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 4 matches)

Label	Polynomial	Discriminant	Galois group	Class group
13.1.51185893014090757.1	x^13 - 13x^8 + 39x^7 - 78x^6 + 117x^5 - 130x^4 + 104x^3 - 65x^2 + 26x - 5	\( 13^{15} \)	$C_{13}:C_4$ (as 13T4)	Trivial
13.1.2097152000000000000.1	x^13 - 2x^12 + 8x^11 - 24x^10 + 50x^9 - 108x^8 + 196x^7 - 304x^6 + 367x^5 - 270x^4 + 136x^3 - 72x^2 + 18x - 4	\( 2^{33}\cdot 5^{12} \)	$C_{13}:C_4$ (as 13T4)	Trivial (GRH)
13.13.9109989259587930139892578125.1	x^13 - 130x^11 - 390x^10 + 3900x^9 + 21255x^8 + 10985x^7 - 119145x^6 - 213785x^5 + 106470x^4 + 499395x^3 + 197730x^2 - 296595x - 205335	\( 3^{6}\cdot 5^{12}\cdot 13^{15} \)	$C_{13}:C_4$ (as 13T4)	Trivial (GRH)
13.13.11623368434110587434575082172853.1	x^13 - 91x^11 - 26x^10 + 2951x^9 + 1339x^8 - 41431x^7 - 25922x^6 + 234988x^5 + 213772x^4 - 406770x^3 - 373113x^2 + 223587x + 170991	\( 13^{21}\cdot 19^{6} \)	$C_{13}:C_4$ (as 13T4)	Trivial (GRH)