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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.80157081600000000.1	x^16 - 2x^15 + x^14 - 3x^12 - 2x^11 + 19x^10 - 4x^9 - 37x^8 + 28x^7 + 19x^6 - 30x^5 + 6x^4 + 10x^3 - 6x^2 + 1	\( -\,2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151 \)	16T1577	Trivial
16.0.287365367070720000.1	x^16 - 4x^15 + 2x^14 + 10x^13 - 5x^12 - 32x^11 + 35x^10 + 24x^9 - 42x^8 - 8x^7 + 27x^6 - 4x^5 - 5x^4 - 4x^3 + 11x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{4}\cdot 4177 \)	16T1577	Trivial
16.4.403970457600000000.1	x^16 - 2x^14 - 2x^13 + x^12 + 10x^11 + x^10 - 14x^9 - 2x^8 + 6x^7 + 6x^6 - 6x^5 - 4x^4 + 4x^3 - x^2 + 2x - 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 761 \)	16T1577	Trivial
16.0.526614392658198528.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 156x^12 - 200x^11 + 156x^10 - 8x^9 - 176x^8 + 272x^7 - 200x^6 + 8x^5 + 152x^4 - 176x^3 + 104x^2 - 32x + 4	\( 2^{40}\cdot 3^{8}\cdot 73 \)	16T1577	Trivial
16.2.5424849633958428672.1	x^16 - 4x^15 + 8x^14 - 12x^13 + 24x^12 - 36x^11 + 40x^10 - 44x^9 + 38x^8 - 44x^7 + 40x^6 - 36x^5 + 24x^4 - 12x^3 + 8x^2 - 4x + 1	\( -\,2^{44}\cdot 3^{8}\cdot 47 \)	16T1577	Trivial
16.6.5424849633958428672.1	x^16 - 4x^15 + 20x^13 - 28x^12 + 20x^10 - 16x^9 + 54x^8 - 128x^7 + 136x^6 - 56x^5 - 36x^4 + 72x^3 - 48x^2 + 16x - 2	\( -\,2^{44}\cdot 3^{8}\cdot 47 \)	16T1577	Trivial
16.6.5802498457600000000.1	x^16 - 2x^15 - x^14 - 2x^13 + 6x^12 + 4x^11 + 5x^10 - 8x^9 - 7x^8 - 8x^7 + 5x^6 + 4x^5 + 6x^4 - 2x^3 - x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 31 \)	16T1577	Trivial
16.6.6492723609600000000.1	x^16 - 4x^15 + 6x^14 - 8x^13 + 16x^12 - 30x^11 + 18x^10 + 10x^9 - 9x^8 - 10x^7 - 3x^6 + 30x^5 - 4x^4 - 14x^3 - x^2 + 2x + 1	\( -\,2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 151 \)	16T1577	Trivial
16.4.7674272153600000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 + 2x^12 + 2x^11 - x^10 - 2x^9 + 5x^8 - 2x^7 - x^6 + 2x^5 + 2x^4 - 6x^3 + 6x^2 - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41 \)	16T1577	Trivial
16.6.13289593241600000000.1	x^16 - 6x^14 - 2x^13 - 6x^11 - 13x^10 - 10x^9 + x^8 - 10x^7 - 13x^6 - 6x^5 - 2x^3 - 6x^2 + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 71 \)	16T1577	Trivial
16.8.16658785894400000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 - 5x^12 + 50x^11 - 101x^10 + 62x^9 + 90x^8 - 174x^7 + 90x^6 - 6x^5 + 20x^4 - 28x^3 - 3x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 89 \)	16T1577	Trivial
16.4.22276510199020781568.1	x^16 - 4x^15 + 16x^13 + 4x^12 - 68x^11 + 20x^10 + 112x^9 - 12x^8 - 156x^7 + 16x^6 + 96x^5 - 4x^4 - 20x^3 - 4x^2 + 1	\( 2^{44}\cdot 3^{8}\cdot 193 \)	16T1577	Trivial
