Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2110890384014935069.1	x^16 - 2x^15 - 7x^14 + 11x^13 + 35x^12 - 38x^11 - 106x^10 + 67x^9 + 227x^8 - 59x^7 - 310x^6 - 22x^5 + 271x^4 + 84x^3 - 146x^2 - 52x + 47	\( 1103^{3}\cdot 1163^{3} \)	16T1946	Trivial
16.0.3202609159111320197.1	x^16 - 4x^14 - x^13 - x^12 + 13x^11 + 29x^10 - 65x^9 + 2x^8 + 42x^7 - 26x^6 + 40x^5 - 13x^4 - 205x^3 + 439x^2 - 305x + 83	\( 617^{3}\cdot 2389^{3} \)	16T1946	Trivial
16.2.83143722412755610003.1	x^16 - 3x^15 + 9x^14 - 25x^13 + 58x^12 - 130x^11 + 275x^10 - 577x^9 + 1001x^8 - 1387x^7 + 1440x^6 - 1097x^5 + 728x^4 - 576x^3 + 295x^2 + 138x - 151	\( -\,29^{3}\cdot 150503^{3} \)	16T1946	Trivial
16.6.275974035764908516131979.1	x^16 - 5x^15 + 10x^14 + 18x^13 - 128x^12 + 281x^11 - 250x^10 - 189x^9 + 1171x^8 - 3693x^7 + 7305x^6 - 11502x^5 + 13239x^4 - 17186x^3 + 12984x^2 - 1132x - 577	\( -\,89^{3}\cdot 731531^{3} \)	16T1946	Trivial (GRH)
16.2.321343496554700895669883.1	x^16 - x^15 + 18x^14 - 31x^13 + 119x^12 - 294x^11 + 382x^10 - 957x^9 + 491x^8 + 328x^7 - 1362x^6 + 5016x^5 - 6105x^4 - 5084x^3 - 5268x^2 - 22251x - 13093	\( -\,811^{3}\cdot 84457^{3} \)	16T1946	$[2]$
16.2.333784724014605235447531.1	x^16 - 2x^15 + 8x^14 - 20x^13 + 19x^12 - 63x^11 - 96x^10 + 197x^9 - 943x^8 + 1950x^7 - 4531x^6 + 5551x^5 - 12552x^4 + 8502x^3 - 17031x^2 + 7756x - 9103	\( -\,69367411^{3} \)	16T1946	Trivial
16.2.5196808802449754811990016.1	x^16 + 7x^14 + 79x^12 + 364x^10 + 3937x^8 + 29053x^6 + 81387x^4 - 4296211	\( -\,2^{16}\cdot 199^{3}\cdot 21589^{3} \)	16T1946	Trivial (GRH)
16.0.7443943506504247809229997.1	x^16 - 5x^15 + 36x^14 - 124x^13 + 599x^12 - 1573x^11 + 6120x^10 - 15786x^9 + 50041x^8 - 120034x^7 + 269934x^6 - 479333x^5 + 777872x^4 - 1087117x^3 + 1286409x^2 - 1034650x + 531977	\( 43^{5}\cdot 369959^{3} \)	16T1946	$[12]$ (GRH)
16.4.7443943506504247809229997.1	x^16 - 7x^15 + 28x^14 - 88x^13 + 117x^12 + 497x^11 - 3607x^10 + 17346x^9 - 59981x^8 + 160867x^7 - 401166x^6 + 739003x^5 - 1248979x^4 + 1654575x^3 - 1512872x^2 + 1442814x - 123467	\( 43^{5}\cdot 369959^{3} \)	16T1946	Trivial (GRH)
16.8.7443943506504247809229997.1	x^16 - 3x^15 - 18x^14 - 3x^13 + 325x^12 + 200x^11 - 3396x^10 + 3424x^9 + 9225x^8 - 18247x^7 + 5734x^6 - 54102x^5 + 133587x^4 + 9013x^3 - 401822x^2 + 430378x - 59089	\( 43^{5}\cdot 369959^{3} \)	16T1946	Trivial (GRH)
16.8.112920250769252553123463877.1	x^16 - 22x^14 - 73x^13 - 195x^12 - 40x^11 + 1596x^10 + 6787x^9 + 17235x^8 + 26339x^7 + 19409x^6 - 34363x^5 - 150370x^4 - 228323x^3 - 177186x^2 - 75737x - 15541	\( 483345053^{3} \)	16T1946	Trivial (GRH)
16.8.112920250769252553123463877.2	x^16 - 4x^15 + 6x^14 + 13x^13 - 224x^12 + 398x^11 - 655x^10 + 367x^9 + 7888x^8 - 4578x^7 + 28384x^6 - 17273x^5 - 37833x^4 - 26265x^3 - 39725x^2 + 3088x + 1793	\( 483345053^{3} \)	16T1946	Trivial (GRH)
16.0.263843310785431251717521408.1	x^16 + 25x^14 + 431x^12 + 6325x^10 + 53736x^8 + 393568x^6 + 3479773x^4 + 15908237x^2 + 15908237	\( 2^{16}\cdot 43^{3}\cdot 369959^{3} \)	16T1946	$[2]$ (GRH)
