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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.7232231569547411163.1	x^15 - x^12 + 3x^9 + 5x^6 - 6x^3 + 11	\( -\,3^{15}\cdot 11^{2}\cdot 1609^{3} \)	15T83	Trivial
15.1.17273677054538858067.1	x^15 - 5x^12 + 4x^9 + 11x^6 - 5x^3 - 17	\( -\,3^{15}\cdot 17^{2}\cdot 1609^{3} \)	15T83	Trivial
15.3.380658160734045888213.1	x^15 - 10x^12 + 39x^9 - 72x^6 + 60x^3 - 17	\( 3^{15}\cdot 13^{3}\cdot 17^{2}\cdot 347^{3} \)	15T83	Trivial
15.3.475493411851178427837.1	x^15 - 5x^12 + 6x^9 - 14x^6 + 25x^3 + 19	\( 3^{15}\cdot 13^{3}\cdot 19^{2}\cdot 347^{3} \)	15T83	Trivial
15.5.5094714534748474747275.1	x^15 - 7x^12 + 15x^9 - 7x^6 - 8x^3 + 5	\( -\,3^{15}\cdot 5^{2}\cdot 61^{3}\cdot 397^{3} \)	15T83	Trivial
15.5.58894900021692368078499.1	x^15 - 12x^12 + 53x^9 - 104x^6 + 84x^3 - 17	\( -\,3^{15}\cdot 17^{2}\cdot 61^{3}\cdot 397^{3} \)	15T83	Trivial
15.3.83789646439334343994368.1	x^15 - 12x^13 - 14x^12 + 153x^11 - 18x^10 - 921x^9 + 396x^8 + 3903x^7 - 4268x^6 - 6255x^5 + 11628x^4 - 3132x^3 - 5328x^2 + 3552x - 1184	\( 2^{10}\cdot 3^{15}\cdot 37^{2}\cdot 1609^{3} \)	15T83	Trivial (GRH)
15.3.129360931662155595885674496.1	x^15 - 42x^13 - 6x^12 + 756x^11 + 366x^10 - 6915x^9 - 5940x^8 + 31182x^7 + 38392x^6 - 54639x^5 - 96852x^4 - 992x^3 + 55512x^2 - 8224	\( 2^{15}\cdot 3^{15}\cdot 257^{2}\cdot 1609^{3} \)	15T83	Trivial (GRH)
15.9.773560756544273759852688384.1	x^15 - 33x^13 - 40x^12 - 90x^11 + 54x^10 + 1791x^9 - 954x^8 + 6819x^7 + 25096x^6 - 2367x^5 - 52062x^4 - 63600x^3 - 29592x^2 + 6576x + 4384	\( -\,2^{10}\cdot 3^{21}\cdot 137^{2}\cdot 1567^{3} \)	15T83	Trivial (GRH)
15.9.2193046267403549887000547200000.1	x^15 - 2x^14 - 62x^13 + 277x^12 + 528x^11 - 6311x^10 - 4807x^9 + 35528x^8 + 482688x^7 + 926663x^6 - 6248483x^5 - 33152761x^4 + 2783240x^3 + 376105913x^2 + 110428690x - 1265140391	\( -\,2^{10}\cdot 5^{5}\cdot 13^{3}\cdot 19^{2}\cdot 31^{2}\cdot 347^{3}\cdot 4639^{2} \)	15T83	$[3]$ (GRH)
15.15.1103798189912877152281465916777600000.1	x^15 - 2x^14 - 393x^13 - 84x^12 + 55169x^11 + 82577x^10 - 3483491x^9 - 6928850x^8 + 107371802x^7 + 181291735x^6 - 1822041101x^5 - 1625667330x^4 + 16802789919x^3 - 1626100824x^2 - 65562916998x + 65199753925	\( 2^{10}\cdot 5^{5}\cdot 61^{3}\cdot 109^{2}\cdot 397^{3}\cdot 1429759^{2} \)	15T83	$[3]$ (GRH)
15.15.1435834106724053230466538641825103125.1	x^15 - 157x^13 - 322x^12 + 9363x^11 + 37099x^10 - 228980x^9 - 1521725x^8 + 698150x^7 + 24552875x^6 + 53553625x^5 - 77255625x^4 - 536596250x^3 - 999059375x^2 - 858165625x - 291503125	\( 5^{5}\cdot 61^{3}\cdot 397^{3}\cdot 5687830021^{2} \)	15T83	$[3]$ (GRH)