16.4.22276510199020781568.2	x^16 - 4x^15 + 12x^13 - 4x^12 - 20x^11 + 32x^10 - 12x^9 - 14x^8 + 44x^7 - 64x^6 + 44x^5 + 4x^4 - 20x^3 + 4x + 1	\( 2^{44}\cdot 3^{8}\cdot 193 \)	16T1577	Trivial
16.10.28263782809600000000.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 4x^11 + 2x^10 - 8x^9 + 7x^8 - 4x^7 + 13x^6 + 28x^5 - 25x^4 - 28x^3 + 3x^2 + 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 151 \)	16T1577	Trivial
16.4.32721607065600000000.1	x^16 - 6x^15 + 17x^14 - 28x^13 + 26x^12 - 12x^11 - 6x^10 - 12x^9 + 41x^8 - 56x^7 + 21x^6 + 36x^5 - 59x^4 + 36x^3 - 7x^2 - 2x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 761 \)	16T1577	Trivial
16.6.35750877593600000000.1	x^16 - 6x^14 - 12x^13 - 11x^12 + 4x^11 + 30x^10 + 56x^9 + 67x^8 + 56x^7 + 30x^6 + 4x^5 - 11x^4 - 12x^3 - 6x^2 + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 191 \)	16T1577	Trivial
16.6.35750877593600000000.2	x^16 - 4x^15 + 4x^14 + 8x^13 - 26x^12 + 32x^11 - 18x^10 - 26x^9 + 47x^8 + 136x^7 - 538x^6 + 738x^5 - 501x^4 + 162x^3 - 11x^2 - 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 191 \)	16T1577	Trivial
16.10.37248296550400000000.1	x^16 - 8x^14 - 2x^13 + 27x^12 - 6x^11 - 41x^10 + 58x^9 + 23x^8 - 96x^7 + 20x^6 + 42x^5 - 56x^4 - 8x^3 + 34x^2 + 12x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 199 \)	16T1577	Trivial
16.10.37248296550400000000.2	x^16 - 6x^15 + 9x^14 + 8x^13 - 17x^12 - 32x^11 + 31x^10 + 96x^9 - 63x^8 - 144x^7 + 52x^6 + 126x^5 + x^4 - 52x^3 - 14x^2 + 4x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 199 \)	16T1577	Trivial
16.8.49156463001600000000.1	x^16 - 2x^15 - 3x^14 + 16x^12 + 24x^11 - 92x^10 + 4x^9 + 159x^8 - 112x^7 - 71x^6 + 84x^5 + 27x^4 - 44x^3 + 3x^2 + 6x - 1	\( 2^{24}\cdot 3^{6}\cdot 5^{8}\cdot 10289 \)	16T1577	Trivial
16.4.142441978265600000000.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 197x^12 - 272x^11 + 205x^10 + 86x^9 - 511x^8 + 824x^7 - 821x^6 + 548x^5 - 232x^4 + 46x^3 + 7x^2 - 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 761 \)	16T1577	Trivial
16.0.2156660704281600000000.1	x^16 + 6x^14 - 12x^13 + 31x^12 - 60x^11 + 141x^10 - 246x^9 + 369x^8 - 564x^7 + 831x^6 - 882x^5 + 850x^4 - 1008x^3 + 1215x^2 - 792x + 241	\( 2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 11\cdot 14411 \)	16T1577	$[2]$
16.8.2156660704281600000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 99x^12 + 48x^11 + 211x^10 - 208x^9 - 198x^8 + 280x^7 + 61x^6 - 144x^5 + 22x^3 + 2x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 11\cdot 14411 \)	16T1577	Trivial
16.0.3981673503129600000000.1	x^16 - 6x^15 + 27x^14 - 74x^13 + 186x^12 - 332x^11 + 613x^10 - 822x^9 + 1378x^8 - 1410x^7 + 2080x^6 - 1562x^5 + 1824x^4 - 1124x^3 + 1857x^2 + 486x + 919	\( 2^{24}\cdot 3^{10}\cdot 5^{8}\cdot 10289 \)	16T1577	$[2]$
