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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2153671407156250000.1	x^16 - 2x^15 + x^14 + 5x^12 - 13x^11 + 5x^10 + 36x^9 - 72x^8 + 59x^7 + x^6 - 63x^5 + 89x^4 - 76x^3 + 42x^2 - 16x + 4	\( 2^{4}\cdot 5^{9}\cdot 29^{3}\cdot 41^{4} \)	16T1770	Trivial
16.0.2241019515056640625.1	x^16 - 7x^15 + 23x^14 - 43x^13 + 49x^12 - 32x^11 + 4x^10 + 13x^9 - 7x^8 - 12x^7 + 20x^6 - 10x^5 + 3x^4 - 7x^3 + 2x^2 + 3x + 1	\( 5^{9}\cdot 19^{6}\cdot 29^{3} \)	16T1770	Trivial
16.0.2241019515056640625.2	x^16 - x^15 - 3x^14 + 9x^13 - 5x^12 - 15x^11 + 35x^10 - 6x^9 - 17x^8 + 54x^7 + 19x^6 + 14x^5 + 38x^4 + 28x^3 + 35x^2 + 34x + 19	\( 5^{9}\cdot 19^{6}\cdot 29^{3} \)	16T1770	Trivial
16.0.34458742514500000000.1	x^16 - 2x^15 + 7x^14 - 3x^13 + 3x^12 + 18x^11 - 13x^10 + 12x^9 + 16x^8 - 24x^7 + 13x^6 - 10x^5 - 15x^4 + 11x^3 + x^2 + 5	\( 2^{8}\cdot 5^{9}\cdot 29^{3}\cdot 41^{4} \)	16T1770	Trivial
16.2.1093211783168000000000.1	x^16 + 8x^14 + 26x^12 + 44x^10 + 41x^8 + 20x^6 + 24x^4 + 40x^2 - 5	\( -\,2^{32}\cdot 5^{9}\cdot 19^{4} \)	16T1770	Trivial (GRH)
16.2.1093211783168000000000.2	x^16 - 4x^14 + 15x^12 - 40x^10 + 20x^8 - 24x^6 - 4x^4 - 30x^2 - 5	\( -\,2^{32}\cdot 5^{9}\cdot 19^{4} \)	16T1770	Trivial (GRH)
16.4.4045040224677236328125.1	x^16 - 4x^15 - 4x^14 + 39x^13 - 47x^12 - 79x^11 + 288x^10 - 203x^9 - 296x^8 + 409x^7 + 117x^6 - 316x^5 - 14x^4 + 170x^3 + 70x^2 + 15x + 5	\( 5^{10}\cdot 19^{8}\cdot 29^{3} \)	16T1770	Trivial (GRH)
16.4.4045040224677236328125.2	x^16 - 2x^15 - 2x^14 + 7x^13 - 2x^12 - 27x^11 + 25x^10 + 64x^9 - 111x^8 + 160x^7 - 249x^6 - 10x^5 + 261x^4 - 35x^3 - 84x^2 - 13x + 1	\( 5^{10}\cdot 19^{8}\cdot 29^{3} \)	16T1770	Trivial (GRH)
16.0.254271909520000000000000.1	x^16 + 17x^14 + 114x^12 + 403x^10 + 881x^8 + 1400x^6 + 1600x^4 + 970x^2 + 145	\( 2^{16}\cdot 5^{13}\cdot 19^{4}\cdot 29^{3} \)	16T1770	$[6]$ (GRH)
16.8.254271909520000000000000.1	x^16 - 8x^14 + 14x^12 - 17x^10 + 136x^8 - 355x^6 + 535x^4 - 650x^2 + 145	\( 2^{16}\cdot 5^{13}\cdot 19^{4}\cdot 29^{3} \)	16T1770	Trivial (GRH)
16.0.254271909520000000000000.2	x^16 + 8x^14 + 14x^12 + 17x^10 + 136x^8 + 355x^6 + 535x^4 + 650x^2 + 145	\( 2^{16}\cdot 5^{13}\cdot 19^{4}\cdot 29^{3} \)	16T1770	$[2]$ (GRH)
16.8.254271909520000000000000.2	x^16 - 4x^14 - 4x^12 + x^10 + 156x^8 - 405x^6 + 495x^4 - 480x^2 + 145	\( 2^{16}\cdot 5^{13}\cdot 19^{4}\cdot 29^{3} \)	16T1770	Trivial (GRH)
16.10.258035569111641280741376.1	x^16 - 8x^14 + 18x^12 + 36x^10 - 232x^8 + 404x^6 - 316x^4 + 112x^2 - 14	\( -\,2^{53}\cdot 7^{3}\cdot 17^{4} \)	16T1770	Trivial (GRH)
16.2.258035569111641280741376.1	x^16 + 8x^14 + 18x^12 - 36x^10 - 232x^8 - 404x^6 - 316x^4 - 112x^2 - 14	\( -\,2^{53}\cdot 7^{3}\cdot 17^{4} \)	16T1770	Trivial (GRH)
16.10.258035569111641280741376.2	x^16 - 12x^14 + 58x^12 - 144x^10 + 188x^8 - 100x^6 - 32x^4 + 56x^2 - 14	\( -\,2^{53}\cdot 7^{3}\cdot 17^{4} \)	16T1770	Trivial (GRH)
16.2.258035569111641280741376.2	x^16 + 12x^14 + 58x^12 + 144x^10 + 188x^8 + 100x^6 - 32x^4 - 56x^2 - 14	\( -\,2^{53}\cdot 7^{3}\cdot 17^{4} \)	16T1770	Trivial (GRH)
