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 49 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.8067379209183488.1	x^16 - 3x^15 + 3x^14 + x^13 + x^12 - 18x^11 + 36x^10 - 33x^9 + 23x^8 - 42x^7 + 92x^6 - 129x^5 + 120x^4 - 76x^3 + 32x^2 - 8x + 1	\( 2^{8}\cdot 17^{3}\cdot 283^{4} \)	16T1851	Trivial
16.2.319040277384290048.2	x^16 - 6x^15 + 15x^14 - 23x^13 + 29x^12 - 34x^11 + 28x^10 - 14x^9 + x^8 + 40x^7 - 80x^6 + 58x^5 - 30x^4 + 29x^3 - 20x^2 + 6x - 1	\( -\,2^{8}\cdot 47^{3}\cdot 331^{4} \)	16T1851	Trivial
16.0.1231527208989986816.1	x^16 + 7x^14 + 23x^12 + 58x^10 + 113x^8 + 149x^6 + 154x^4 + 101x^2 + 41	\( 2^{12}\cdot 41^{3}\cdot 257^{4} \)	16T1851	Trivial
16.0.1231527208989986816.2	x^16 - 4x^14 + 3x^12 + 12x^10 - 19x^8 - 29x^6 + 106x^4 - 110x^2 + 41	\( 2^{12}\cdot 41^{3}\cdot 257^{4} \)	16T1851	Trivial
16.0.1400341099323392000.3	x^16 - 2x^12 + 4x^10 - 3x^8 - 5x^6 + 11x^4 - 10x^2 + 5	\( 2^{16}\cdot 5^{3}\cdot 643^{4} \)	16T1851	Trivial
16.4.2065249077550972928.1	x^16 - 2x^15 - 3x^14 + 6x^13 - 11x^12 + 8x^11 + 11x^10 + 2x^9 + 5x^8 + 8x^7 - 4x^6 - 20x^5 - 25x^4 - 18x^3 - 10x^2 - 2x + 1	\( 2^{16}\cdot 17^{3}\cdot 283^{4} \)	16T1851	Trivial
16.2.62545673362377736192.2	x^16 + 2x^14 + 3x^12 + 17x^10 + 76x^8 + 191x^6 + 150x^4 - 43	\( -\,2^{16}\cdot 43^{3}\cdot 331^{4} \)	16T1851	Trivial (GRH)
16.4.358487321426788352000.3	x^16 - 4x^15 + 6x^14 - 12x^13 + 24x^12 - 18x^11 - 20x^10 + 68x^9 - 30x^8 - 68x^7 + 64x^6 + 14x^5 - 43x^4 + 2x^3 + 18x^2 - 8x + 1	\( 2^{24}\cdot 5^{3}\cdot 643^{4} \)	16T1851	Trivial (GRH)
16.6.382774236666632394263.1	x^16 - 2x^15 - x^14 - 3x^13 + x^12 + 13x^11 + 13x^10 + 3x^9 - 31x^8 - 42x^7 + 8x^6 + 47x^5 + 23x^4 - 9x^3 - 14x^2 - 7x - 1	\( -\,23^{5}\cdot 2777^{4} \)	16T1851	Trivial
16.10.389849374503958585088.1	x^16 - x^15 - 14x^14 + 22x^13 + 48x^12 - 112x^11 - 5x^10 + 159x^9 - 116x^8 + 29x^7 - 24x^6 - 39x^5 + 143x^4 - 143x^3 + 66x^2 - 14x + 1	\( -\,2^{8}\cdot 19^{4}\cdot 47^{3}\cdot 103^{4} \)	16T1851	Trivial (GRH)
16.2.389849374503958585088.1	x^16 - 2x^15 + x^14 + 6x^13 - 8x^12 + 13x^11 - 26x^10 + 32x^9 - 23x^8 + 54x^7 - 23x^6 + 133x^5 + 103x^4 + 129x^3 - 8x^2 + 26x + 1	\( -\,2^{8}\cdot 19^{4}\cdot 47^{3}\cdot 103^{4} \)	16T1851	Trivial
16.2.389849374503958585088.2	x^16 + 6x^14 - 3x^12 - 43x^10 + 18x^8 + 183x^6 + 131x^4 - 47x^2 - 47	\( -\,2^{8}\cdot 19^{4}\cdot 47^{3}\cdot 103^{4} \)	16T1851	Trivial
16.4.567451821632222199808.2	x^16 + 8x^14 + 10x^12 - 41x^10 - 107x^8 + 15x^6 + 65x^4 - 37x^2 + 37	\( 2^{16}\cdot 37^{3}\cdot 643^{4} \)	16T1851	Trivial (GRH)
