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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.575328683712804296875.1	x^16 - 3x^15 - 7x^14 + 20x^13 + 36x^12 - 84x^11 - 123x^10 + 258x^9 + 426x^8 - 384x^7 - 1087x^6 - 232x^5 + 1016x^4 + 770x^3 - 273x^2 - 534x - 179	\( -\,5^{8}\cdot 19^{5}\cdot 29^{6} \)	16T1262	$[2]$
16.2.575328683712804296875.2	x^16 - 5x^15 + 14x^14 - 22x^13 - 3x^12 + 98x^11 - 284x^10 + 425x^9 - 297x^8 - 323x^7 + 1295x^6 - 2211x^5 + 2227x^4 - 1806x^3 + 456x^2 - 133x - 361	\( -\,5^{8}\cdot 19^{5}\cdot 29^{6} \)	16T1262	$[2]$
16.6.207693654820322351171875.1	x^16 - 3x^15 + 8x^14 - 42x^13 + 66x^12 - 11x^11 + 30x^10 + 127x^9 - 647x^8 + 831x^7 - 1245x^6 + 1580x^5 - 971x^4 + 1004x^3 - 170x^2 - 756x - 121	\( -\,5^{8}\cdot 19^{7}\cdot 29^{6} \)	16T1262	$[2]$
16.6.207693654820322351171875.2	x^16 - 5x^15 - x^14 + 41x^13 - 2x^12 - 211x^11 - 131x^10 + 595x^9 + 898x^8 - 372x^7 - 1745x^6 - 1133x^5 + 388x^4 + 758x^3 + 298x^2 + 33x - 1	\( -\,5^{8}\cdot 19^{7}\cdot 29^{6} \)	16T1262	$[2]$
16.0.2230808147575757441788280832.1	x^16 + 4x^12 + 60x^8 + 96x^4 + 162	\( 2^{75}\cdot 3^{10} \)	16T1262	Trivial (GRH)
16.0.2230808147575757441788280832.2	x^16 + 8x^12 + 240x^8 + 768x^4 + 2592	\( 2^{75}\cdot 3^{10} \)	16T1262	Trivial (GRH)
16.0.15875052080993898958961521972146601984.1	x^16 + 734x^14 + 172067x^12 + 18808958x^10 + 1052160156x^8 + 29212870230x^6 + 350532723051x^4 + 1798940113166x^2 + 3275329739569	\( 2^{40}\cdot 41^{6}\cdot 1249^{5} \)	16T1262	$[2, 2, 2, 2, 2569992]$ (GRH)
16.16.15875052080993898958961521972146601984.1	x^16 - 592x^14 + 139762x^12 - 16735612x^10 + 1070625863x^8 - 35507044188x^6 + 551265806762x^4 - 3283196824612x^2 + 3275329739569	\( 2^{40}\cdot 41^{6}\cdot 1249^{5} \)	16T1262	$[2]$ (GRH)
16.0.15875052080993898958961521972146601984.2	x^16 + 592x^14 + 139762x^12 + 16735612x^10 + 1070625863x^8 + 35507044188x^6 + 551265806762x^4 + 3283196824612x^2 + 3275329739569	\( 2^{40}\cdot 41^{6}\cdot 1249^{5} \)	16T1262	$[2, 2, 2, 2, 1918024]$ (GRH)
16.16.15875052080993898958961521972146601984.2	x^16 - 734x^14 + 172067x^12 - 18808958x^10 + 1052160156x^8 - 29212870230x^6 + 350532723051x^4 - 1798940113166x^2 + 3275329739569	\( 2^{40}\cdot 41^{6}\cdot 1249^{5} \)	16T1262	$[2]$ (GRH)
16.8.2355182957996385665344213110300455032987816125842857635730792102196757438299209990144.1	x^16 + 188252080x^14 - 1080028460485598x^12 - 1564271640991422128285156x^10 - 25860784484023364640720717188425x^8 + 3320365750251247350251659225492284179292x^6 + 12233549536667813425509652749327206454640589402x^4 - 462734523383447162851140406549194225919814502900297596x^2 + 485919715103617715396797698138138113212445995123402968178129	\( 2^{40}\cdot 41^{6}\cdot 1249^{5}\cdot 620622294839^{4} \)	16T1262	n/a