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
16.2.47375394326171875.1	x^16 - 5x^15 + 8x^14 + 4x^13 - 29x^12 + 31x^11 + 4x^10 - 19x^9 - 23x^8 + 59x^7 - 30x^6 - 16x^5 + 20x^4 - 6x^2 + x + 1	\( -\,5^{10}\cdot 19^{3}\cdot 29^{4} \)	16T1561	Trivial
16.0.147310907626953125.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 8x^12 - 12x^11 - 2x^10 + 15x^9 - 18x^8 + 35x^7 + 2x^6 + 9x^5 + 23x^4 - 5x^3 + 10x^2 - x + 1	\( 5^{10}\cdot 11^{4}\cdot 101^{3} \)	16T1561	Trivial
16.4.476040173837890625.1	x^16 - 3x^15 + 6x^14 - 8x^13 + 13x^11 - 9x^10 + 4x^9 - 27x^8 + 31x^7 + 21x^6 - 60x^5 + 29x^4 + 15x^3 - 21x^2 + 8x - 1	\( 5^{10}\cdot 29^{4}\cdot 41^{3} \)	16T1561	Trivial
16.6.1184384858154296875.1	x^16 - 3x^15 - 3x^14 + 15x^13 - 29x^11 + 15x^10 + 8x^9 - 9x^8 + 25x^7 - 15x^6 - 18x^5 + 13x^4 - 3x^3 - 2x^2 + 5x + 1	\( -\,5^{12}\cdot 19^{3}\cdot 29^{4} \)	16T1561	Trivial
16.2.3553138931826171875.1	x^16 - 2x^15 - 5x^14 + x^13 + 35x^12 + 3x^11 - 79x^10 - 83x^9 + 164x^8 + 145x^7 - 100x^6 - 253x^5 + 153x^4 + 25x^3 - 40x^2 + 11x - 1	\( -\,5^{10}\cdot 11^{6}\cdot 59^{3} \)	16T1561	Trivial
16.4.3682772690673828125.1	x^16 - x^15 - 4x^14 + 9x^13 + 2x^12 - 27x^11 - 12x^10 + 61x^9 + 36x^8 - 78x^7 - 79x^6 + 55x^5 + 61x^4 - 19x^3 - 20x^2 + 5x + 1	\( 5^{12}\cdot 11^{4}\cdot 101^{3} \)	16T1561	Trivial
16.4.11901004345947265625.1	x^16 - 4x^15 + 10x^14 - 17x^13 + 11x^12 + x^11 + 17x^10 - 63x^9 + 93x^8 - 92x^7 + 77x^6 - 41x^5 + x^4 + 7x^3 + 5x^2 - 6x + 1	\( 5^{12}\cdot 29^{4}\cdot 41^{3} \)	16T1561	Trivial
16.2.17102517351748046875.1	x^16 - 2x^15 - x^14 - 4x^13 + 9x^12 + 13x^11 + 13x^10 - 48x^9 + x^8 - 27x^7 + 49x^6 - 30x^5 + 68x^4 - 52x^3 - 9x^2 + 19x - 11	\( -\,5^{10}\cdot 19^{5}\cdot 29^{4} \)	16T1561	Trivial
16.6.39614221711513671875.1	x^16 - 2x^15 - 4x^14 + 11x^13 - 23x^12 + 8x^11 + 23x^10 - 68x^9 + 83x^8 - 68x^7 + 23x^6 + 8x^5 - 23x^4 + 11x^3 - 4x^2 - 2x + 1	\( -\,5^{10}\cdot 29^{4}\cdot 179^{3} \)	16T1561	Trivial
16.2.88828473295654296875.1	x^16 - 2x^15 - 4x^14 + 7x^13 + 4x^12 + 12x^11 - 18x^10 - 54x^9 + 21x^8 + 60x^7 + 197x^6 - 469x^5 + 264x^4 + 70x^3 - 110x^2 + 21x - 9	\( -\,5^{12}\cdot 11^{6}\cdot 59^{3} \)	16T1561	Trivial
16.0.1502718568702548828125.1	x^16 - 4x^15 + 14x^14 - 33x^13 + 67x^12 - 109x^11 + 137x^10 - 115x^9 + 148x^8 - 588x^7 + 2040x^6 - 4461x^5 + 6759x^4 - 6939x^3 + 4968x^2 - 2237x + 701	\( 5^{10}\cdot 11^{4}\cdot 101^{5} \)	16T1561	$[2]$
16.8.5755206424008798828125.1	x^16 - 6x^15 + 6x^14 + 36x^13 - 142x^12 + 229x^11 - 80x^10 - 378x^9 + 709x^8 - 511x^7 - 107x^6 + 615x^5 - 384x^4 + 109x^3 + x^2 - 10x + 1	\( 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial
16.4.37567964217563720703125.1	x^16 - 2x^15 + 3x^14 + 6x^13 - 42x^12 + 74x^11 - 77x^10 - 217x^9 + 205x^8 + 1049x^7 - 828x^6 - 334x^5 - 179x^4 - 196x^3 + 52x^2 - 15x + 1	\( 5^{12}\cdot 11^{4}\cdot 101^{5} \)	16T1561	$[2]$ (GRH)