16.8.567451821632222199808.2	x^16 - 15x^14 + 89x^12 - 271x^10 + 472x^8 - 518x^6 + 391x^4 - 185x^2 + 37	\( 2^{16}\cdot 37^{3}\cdot 643^{4} \)	16T1851	Trivial (GRH)
16.0.567451821632222199808.3	x^16 + 15x^14 + 89x^12 + 271x^10 + 472x^8 + 518x^6 + 391x^4 + 185x^2 + 37	\( 2^{16}\cdot 37^{3}\cdot 643^{4} \)	16T1851	Trivial
16.4.567451821632222199808.3	x^16 - 8x^14 + 10x^12 + 41x^10 - 107x^8 - 15x^6 + 65x^4 + 37x^2 + 37	\( 2^{16}\cdot 37^{3}\cdot 643^{4} \)	16T1851	Trivial (GRH)
16.0.2057589115996741632000.1	x^16 + 8x^14 + 22x^12 + 20x^10 + x^8 + 31x^6 + 84x^4 + 55x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.4.2057589115996741632000.1	x^16 + 3x^14 - 4x^12 - 32x^10 - 43x^8 - 17x^6 + 39x^4 + 35x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.8.2057589115996741632000.1	x^16 - 7x^14 + 19x^12 - 40x^10 + 88x^8 - 128x^6 + 96x^4 - 35x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.0.2057589115996741632000.2	x^16 + 7x^14 + 19x^12 + 40x^10 + 88x^8 + 128x^6 + 96x^4 + 35x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.4.2057589115996741632000.2	x^16 - 2x^14 - 9x^12 + 28x^10 - 9x^8 - 29x^6 + x^4 + 5x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.8.2057589115996741632000.2	x^16 - 8x^14 + 22x^12 - 20x^10 + x^8 - 31x^6 + 84x^4 - 55x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{3}\cdot 1327^{4} \)	16T1851	Trivial (GRH)
16.0.2602260148834744991744.1	x^16 + 9x^14 + 30x^12 + 77x^10 + 275x^8 + 701x^6 + 929x^4 + 596x^2 + 149	\( 2^{16}\cdot 149^{3}\cdot 331^{4} \)	16T1851	Trivial (GRH)
16.8.2602260148834744991744.1	x^16 - 9x^14 + 30x^12 - 77x^10 + 275x^8 - 701x^6 + 929x^4 - 596x^2 + 149	\( 2^{16}\cdot 149^{3}\cdot 331^{4} \)	16T1851	Trivial (GRH)
16.10.2963786906212715098112.1	x^16 - 51x^10 + 73x^8 + 114x^6 - 251x^4 + 138x^2 - 23	\( -\,2^{12}\cdot 23^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.6.2963786906212715098112.1	x^16 - 16x^12 + 15x^10 + 99x^8 - 72x^6 - 143x^4 + 138x^2 - 23	\( -\,2^{12}\cdot 23^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.12.309876624380378846789632.1	x^16 - 14x^14 + 59x^12 + 9x^10 - 734x^8 + 2103x^6 - 2343x^4 + 860x^2 + 43	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.4.309876624380378846789632.1	x^16 + 14x^14 + 51x^12 - 30x^10 - 390x^8 - 289x^6 + 657x^4 + 731x^2 + 43	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.8.309876624380378846789632.1	x^16 + x^14 - 51x^12 - 20x^10 + 681x^8 - 183x^6 - 2280x^4 + 1204x^2 + 43	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.12.309876624380378846789632.2	