 767x^7 + 4477x^6 - 6824x^5 + 3694x^4 + 5597x^3 - 11096x^2 + 6340x - 1039	\( 5^{12}\cdot 97^{2}\cdot 439^{2}\cdot 2411^{2} \)	16T1884	Trivial (GRH)
16.4.16072565967377109619140625.1	x^16 - 4x^15 + 4x^14 - 38x^13 - 28x^12 + 5x^11 - 17x^10 + 1574x^9 + 2734x^8 + 10926x^7 + 22489x^6 + 41414x^5 + 77203x^4 + 79233x^3 + 109439x^2 + 59685x + 46591	\( 5^{12}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.8.16072565967377109619140625.1	x^16 - 6x^15 + 22x^14 - 28x^13 - 102x^12 + 527x^11 - 1283x^10 + 201x^9 + 4110x^8 - 12493x^7 + 11763x^6 + 15927x^5 - 40884x^4 + 57997x^3 + 42138x^2 - 71740x - 1459	\( 5^{12}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.0.62994975926473753600000000.1	x^16 + 27x^14 + 270x^12 + 1392x^10 + 4145x^8 + 7369x^6 + 7657x^4 + 4247x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	$[2, 116]$ (GRH)
16.12.62994975926473753600000000.1	x^16 - 9x^14 - 33x^12 + 532x^10 - 1682x^8 + 1231x^6 + 2263x^4 - 3503x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial (GRH)
16.16.62994975926473753600000000.1	x^16 - 27x^14 + 270x^12 - 1392x^10 + 4145x^8 - 7369x^6 + 7657x^4 - 4247x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial (GRH)
16.4.62994975926473753600000000.1	x^16 + 9x^14 - 33x^12 - 532x^10 - 1682x^8 - 1231x^6 + 2263x^4 + 3503x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	$[3]$ (GRH)
16.8.62994975926473753600000000.1	x^16 + x^14 - 55x^12 - 151x^10 + 385x^8 + 1092x^6 - 992x^4 - 1891x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial (GRH)
16.12.62994975926473753600000000.2	x^16 + x^14 - 118x^12 + 399x^10 + 1503x^8 - 8929x^6 + 12803x^4 - 6200x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial (GRH)
16.4.62994975926473753600000000.2	x^16 + 11x^14 + 4x^12 - 330x^10 - 1262x^8 - 1041x^6 + 2015x^4 + 3410x^2 + 961	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	$[2]$ (GRH)
16.0.1685330693180842009600000000.1	x^16 + 49x^14 + 1066x^12 + 13730x^10 + 115626x^8 + 645702x^6 + 2274197x^4 + 4465449x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	$[6]$ (GRH)
16.12.1685330693180842009600000000.1	x^16 - 57x^14 + 1263x^12 - 15414x^10 + 120536x^8 - 635230x^6 + 2174744x^4 - 4282953x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.4.1685330693180842009600000000.1	x^16 + 21x^14 - 47x^12 + 905x^10 + 37995x^8 - 160043x^6 - 1126950x^4 + 1041748x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	$[4]$ (GRH)
16.8.1685330693180842009600000000.1	x^16 - 14x^14 - 541x^12 + 8345x^10 - 31737x^8 + 112414x^6 - 836440x^4 + 1235650x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.4.1685330693180842009600000000.2	x^16 + 28x^14 - 217x^12 - 8279x^10 - 33294x^8 + 16250x^6 - 675226x^4 + 1058857x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.8.1685330693180842009600000000.2	x^16 - 15x^14 + 214x^12 - 3581x^10 + 22321x^8 + 27603x^6 - 561737x^4 + 349784x^2 + 3613801	\( 2^{16}\cdot 5^{8}\cdot 71^{2}\cdot 1901^{4} \)	16T1884	Trivial (GRH)
16.16.39371859954046096000000000000.1	x^16 - 55x^14 + 1235x^12 - 14825x^10 + 103975x^8 - 434500x^6 + 1046250x^4 - 1298125x^2 + 600625	\( 2^{16}\cdot 5^{12}\cdot 31^{4}\cdot 41^{2}\cdot 1259^{2} \)	16T1884	Trivial (GRH)