16.4.263843310785431251717521408.1	x^16 + 12x^14 - 337x^12 - 1058x^10 + 37670x^8 + 6641x^6 - 1636755x^4 + 15908237	\( 2^{16}\cdot 43^{3}\cdot 369959^{3} \)	16T1946	Trivial (GRH)
16.8.263843310785431251717521408.1	x^16 - 63x^14 + 1725x^12 - 27084x^10 + 268414x^8 - 1719270x^6 + 6919970x^4 - 15908237x^2 + 15908237	\( 2^{16}\cdot 43^{3}\cdot 369959^{3} \)	16T1946	Trivial (GRH)
16.12.353835993576955502001117637.1	x^16 - 5x^15 - 34x^14 + 164x^13 + 421x^12 - 1670x^11 - 3367x^10 + 7736x^9 + 17675x^8 - 29840x^7 - 29869x^6 + 108824x^5 + 19226x^4 - 244486x^3 - 190853x^2 - 21497x + 8227	\( 9973^{3}\cdot 70921^{3} \)	16T1946	Trivial (GRH)
16.4.353835993576955502001117637.1	x^16 - x^15 + 10x^14 + 88x^13 - 6x^12 + 882x^11 - 995x^10 - 336x^9 - 5317x^8 - 4602x^7 + 9056x^6 + 2803x^5 + 32858x^4 - 41771x^3 + 9976x^2 - 59682x + 96337	\( 9973^{3}\cdot 70921^{3} \)	16T1946	Trivial (GRH)
16.12.1249398643965236330510560517.1	x^16 - 5x^15 + 14x^14 - 72x^13 - 142x^12 + 1665x^11 - 1991x^10 - 202x^9 + 4677x^8 - 56356x^7 + 68947x^6 + 152641x^5 - 165890x^4 - 125115x^3 + 39402x^2 + 25446x + 2807	\( 11^{3}\cdot 97913143^{3} \)	16T1946	Trivial (GRH)
16.6.2185990337293840356281405659.1	x^16 - x^15 + 7x^14 + 9x^13 - 8x^12 + 159x^11 - 2272x^10 + 5336x^9 - 13011x^8 + 113846x^7 - 101199x^6 - 547626x^5 + 514569x^4 - 3453444x^3 + 4709935x^2 + 8557479x - 7643617	\( -\,89^{5}\cdot 731531^{3} \)	16T1946	Trivial (GRH)
16.10.18086234407889044513225375744.1	x^16 - 71x^14 + 1673x^12 - 7310x^10 - 303751x^8 + 5240903x^6 - 33340339x^4 + 86962434x^2 - 65106259	\( -\,2^{16}\cdot 89^{3}\cdot 731531^{3} \)	16T1946	Trivial (GRH)
16.10.18086234407889044513225375744.2	x^16 - 18x^14 - 394x^12 + 17728x^10 - 355651x^8 + 4045031x^6 - 23803474x^4 + 65106259x^2 - 65106259	\( -\,2^{16}\cdot 89^{3}\cdot 731531^{3} \)	16T1946	Trivial (GRH)
16.4.151177235919793595991777822557.1	x^16 + 29x^14 - 87x^13 - 4x^12 - 1606x^11 - 2796x^10 + 913x^9 - 29567x^8 + 76536x^7 - 184611x^6 + 264709x^5 + 953360x^4 - 1715142x^3 + 4376031x^2 - 1470532x + 4535759	\( 11^{5}\cdot 97913143^{3} \)	16T1946	Trivial (GRH)
16.0.7400341554413735321499328643072.1	x^16 + 141x^14 + 8167x^12 + 250588x^10 + 4377723x^8 + 43484289x^6 + 230965013x^4 + 567039862x^2 + 483345053	\( 2^{16}\cdot 483345053^{3} \)	16T1946	$[86004]$ (GRH)
16.16.7400341554413735321499328643072.1	x^16 - 141x^14 + 8167x^12 - 250588x^10 + 4377723x^8 - 43484289x^6 + 230965013x^4 - 567039862x^2 + 483345053	\( 2^{16}\cdot 483345053^{3} \)	16T1946	Trivial (GRH)
16.0.7400341554413735321499328643072.2	x^16 + 155x^14 + 9384x^12 + 284936x^10 + 4684188x^8 + 42761137x^6 + 212450356x^4 + 524089873x^2 + 483345053	\( 2^{16}\cdot 483345053^{3} \)	16T1946	$[115424]$ (GRH)
16.16.7400341554413735321499328643072.2	x^16 - 155x^14 + 9384x^12 - 284936x^10 + 4684188x^8 - 42761137x^6 + 212450356x^4 - 524089873x^2 + 483345053	\( 2^{16}\cdot 483345053^{3} \)	16T1946	Trivial (GRH)