x^16 - 14x^14 + 51x^12 + 30x^10 - 390x^8 + 289x^6 + 657x^4 - 731x^2 + 43	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.4.309876624380378846789632.2	x^16 + 14x^14 + 59x^12 - 9x^10 - 734x^8 - 2103x^6 - 2343x^4 - 860x^2 + 43	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.8.309876624380378846789632.2	x^16 - 2x^15 - 8x^14 + 24x^13 - 35x^12 - 8x^11 + 154x^10 - 132x^9 + 198x^8 - 174x^7 - 422x^6 + 1034x^5 - 563x^4 - 704x^3 + 997x^2 - 376x + 32	\( 2^{16}\cdot 43^{3}\cdot 2777^{4} \)	16T1851	Trivial (GRH)
16.6.861177268279244514459392.1	x^16 - 3x^15 - 8x^14 + 8x^13 + 62x^12 - 31x^11 - 441x^10 + 760x^9 + 1366x^8 - 2413x^7 + 298x^6 + 3368x^5 - 1982x^4 - 1441x^3 + 2375x^2 + 2168x - 4231	\( -\,2^{8}\cdot 19^{4}\cdot 47^{5}\cdot 103^{4} \)	16T1851	Trivial (GRH)
16.6.861177268279244514459392.2	x^16 - 6x^15 + 18x^14 - 10x^13 - 117x^12 + 425x^11 - 842x^10 + 822x^9 + 124x^8 - 1720x^7 + 3279x^6 - 3679x^5 + 2968x^4 - 1911x^3 + 404x^2 + 718x - 337	\( -\,2^{8}\cdot 19^{4}\cdot 47^{5}\cdot 103^{4} \)	16T1851	Trivial (GRH)
16.2.486999189920985889904844013568.1	x^16 - 12x^13 + 19x^12 + 70x^11 + 969x^10 - 2488x^9 + 4901x^8 - 1182x^7 + 7934x^6 - 664x^5 - 4937x^4 + 34400x^3 + 41639x^2 + 61340x + 16941	\( -\,2^{16}\cdot 19^{4}\cdot 47^{7}\cdot 103^{4} \)	16T1851	$[8]$ (GRH)
16.2.486999189920985889904844013568.2	x^16 - 2x^15 - 27x^14 + 58x^13 + 148x^12 - 184x^11 - 197x^10 - 686x^9 - 3631x^8 + 13670x^7 - 4698x^6 - 56764x^5 + 19758x^4 - 35174x^3 - 399478x^2 + 326768x - 486121	\( -\,2^{16}\cdot 19^{4}\cdot 47^{7}\cdot 103^{4} \)	16T1851	$[8]$ (GRH)
16.0.9558738202625098335096647974912.1	x^16 - 4x^15 + 125x^14 - 242x^13 + 6009x^12 - 2806x^11 + 152163x^10 + 77764x^9 + 2270754x^8 + 2268820x^7 + 20419650x^6 + 23613418x^5 + 108544365x^4 + 144136500x^3 + 338502596x^2 + 272619382x + 291449783	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2, 2, 2, 8750]$ (GRH)
16.12.9558738202625098335096647974912.1	x^16 - 4x^15 - 33x^14 + 36x^13 - 884x^12 + 1210x^11 + 23694x^10 + 11150x^9 + 424406x^8 + 137390x^7 - 9744704x^6 - 388076x^5 + 60431975x^4 - 23851486x^3 - 124550684x^2 + 95251700x + 9929702	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	Trivial (GRH)
16.16.9558738202625098335096647974912.1	x^16 - 4x^15 - 135x^14 + 304x^13 + 7374x^12 - 5946x^11 - 200122x^10 - 48966x^9 + 2748932x^8 + 2601138x^7 - 17524028x^6 - 23731020x^5 + 40126595x^4 + 53871346x^3 - 38914636x^2 - 32002336x + 13923454	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	Trivial (GRH)