16.10.5349888360606400000000.1	x^16 - 8x^15 + 25x^14 - 35x^13 + 2x^12 + 79x^11 - 137x^10 + 80x^9 + 63x^8 - 149x^7 + 103x^6 - 2x^5 - 42x^4 + 25x^3 - x^2 - 4x + 1	\( -\,2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 4099 \)	16T1577	Trivial (GRH)
16.10.12266856094105600000000.1	x^16 - 2x^14 - 19x^12 + 32x^10 + 57x^8 - 124x^6 + 61x^4 - 6x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.14.12266856094105600000000.1	x^16 - 10x^14 + 33x^12 - 28x^10 - 63x^8 + 148x^6 - 105x^4 + 26x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.2.12266856094105600000000.1	x^16 + 10x^14 + 33x^12 + 28x^10 - 63x^8 - 148x^6 - 105x^4 - 26x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial
16.6.12266856094105600000000.1	x^16 - 2x^14 - 21x^12 - 8x^10 + 65x^8 + 56x^6 - 29x^4 - 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial
16.10.12266856094105600000000.2	x^16 + 2x^14 - 21x^12 + 8x^10 + 65x^8 - 56x^6 - 29x^4 + 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.14.12266856094105600000000.2	x^16 - 10x^14 + 35x^12 - 40x^10 - 41x^8 + 140x^6 - 115x^4 + 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial (GRH)
16.2.12266856094105600000000.2	x^16 + 10x^14 + 35x^12 + 40x^10 - 41x^8 - 140x^6 - 115x^4 - 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial
16.6.12266856094105600000000.2	x^16 + 10x^14 + 33x^12 + 32x^10 - 23x^8 - 32x^6 + 5x^4 + 6x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 13^{4} \)	16T1577	Trivial
16.12.12900451490201600000000.1	x^16 - 2x^15 - 13x^14 + 26x^13 + 54x^12 - 102x^11 - 141x^10 + 164x^9 + 574x^8 - 394x^7 - 1183x^6 + 550x^5 + 1048x^4 - 258x^3 - 360x^2 + 36x + 41	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{3} \)	16T1577	Trivial (GRH)
16.4.12900451490201600000000.1	x^16 - 2x^15 - x^14 + 16x^13 - 47x^12 + 100x^11 - 115x^10 + 80x^9 - 35x^8 + 56x^7 - 122x^6 + 66x^5 + 195x^4 - 320x^3 + 238x^2 - 80x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{3} \)	16T1577	Trivial
16.12.12900451490201600000000.2	x^16 - 8x^14 - 8x^13 - 3x^12 + 54x^11 + 146x^10 - 90x^9 - 322x^8 - 8x^7 + 53x^6 + 18x^5 + 335x^4 + 122x^3 - 188x^2 - 72x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{3} \)	16T1577	Trivial (GRH)
16.8.131954243069542400000000.1	x^16 - 6x^15 + 5x^14 + 38x^13 - 108x^12 + 132x^11 - 169x^10 - 114x^9 + 1662x^8 - 2822x^7 - 44x^6 + 3970x^5 - 3084x^4 - 132x^3 + 721x^2 + 198x + 41	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 89^{3} \)	16T1577	Trivial (GRH)
16.0.1638190924011929600000000.1	x^16 + 4x^14 + 4x^12 + 162x^10 + 762x^8 - 524x^6 + 1321x^4 + 1678x^2 + 521	\( 2^{32}\cdot 5^{8}\cdot 37^{4}\cdot 521 \)	16T1577	Trivial
