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 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.28937457747213411097802363989.1	x^20 - 4x^17 + 25x^16 - 31x^14 - 36x^13 + 184x^12 + 60x^11 - 157x^10 - 149x^9 + 445x^8 - 27x^7 - 180x^6 + 67x^5 + 156x^4 + 4x^3 - 3x^2 - 3x + 1	\( 11^{16}\cdot 229^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)
20.0.51516764471191285365957386177.1	x^20 + 9x^18 - 4x^17 + 53x^16 - 20x^15 + 151x^14 - 68x^13 + 368x^12 - 76x^11 + 496x^10 - 166x^9 + 634x^8 - 55x^7 + 277x^6 + 61x^5 + 175x^4 + x^3 + 12x^2 - 3x + 1	\( 11^{16}\cdot 257^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)
20.10.83409427467164005293746820523.1	x^20 - 4x^17 - 25x^16 - 31x^14 + 36x^13 + 184x^12 + 60x^11 + 157x^10 - 149x^9 - 361x^8 + 27x^7 - 180x^6 - 69x^5 + 154x^4 + 4x^3 + 3x^2 - 3x - 1	\( -\,11^{16}\cdot 283^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)
20.10.182567274194490055859030886811.1	x^20 - x^19 + 5x^18 + 2x^17 + 12x^16 - 3x^15 - 81x^14 + 94x^13 - 79x^12 - 271x^11 + 174x^10 + 348x^9 + 350x^8 - 334x^7 - 473x^6 + 234x^5 + 74x^4 - 49x^3 + 18x^2 + 3x - 1	\( -\,11^{16}\cdot 331^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)
20.20.1318976600112975820532265102854677.1	x^20 - 36x^18 - 4x^17 + 473x^16 + 80x^15 - 2859x^14 - 548x^13 + 8448x^12 + 1324x^11 - 12749x^10 - 1241x^9 + 9949x^8 + 445x^7 - 3988x^6 - 69x^5 + 780x^4 + 16x^3 - 63x^2 - 3x + 1	\( 11^{16}\cdot 19^{5}\cdot 103^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)
20.20.7588612227812438544203562395366777.1	x^20 - x^19 - 39x^18 + 28x^17 + 593x^16 - 302x^15 - 4531x^14 + 1664x^13 + 18779x^12 - 5250x^11 - 42734x^10 + 10050x^9 + 52063x^8 - 11604x^7 - 32303x^6 + 7629x^5 + 8990x^4 - 2522x^3 - 785x^2 + 296x - 23	\( 11^{16}\cdot 2777^{5} \)	$C_5\times S_4$ (as 20T34)	Trivial (GRH)