16.4.9558738202625098335096647974912.1	x^16 - 8x^15 + 68x^14 - 314x^13 + 350x^12 - 688x^11 - 24472x^10 + 96314x^9 - 493772x^8 + 1212420x^7 - 2940785x^6 + 3210556x^5 - 532257x^4 - 11926574x^3 + 44670558x^2 - 47608916x + 127676806	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2, 4]$ (GRH)
16.8.9558738202625098335096647974912.1	x^16 + 64x^14 - 660x^12 - 80233x^10 - 306573x^8 + 13200410x^6 + 34332051x^4 - 586188599x^2 + 331604347	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2]$ (GRH)
16.0.9558738202625098335096647974912.2	x^16 + 126x^14 + 6340x^12 + 165147x^10 + 2439631x^8 + 21187266x^6 + 107133883x^4 + 291959895x^2 + 331604347	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2, 2, 2, 8736]$ (GRH)
16.12.9558738202625098335096647974912.2	x^16 - 8x^15 - 30x^14 + 328x^13 - 487x^12 - 3066x^11 + 15756x^10 + 4348x^9 + 37618x^8 - 671848x^7 - 2244869x^6 + 11266314x^5 + 14512803x^4 - 58604724x^3 - 31353063x^2 + 94541772x + 4936909	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	Trivial (GRH)
16.16.9558738202625098335096647974912.2	x^16 - 126x^14 + 6340x^12 - 165147x^10 + 2439631x^8 - 21187266x^6 + 107133883x^4 - 291959895x^2 + 331604347	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	Trivial (GRH)
16.4.9558738202625098335096647974912.2	x^16 - 4x^15 + 58x^14 - 64x^13 + 453x^12 + 480x^11 - 17804x^10 - 57284x^9 - 674365x^8 - 2238350x^7 - 10359495x^6 - 27435284x^5 - 69777623x^4 - 112360206x^3 - 124062282x^2 - 35452296x + 177574518	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2, 2]$ (GRH)
16.8.9558738202625098335096647974912.2	x^16 - 15x^14 - 1968x^12 + 43315x^10 + 355421x^8 - 8765459x^6 - 5762275x^4 + 175653581x^2 + 331604347	\( 2^{18}\cdot 43^{3}\cdot 2777^{6} \)	16T1851	$[2]$ (GRH)
16.8.4418526734163451705398425526403072.1	x^16 - 2x^15 - 229x^14 + 762x^13 + 9237x^12 - 49786x^11 + 477071x^10 - 2101004x^9 - 3133551x^8 + 22939648x^7 - 192051301x^6 + 441290118x^5 - 234692115x^4 + 4703434420x^3 + 5421674073x^2 + 22716955742x + 46303919009	\( 2^{16}\cdot 43^{5}\cdot 2777^{6} \)	16T1851	Trivial (GRH)
16.0.1008059438600408027895860714799583101155540992.1	x^16 + 251x^14 + 29216x^12 + 1553004x^10 - 384112x^8 - 6482672352x^6 - 126783269440x^4 + 10760419375552x^2 + 730449208214272	\( 2^{20}\cdot 43^{7}\cdot 2777^{8} \)	16T1851	$[2, 4, 213576]$ (GRH)
16.0.1008059438600408027895860714799583101155540992.2	x^16 + 141x^14 + 43354x^12 - 633300x^10 + 100756291x^8 - 196269501x^6 + 125165260291x^4 - 486137024499x^2 + 18913214532748	\( 2^{20}\cdot 43^{7}\cdot 2777^{8} \)	16T1851	$[2, 4, 213576]$ (GRH)