16.12.1685503651243622400000000.1	x^16 - 8x^15 + 20x^14 - 80x^12 + 116x^11 + 22x^10 - 220x^9 + 204x^8 + 64x^7 - 240x^6 + 116x^5 + 55x^4 - 72x^3 + 18x^2 + 4x - 1	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 48449 \)	16T1577	Trivial (GRH)
16.4.4068285341243801600000000.1	x^16 - 2x^15 + 3x^14 - 8x^13 - 10x^12 - 74x^11 + 64x^10 - 918x^9 + 514x^8 - 3842x^7 - 867x^6 - 6550x^5 - 8713x^4 - 6242x^3 - 9620x^2 - 1664x + 2239	\( 2^{24}\cdot 5^{8}\cdot 13^{8}\cdot 761 \)	16T1577	$[2]$
16.0.5217669504670105600000000.1	x^16 + 19x^14 + 149x^12 + 625x^10 + 1518x^8 + 2151x^6 + 1685x^4 + 620x^2 + 61	\( 2^{28}\cdot 5^{8}\cdot 13^{8}\cdot 61 \)	16T1577	$[2, 32]$
16.16.5217669504670105600000000.1	x^16 - 19x^14 + 149x^12 - 625x^10 + 1518x^8 - 2151x^6 + 1685x^4 - 620x^2 + 61	\( 2^{28}\cdot 5^{8}\cdot 13^{8}\cdot 61 \)	16T1577	Trivial (GRH)
16.12.14357085207053807547265625.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 59x^12 + 172x^11 - 175x^10 - 82x^9 + 405x^8 - 380x^7 - 27x^6 + 394x^5 - 258x^4 - 92x^3 + 95x^2 + 6x - 9	\( 5^{8}\cdot 13^{8}\cdot 29\cdot 37^{4}\cdot 829 \)	16T1577	Trivial (GRH)
16.4.20027420219781061100000000.1	x^16 + 14x^14 + 67x^12 + 112x^10 - 54x^8 - 320x^6 - 154x^4 + 194x^2 + 131	\( 2^{8}\cdot 5^{8}\cdot 13^{8}\cdot 37^{4}\cdot 131 \)	16T1577	Trivial (GRH)
16.16.30921061301673774400000000.1	x^16 - 8x^15 + 9x^14 + 77x^13 - 180x^12 - 285x^11 + 973x^10 + 536x^9 - 2629x^8 - 697x^7 + 3981x^6 + 1006x^5 - 3250x^4 - 1219x^3 + 1065x^2 + 620x + 61	\( 2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 23691229 \)	16T1577	Trivial (GRH)
16.4.35647999157790310400000000.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 195x^12 - 260x^11 + 163x^10 + 186x^9 - 654x^8 + 928x^7 - 699x^6 + 106x^5 + 460x^4 - 614x^3 + 440x^2 - 180x + 41	\( 2^{24}\cdot 5^{8}\cdot 53^{4}\cdot 689369 \)	16T1577	Trivial (GRH)
16.8.73335106393502928118750000.1	x^16 - 5x^15 + x^14 + 23x^13 - 29x^12 + 2x^11 + 28x^10 - 38x^9 + 38x^8 - 38x^7 + 28x^6 + 2x^5 - 29x^4 + 23x^3 + x^2 - 5x + 1	\( 2^{4}\cdot 5^{8}\cdot 17^{8}\cdot 19\cdot 97^{4} \)	16T1577	Trivial (GRH)
16.8.73335106393502928118750000.2	x^16 - 3x^15 - 5x^14 + 52x^13 - 52x^12 - 321x^11 + 609x^10 + 960x^9 - 3079x^8 - 2049x^7 + 8891x^6 + 3750x^5 - 13564x^4 - 3016x^3 + 10182x^2 + 782x - 2909	\( 2^{4}\cdot 5^{8}\cdot 17^{8}\cdot 19\cdot 97^{4} \)	16T1577	Trivial (GRH)
16.0.83482712074721689600000000.1	x^16 + 24x^14 + 240x^12 + 1296x^10 + 4095x^8 + 7668x^6 + 8208x^4 + 4536x^2 + 976	\( 2^{32}\cdot 5^{8}\cdot 13^{8}\cdot 61 \)	16T1577	$[2, 102]$ (GRH)
16.0.57322337335634401689600000000.1	x^16 + 12x^14 - 24x^12 - 120x^10 + 4518x^8 - 4212x^6 + 3960x^4 + 3240x^2 + 981	\( 2^{48}\cdot 3^{14}\cdot 5^{8}\cdot 109 \)	16T1577	$[2, 4]$ (GRH)