16.6.378245083474811464712192.1	x^16 - 6x^14 + 11x^12 + 2x^10 - 23x^8 + 8x^6 + 14x^4 - 4x^2 - 2	\( -\,2^{49}\cdot 7^{4}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.6.378245083474811464712192.2	x^16 + 6x^14 + 11x^12 - 2x^10 - 23x^8 - 8x^6 + 14x^4 + 4x^2 - 2	\( -\,2^{49}\cdot 7^{4}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.8.506789311061954423422976.1	x^16 - 2x^15 - 17x^14 + 20x^13 + 130x^12 - 96x^11 - 520x^10 + 344x^9 + 1135x^8 - 878x^7 - 1319x^6 + 1244x^5 + 692x^4 - 804x^3 - 118x^2 + 168x + 4	\( 2^{41}\cdot 7^{7}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.12.1013578622123908846845952.1	x^16 - 6x^14 - x^12 + 58x^10 - 62x^8 - 126x^6 + 203x^4 - 70x^2 + 7	\( 2^{42}\cdot 7^{7}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.6.1512980333899245858848768.1	x^16 - 4x^14 - 22x^12 + 64x^10 + 94x^8 - 192x^6 - 60x^4 + 48x^2 - 8	\( -\,2^{51}\cdot 7^{4}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.6.1512980333899245858848768.2	x^16 + 4x^14 - 22x^12 - 64x^10 + 94x^8 + 192x^6 - 60x^4 - 48x^2 - 8	\( -\,2^{51}\cdot 7^{4}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.0.2027157244247817693691904.1	x^16 + 8x^14 + 48x^12 + 340x^10 + 1261x^8 + 1988x^6 + 1442x^4 + 504x^2 + 56	\( 2^{43}\cdot 7^{7}\cdot 23^{4} \)	16T1770	$[2, 2]$ (GRH)
16.8.2027157244247817693691904.1	x^16 - 2x^14 - 19x^12 - 16x^10 + 232x^8 + 168x^6 - 252x^4 - 1792x^2 + 896	\( 2^{43}\cdot 7^{7}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.12.4054314488495635387383808.1	x^16 - 4x^15 - 2x^14 + 32x^13 - 43x^12 - 56x^11 + 118x^10 + 28x^9 + 125x^8 - 176x^7 - 456x^6 + 352x^5 + 294x^4 - 208x^3 - 32x^2 + 32x - 4	\( 2^{44}\cdot 7^{7}\cdot 23^{4} \)	16T1770	Trivial (GRH)
16.4.4054314488495635387383808.1	x^16 + 6x^14 - x^12 - 58x^10 - 62x^8 + 126x^6 + 203x^4 + 70x^2 + 7	\( 2^{44}\cdot 7^{7}\cdot 23^{4} \)	16T1770	$[2]$ (GRH)
16.0.8108628976991270774767616.1	x^16 + 2x^14 - 19x^12 + 16x^10 + 232x^8 - 168x^6 - 252x^4 + 1792x^2 + 896	\( 2^{45}\cdot 7^{7}\cdot 23^{4} \)	16T1770	$[2, 2]$ (GRH)
16.4.16217257953982541549535232.1	x^16 + 12x^14 - 28x^12 - 412x^10 - 671x^8 + 280x^6 + 1050x^4 + 504x^2 + 28	\( 2^{46}\cdot 7^{7}\cdot 23^{4} \)	16T1770	$[2]$ (GRH)
16.0.159956507000907392000000000.1	x^16 + 34x^14 + 465x^12 + 3338x^10 + 13636x^8 + 31798x^6 + 39404x^4 + 20610x^2 + 1145	\( 2^{16}\cdot 5^{9}\cdot 101^{4}\cdot 229^{3} \)	16T1770	$[2, 126]$ (GRH)
16.16.159956507000907392000000000.1	x^16 - 34x^14 + 465x^12 - 3338x^10 + 13636x^8 - 31798x^6 + 39404x^4 - 20610x^2 + 1145	\( 2^{16}\cdot 5^{9}\cdot 101^{4}\cdot 229^{3} \)	16T1770	Trivial (GRH)
16.0.3998912675022684800000000000.1	x^16 + 58x^14 + 1201x^12 + 11385x^10 + 56550x^8 + 153400x^6 + 219250x^4 + 143125x^2 + 28625	\( 2^{16}\cdot 5^{11}\cdot 101^{4}\cdot 229^{3} \)	16T1770	$[2, 2, 432]$ (GRH)
16.16.3998912675022684800000000000.1	x^16 - 58x^14 + 1201x^12 - 11385x^10 + 56550x^8 - 153400x^6 + 219250x^4 - 143125x^2 + 28625	\( 2^{16}\cdot 5^{11}\cdot 101^{4}\cdot 229^{3} \)	16T1770	Trivial (GRH)