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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
5.1.2064609765625.4	x^5 - 110x^3 - 1045x^2 - 4290x - 7524	\( 5^{8}\cdot 11^{4}\cdot 19^{2} \)	$D_{5}$ (as 5T2)	$[5, 15, 15]$
5.1.432682531250000.12	x^5 - 76250	\( 2^{4}\cdot 5^{9}\cdot 61^{4} \)	$F_5$ (as 5T3)	$[5, 420]$ (GRH)
5.5.650892809785201.1	x^5 - x^4 - 2020x^3 + 55965x^2 - 558681x + 1920311	\( 5051^{4} \)	$C_5$ (as 5T1)	$[1451]$
5.1.676063548050000.4	x^5 - 1364	\( 2^{4}\cdot 5^{5}\cdot 11^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 5, 110]$
5.1.744104843042000.1	x^5 - 3124	\( 2^{4}\cdot 5^{3}\cdot 11^{4}\cdot 71^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$
5.1.2435646308550125.1	x^5 - 2101	\( 5^{3}\cdot 11^{4}\cdot 191^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$
5.1.3422571712003125.2	x^5 - 1023	\( 3^{4}\cdot 5^{5}\cdot 11^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$
5.1.8623546686722000.1	x^5 - 2882	\( 2^{4}\cdot 5^{3}\cdot 11^{4}\cdot 131^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$ (GRH)
5.1.10135847904050000.3	x^5 - 1786202	\( 2^{4}\cdot 5^{5}\cdot 11^{4}\cdot 61^{4} \)	$F_5$ (as 5T3)	$[5, 5, 195]$ (GRH)
5.1.10138506751500125.1	x^5 - 3001	\( 5^{3}\cdot 3001^{4} \)	$F_5$ (as 5T3)	$[5, 35, 35]$ (GRH)
5.1.11936195069922000.1	x^5 - 3126	\( 2^{4}\cdot 3^{4}\cdot 5^{3}\cdot 521^{4} \)	$F_5$ (as 5T3)	$[5, 5, 90]$ (GRH)
5.1.13962972767250125.1	x^5 - 3251	\( 5^{3}\cdot 3251^{4} \)	$F_5$ (as 5T3)	$[5, 5, 50]$ (GRH)
5.5.38207880152026321.15	x^5 - x^4 - 5592x^3 + 261165x^2 - 4479065x + 26832541	\( 11^{4}\cdot 31^{4}\cdot 41^{4} \)	$C_5$ (as 5T1)	$[5, 5, 55]$ (GRH)
5.1.41938969540050000.1	x^5 - 7656	\( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 11^{4}\cdot 29^{4} \)	$F_5$ (as 5T3)	$[5, 10, 140]$ (GRH)
5.1.54761147392050000.1	x^5 - 8184	\( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 11^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 15]$ (GRH)
5.1.422539717531250000.31	x^5 - 27280	\( 2^{4}\cdot 5^{9}\cdot 11^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$ (GRH)
5.1.950441719585442000.1	x^5 - 227744482	\( 2^{4}\cdot 5^{3}\cdot 7^{4}\cdot 23^{4}\cdot 29^{4} \)	$F_5$ (as 5T3)	$[5, 1740]$ (GRH)
5.1.1275759485158203125.1	x^5 - 4495	\( 5^{9}\cdot 29^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 5, 100]$ (GRH)
5.1.2975680334064453125.2	x^5 - 3360775	\( 5^{9}\cdot 11^{4}\cdot 101^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 10]$ (GRH)
5.1.3097498441215753125.1	x^5 - 5611	\( 5^{5}\cdot 31^{4}\cdot 181^{4} \)	$F_5$ (as 5T3)	$[5, 5, 10, 10]$ (GRH)
5.1.11396136895032753125.1	x^5 - 7771	\( 5^{5}\cdot 19^{4}\cdot 409^{4} \)	$F_5$ (as 5T3)	$[10, 110]$ (GRH)
5.1.250897373738476003125.1	x^5 - 13539741381	\( 3^{4}\cdot 5^{5}\cdot 31^{4}\cdot 181^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5, 20]$ (GRH)