16.0.143880160600219970703125.1	x^16 - x^15 + 6x^14 - 5x^13 + 2x^12 - 28x^11 + 91x^10 - 274x^9 + 27x^8 - 45x^7 - 111x^6 + 436x^5 + 1515x^4 - 31x^3 + 49x^2 + 798x + 361	\( 5^{12}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[4]$
16.8.4840128602591399814453125.1	x^16 - 2x^15 - 12x^14 + 51x^13 - 4x^12 - 222x^11 - 164x^10 + 779x^9 + 2011x^8 - 3541x^7 - 3661x^6 + 4149x^5 + 4264x^4 + 4993x^3 - 14756x^2 + 1914x + 4021	\( 5^{10}\cdot 29^{6}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.0.377173208203840640000000000.1	x^16 + 49x^14 + 962x^12 + 9681x^10 + 53071x^8 + 155755x^6 + 226545x^4 + 141150x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[2, 330]$ (GRH)
16.12.377173208203840640000000000.1	x^16 - 20x^14 + 41x^12 + 1525x^10 - 12736x^8 + 35340x^6 - 23960x^4 - 23525x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.16.377173208203840640000000000.1	x^16 - 49x^14 + 962x^12 - 9681x^10 + 53071x^8 - 155755x^6 + 226545x^4 - 141150x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.4.377173208203840640000000000.1	x^16 + 18x^14 + 10x^12 - 1874x^10 - 17111x^8 - 66395x^6 - 119090x^4 - 70575x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[2]$ (GRH)
16.8.377173208203840640000000000.1	x^16 + 12x^14 - 167x^12 - 1458x^10 + 9626x^8 + 30055x^6 - 64395x^4 - 141150x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[2]$ (GRH)
16.12.377173208203840640000000000.2	x^16 - 29x^14 + 265x^12 - 262x^10 - 8551x^8 + 38790x^6 - 6135x^4 - 164675x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.4.377173208203840640000000000.2	x^16 + 29x^14 + 265x^12 + 262x^10 - 8551x^8 - 38790x^6 - 6135x^4 + 164675x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[2]$ (GRH)
16.8.377173208203840640000000000.2	x^16 + 17x^14 - 107x^12 - 2638x^10 - 5814x^8 + 35865x^6 + 35265x^4 - 117625x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	$[2]$ (GRH)
16.8.377173208203840640000000000.3	x^16 - 12x^14 - 167x^12 + 1458x^10 + 9626x^8 - 30055x^6 - 64395x^4 + 141150x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.8.377173208203840640000000000.4	x^16 - 17x^14 - 107x^12 + 2638x^10 - 5814x^8 - 35865x^6 + 35265x^4 + 117625x^2 + 23525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{3} \)	16T1561	Trivial (GRH)
16.0.1928062066067290240000000000.1	x^16 + 48x^14 + 943x^12 + 9883x^10 + 59836x^8 + 209680x^6 + 396095x^4 + 324200x^2 + 40525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 1621^{3} \)	16T1561	$[2, 564]$ (GRH)
16.16.1928062066067290240000000000.1	x^16 - 48x^14 + 943x^12 - 9883x^10 + 59836x^8 - 209680x^6 + 396095x^4 - 324200x^2 + 40525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 1621^{3} \)	16T1561	Trivial (GRH)
16.0.101763703869484181098876953125.1	x^16 - 29x^14 + 384x^12 - 2358x^10 + 16164x^8 - 2221x^6 + 115106x^4 + 1244943x^2 + 2259341	\( 5^{12}\cdot 29^{8}\cdot 941^{3} \)	16T1561	$[4, 44]$ (GRH)