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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.59770508839234803.1	x^15 - 2x^12 + 3x^9 - 3x^6 + x^3 - 1	\( -\,3^{15}\cdot 1609^{3} \)	15T70	Trivial
15.1.59770508839234803.2	x^15 - x^9 - x^6 + x^3 + 1	\( -\,3^{15}\cdot 1609^{3} \)	15T70	Trivial
15.3.1317156265515729717.1	x^15 - 5x^12 + 9x^9 - 5x^6 - 2x^3 + 1	\( 3^{15}\cdot 13^{3}\cdot 347^{3} \)	15T70	Trivial
15.3.1317156265515729717.2	x^15 - x^9 - 2x^6 + 1	\( 3^{15}\cdot 13^{3}\cdot 347^{3} \)	15T70	Trivial
15.5.203788581389938989891.1	x^15 - 2x^12 - 3x^9 + 6x^6 - 1	\( -\,3^{15}\cdot 61^{3}\cdot 397^{3} \)	15T70	Trivial
15.5.203788581389938989891.2	x^15 - 5x^9 - x^6 + 3x^3 + 1	\( -\,3^{15}\cdot 61^{3}\cdot 397^{3} \)	15T70	Trivial
15.3.263347952037539318784.1	x^15 - 3x^13 - 2x^12 - 18x^11 - 24x^10 + 19x^9 + 54x^8 + 117x^7 + 224x^6 - 27x^5 - 714x^4 - 1064x^3 - 720x^2 - 240x - 32	\( 2^{10}\cdot 3^{15}\cdot 2617^{3} \)	15T70	Trivial
15.3.1060653771392183783424.1	x^15 - 3x^13 - 2x^12 + 18x^11 + 6x^10 - 84x^9 + 18x^8 + 177x^7 - 162x^6 - 396x^5 + 756x^4 - 663x^3 + 324x^2 - 84x + 8	\( 2^{12}\cdot 3^{15}\cdot 43^{3}\cdot 61^{3} \)	15T70	Trivial
15.9.31256653180970842100294052450870850335221875.1	x^15 - 4x^14 - 1264x^13 - 3539x^12 + 194086x^11 + 14315825x^10 + 207980393x^9 - 11155818269x^8 - 106782015292x^7 + 2695173632356x^6 + 60691267440950x^5 - 75831436048429x^4 - 19327557996736266x^3 + 33906382851120779x^2 + 414276426535790729x - 414601786688651713	\( -\,5^{5}\cdot 13^{3}\cdot 19^{6}\cdot 31^{10}\cdot 41^{4}\cdot 347^{3} \)	15T70	$[3]$ (GRH)
15.9.95997288591377091612527656182883144142091264.1	x^15 - 2055x^13 - 7672x^12 + 1689210x^11 + 12612768x^10 - 716487806x^9 - 7775771472x^8 + 170071858773x^7 + 2260733557600x^6 - 22989137783499x^5 - 325916709388536x^4 + 1930435159845344x^3 + 21988813850200512x^2 - 159305388838030848x + 215817165520608256	\( -\,2^{10}\cdot 3^{21}\cdot 137^{10}\cdot 1567^{3} \)	15T70	Trivial (GRH)
15.15.2029833056749933990877437692446176993120127718812297756397657810230365055931909199614663014853125.1	x^15 - 5x^14 - 350703120x^13 - 779807896785x^12 + 49200196895337165x^11 + 219030836843089675149x^10 - 3218288153233940153496245x^9 - 23053765882121416072139784690x^8 + 72017999183738288707629373330605x^7 + 1045698931780078435682650479628885030x^6 + 1741434416253074466115924536784589820944x^5 - 14342265880481731614912529111681563352984845x^4 - 78383192783129061050530216704529630578004400600x^3 - 160246170978138178880960112966590413992426168835000x^2 - 143899055360198090303599834796122108858596671245045000x - 42062243539779429694928280813246936486645620471338796875	\( 5^{5}\cdot 61^{11}\cdot 397^{3}\cdot 3449539^{10} \)	15T70	n/a