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 58)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.23642137600000000.1	x^16 - x^14 + x^12 + 3x^10 - 4x^8 + 3x^6 + x^4 - x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 31^{4} \)	16T1116	Trivial
16.0.80265618516015625.1	x^16 - x^15 - 3x^14 + 4x^13 + 6x^12 - 8x^11 - 4x^10 + 18x^9 + 2x^8 - 21x^7 + 15x^6 + 21x^5 - 22x^4 + 2x^3 + 14x^2 - 6x + 1	\( 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{4} \)	16T1116	Trivial
16.4.80265618516015625.1	x^16 - 5x^15 + 12x^14 - 21x^13 + 29x^12 - 31x^11 + 28x^10 - 17x^9 - 11x^8 + 54x^7 - 90x^6 + 92x^5 - 63x^4 + 26x^3 - 3x^2 - 3x + 1	\( 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 29^{4} \)	16T1116	Trivial
16.0.115549174227861504.1	x^16 - 3x^14 + 2x^12 + 4x^10 - 9x^8 + 4x^6 + 6x^4 - 5x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{2} \)	16T1116	Trivial
16.0.115549174227861504.2	x^16 - 3x^14 + 5x^12 - 7x^10 + 6x^8 - 7x^6 + 9x^4 - 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{2} \)	16T1116	Trivial
16.0.378274201600000000.1	x^16 - 5x^14 + 16x^12 - 33x^10 + 56x^8 - 69x^6 + 67x^4 - 48x^2 + 16	\( 2^{20}\cdot 5^{8}\cdot 31^{4} \)	16T1116	Trivial
16.4.378274201600000000.1	x^16 - 5x^14 + 5x^12 - 15x^10 + 12x^8 - 15x^6 + 5x^4 - 5x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 31^{4} \)	16T1116	Trivial
16.0.1451882331504640000.1	x^16 - 6x^15 + 21x^14 - 50x^13 + 100x^12 - 164x^11 + 233x^10 - 284x^9 + 305x^8 - 284x^7 + 233x^6 - 164x^5 + 100x^4 - 50x^3 + 21x^2 - 6x + 1	\( 2^{24}\cdot 5^{4}\cdot 7^{2}\cdot 41^{4} \)	16T1116	Trivial
16.0.1451882331504640000.2	x^16 - 4x^15 + 8x^14 - 10x^13 + 12x^12 - 16x^11 + 19x^10 - 18x^9 + 17x^8 - 12x^7 + 10x^6 - 16x^5 + 16x^4 - 16x^3 + 16	\( 2^{24}\cdot 5^{4}\cdot 7^{2}\cdot 41^{4} \)	16T1116	Trivial
16.4.1606201369600000000.1	x^16 + x^14 + x^12 - 10x^6 - 9x^4 - x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.0.2190873625600000000.1	x^16 + 6x^14 + 18x^12 + 32x^10 + 41x^8 + 41x^6 + 29x^4 + 10x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{4} \)	16T1116	Trivial
16.4.2190873625600000000.1	x^16 - 3x^14 + 2x^12 + x^10 + 6x^8 - 8x^6 + 6x^4 - 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{4} \)	16T1116	Trivial
16.4.2885780971334926336.1	x^16 - 4x^15 + 4x^14 + 4x^13 - 33x^12 + 128x^11 - 288x^10 + 424x^9 - 473x^8 + 424x^7 - 288x^6 + 128x^5 - 33x^4 + 4x^3 + 4x^2 - 4x + 1	\( 2^{32}\cdot 7^{4}\cdot 23^{4} \)	16T1116	Trivial
16.4.3507463262499241984.1	x^16 - 2x^14 - 11x^12 + 26x^10 - 4x^8 - 58x^6 + 37x^4 - 6x^2 + 1	\( 2^{32}\cdot 17^{2}\cdot 41^{4} \)	16T1116	Trivial
16.4.3507463262499241984.2	x^16 + 2x^14 - 11x^12 - 26x^10 - 4x^8 + 58x^6 + 37x^4 + 6x^2 + 1	\( 2^{32}\cdot 17^{2}\cdot 41^{4} \)	16T1116	Trivial
16.8.11383787432672265625.1	x^16 - 4x^15 + 3x^14 + x^13 - 14x^12 + 32x^11 + 15x^10 + x^9 + 51x^8 + x^7 + 15x^6 + 32x^5 - 14x^4 + x^3 + 3x^2 - 4x + 1	\( 5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131^{2} \)	16T1116	Trivial
16.8.21254468453484765625.1	x^16 - 6x^15 + 9x^14 + 10x^13 - 47x^12 + 68x^11 - 43x^10 - 7x^9 + 32x^8 - 33x^7 + 33x^6 - 49x^5 + 61x^4 - 20x^3 - 16x^2 + 7x + 1	\( 5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 179^{2} \)	16T1116	Trivial
16.0.22720094233600000000.1	x^16 + 9x^14 + 16x^12 - 14x^10 - 17x^8 + 98x^6 + 154x^4 + 63x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 31^{6} \)	16T1116	Trivial
16.0.25699221913600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 79x^12 - 110x^11 + 163x^10 - 188x^9 + 161x^8 - 154x^7 + 159x^6 - 100x^5 + 47x^4 - 44x^3 + 22x^2 + 4	\( 2^{20}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.4.25699221913600000000.1	x^16 - 8x^14 + 7x^12 - 12x^10 + 8x^8 - 12x^6 + 7x^4 - 8x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.4.25699221913600000000.2	x^16 + x^14 - 11x^12 + 11x^10 - 20x^8 + 11x^6 - 11x^4 + x^2 + 1	\( 2^{20}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.0.30436847641600000000.1	x^16 + 5x^14 + 8x^12 + 5x^10 + 3x^8 + 5x^6 + 8x^4 + 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 41^{2} \)	16T1116	$[2]$
16.8.30436847641600000000.1	x^16 - 5x^14 + 8x^12 - 5x^10 + 3x^8 - 5x^6 + 8x^4 - 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 41^{2} \)	16T1116	Trivial
16.0.31937869849600000000.1	x^16 - 2x^15 + 13x^14 - 30x^13 + 79x^12 - 174x^11 + 310x^10 - 500x^9 + 675x^8 - 760x^7 + 710x^6 - 522x^5 + 294x^4 - 120x^3 + 32x^2 - 6x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 13^{4}\cdot 19^{2} \)	16T1116	$[2]$
16.4.71142234243727360000.1	x^16 + 10x^14 + 19x^12 - 52x^10 - 131x^8 - 52x^6 + 19x^4 + 10x^2 + 1	\( 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{4} \)	16T1116	Trivial
16.0.361206749593600000000.1	x^16 + 2x^14 + 12x^12 + 10x^10 + 50x^8 - 46x^6 + 20x^4 - 6x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 29^{2} \)	16T1116	Trivial
16.8.361206749593600000000.1	x^16 - 6x^14 + 12x^12 - 4x^10 - 17x^8 + 4x^6 + 38x^4 - 30x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 29^{2} \)	16T1116	Trivial
16.0.361206749593600000000.2	x^16 + 6x^14 + 16x^12 + 22x^10 + 26x^8 + 22x^6 + 16x^4 + 6x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 29^{2} \)	16T1116	Trivial
16.8.361206749593600000000.2	x^16 - 6x^14 + 16x^12 - 40x^10 + 55x^8 - 60x^6 + 46x^4 - 14x^2 + 1	\( 2^{40}\cdot 5^{8}\cdot 29^{2} \)	16T1116	Trivial
16.0.401980044313600000000.1	x^16 + 7x^14 + 19x^12 + 30x^10 + 35x^8 + 30x^6 + 19x^4 + 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{2} \)	16T1116	$[3]$
16.8.401980044313600000000.1	x^16 - 7x^14 + 19x^12 - 30x^10 + 35x^8 - 30x^6 + 19x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{2} \)	16T1116	Trivial
16.0.411187550617600000000.1	x^16 + 2x^14 - 4x^12 + 8x^10 + 32x^6 - 64x^4 + 128x^2 + 256	\( 2^{24}\cdot 5^{8}\cdot 89^{4} \)	16T1116	$[2]$
16.12.411187550617600000000.1	x^16 - 15x^14 + 85x^12 - 235x^10 + 352x^8 - 285x^6 + 115x^4 - 20x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial (GRH)
16.8.411187550617600000000.1	x^16 - 5x^14 - 25x^12 + 25x^10 + 72x^8 + 25x^6 - 25x^4 - 5x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.8.411187550617600000000.2	x^16 - 7x^14 + 30x^12 - 88x^10 + 185x^8 - 320x^6 + 318x^4 - 119x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial
16.0.556300790782570266624.1	x^16 - 2x^14 + 21x^12 - 26x^10 + 68x^8 - 46x^6 + 53x^4 - 6x^2 + 1	\( 2^{28}\cdot 3^{4}\cdot 17^{2}\cdot 97^{4} \)	16T1116	$[3]$
16.0.579838694425600000000.1	x^16 + 3x^14 + 27x^12 + 146x^10 + 280x^8 + 268x^6 + 165x^4 + 53x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	$[2]$
16.8.2737511958932953515625.1	x^16 - 6x^15 + 6x^14 + 32x^13 - 114x^12 + 161x^11 - 15x^10 - 403x^9 + 444x^8 + 637x^7 - 483x^6 - 701x^5 + 86x^4 + 255x^3 + 59x^2 + 9x + 1	\( 5^{8}\cdot 13^{4}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1116	Trivial
16.8.2737511958932953515625.2	x^16 - x^15 - 14x^14 + 18x^13 + 74x^12 - 72x^11 - 281x^10 - 122x^9 + 248x^8 + 405x^7 + 342x^6 - 230x^5 - 414x^4 + 96x^3 + 53x^2 + 5x + 1	\( 5^{8}\cdot 13^{4}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1116	Trivial
16.12.6579000809881600000000.1	x^16 - 16x^14 + 107x^12 - 388x^10 + 821x^8 - 1000x^6 + 636x^4 - 176x^2 + 16	\( 2^{28}\cdot 5^{8}\cdot 89^{4} \)	16T1116	Trivial (GRH)
16.0.8718704856053531541504.1	x^16 - 6x^15 + 13x^14 - 2x^13 - 24x^12 + 2x^11 + 99x^10 - 150x^9 + 192x^8 - 274x^7 + 267x^6 - 222x^5 + 219x^4 - 248x^3 + 210x^2 - 104x + 28	\( 2^{28}\cdot 3^{4}\cdot 17^{2}\cdot 193^{4} \)	16T1116	$[5]$
16.0.9277419110809600000000.1	x^16 - 4x^15 + 12x^14 - 20x^13 + 32x^12 - 52x^11 + 34x^10 + 18x^8 - 576x^7 + 1524x^6 - 1300x^5 + 1117x^4 - 752x^3 + 302x^2 - 56x + 4	\( 2^{20}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	$[2]$
16.0.9277419110809600000000.2	x^16 - 4x^15 + 4x^14 + 8x^13 + 29x^12 - 82x^11 + 91x^10 + 82x^9 + 281x^8 - 380x^7 + 112x^6 + 292x^5 + 505x^4 - 600x^3 + 360x^2 - 96x + 16	\( 2^{20}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	$[4]$
16.0.148438705772953600000000.1	x^16 + 9x^14 + 38x^12 + 117x^10 + 190x^8 + 99x^6 + 10x^4 + 31x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	$[2, 2]$
16.8.148438705772953600000000.1	x^16 - 4x^15 - 9x^14 + 88x^13 - 175x^12 - 220x^11 + 1554x^10 - 2616x^9 + 1304x^8 + 1348x^7 - 1774x^6 + 520x^5 + 205x^4 - 204x^3 + 69x^2 - 12x + 1	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	Trivial (GRH)
16.8.148438705772953600000000.2	x^16 - 9x^14 + 38x^12 - 117x^10 + 190x^8 - 99x^6 + 10x^4 - 31x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 19^{2}\cdot 89^{4} \)	16T1116	Trivial (GRH)
16.4.468647734710831677440000.1	x^16 - 4x^15 + 2x^14 + 29x^12 - 56x^11 - 350x^10 + 1132x^9 + 383x^8 - 5540x^7 + 3754x^6 + 11700x^5 - 12691x^4 - 10276x^3 + 13194x^2 + 9400x + 2209	\( 2^{24}\cdot 5^{4}\cdot 41^{6}\cdot 97^{2} \)	16T1116	$[2]$
16.4.468647734710831677440000.2	x^16 - 4x^15 + 10x^14 - 26x^13 + 16x^12 - 116x^11 + 113x^10 + 98x^9 + 65x^8 - 1372x^7 - 3822x^6 - 3936x^5 - 2484x^4 + 2384x^3 + 1480x^2 + 256x + 16	\( 2^{24}\cdot 5^{4}\cdot 41^{6}\cdot 97^{2} \)	16T1116	$[2]$
16.8.561194121999878717440000.1	x^16 - 6x^14 + 39x^12 - 84x^10 + 34x^8 - 10x^6 + 36x^4 - 12x^2 + 1	\( 2^{40}\cdot 5^{4}\cdot 17^{2}\cdot 41^{4} \)	16T1116	Trivial
16.8.561194121999878717440000.2	x^16 - 12x^14 + 64x^12 - 194x^10 + 354x^8 - 392x^6 + 251x^4 - 74x^2 + 1	\( 2^{40}\cdot 5^{4}\cdot 17^{2}\cdot 41^{4} \)	16T1116	Trivial (GRH)