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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.22378993818717495955548767565627.1	x^22 - 2x^21 + 3x^20 + 8x^19 - 22x^18 + 38x^17 - 4x^16 - 57x^15 + 146x^14 - 127x^13 + 42x^12 + 144x^11 - 154x^10 + 123x^9 - 19x^8 - 35x^7 + 41x^6 - 58x^5 + 35x^4 - 12x^3 + 7x^2 - 2x + 1	\( -\,3^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.0.22378993818717495955548767565627.2	x^22 - 2x^21 + x^20 - 10x^19 + 18x^18 + 2x^17 + 31x^16 - 76x^15 - 19x^14 - 8x^13 + 188x^12 - 50x^11 - 76x^10 - 135x^9 + 130x^8 + 29x^7 + 42x^6 - 76x^5 + 11x^4 - 8x^3 + 13x^2 - 4x + 1	\( -\,3^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.6.6168460699614248235671671923828125.1	x^22 - 2x^21 - x^20 - 18x^19 + 62x^18 - 94x^16 - 181x^15 + 176x^14 + 109x^13 - 688x^12 - 104x^11 + 486x^10 - 327x^9 - 459x^8 + 239x^7 + 157x^6 - 80x^5 - 7x^4 + 30x^3 + 13x^2 - 2x - 1	\( 5^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.6.6168460699614248235671671923828125.2	x^22 - 2x^21 + 5x^20 + 14x^19 - 14x^18 + 142x^17 - 5x^16 + 272x^15 + 173x^14 + 218x^13 + 72x^12 + 64x^11 - 24x^10 - 523x^9 - 90x^8 - 459x^7 + 102x^6 - 56x^5 + 85x^4 + 4x^3 + 7x^2 - 4x - 1	\( 5^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.0.174398723209634833558490883294218000698177947.1	x^22 + 20x^20 + 257x^18 - 4x^17 + 1934x^16 - 106x^15 + 10498x^14 - 1280x^13 + 38977x^12 - 9695x^11 + 107932x^10 - 38992x^9 + 209993x^8 - 108043x^7 + 304613x^6 - 168141x^5 + 295910x^4 - 171702x^3 + 186586x^2 - 69384x + 31329	\( -\,3^{11}\cdot 74843^{8} \)	22T13	$[2, 2, 2, 3580]$ (GRH)
22.0.174398723209634833558490883294218000698177947.2	x^22 - 4x^21 + 41x^20 - 62x^19 + 712x^18 - 691x^17 + 8218x^16 - 3289x^15 + 62044x^14 - 12972x^13 + 331973x^12 + 1202x^11 + 1201112x^10 + 23541x^9 + 2960817x^8 + 250587x^7 + 4248123x^6 - 781164x^5 + 3132885x^4 - 746848x^3 + 1635703x^2 - 490413x + 335241	\( -\,3^{11}\cdot 74843^{8} \)	22T13	$[2, 2, 2, 3580]$ (GRH)
22.22.48070600443250243342242248871561405585986328125.1	x^22 - 11x^21 + 4x^20 + 345x^19 - 924x^18 - 3703x^17 + 16135x^16 + 13322x^15 - 121744x^14 + 31850x^13 + 471182x^12 - 395648x^11 - 946985x^10 + 1246157x^9 + 844613x^8 - 1817353x^7 - 7200x^6 + 1206965x^5 - 429617x^4 - 256700x^3 + 164785x^2 - 10224x - 5249	\( 5^{11}\cdot 74843^{8} \)	22T13	Trivial (GRH)
22.22.48070600443250243342242248871561405585986328125.2	x^22 - 3x^21 - 74x^20 + 243x^19 + 2085x^18 - 7414x^17 - 29089x^16 + 114096x^15 + 212871x^14 - 975861x^13 - 758660x^12 + 4759643x^11 + 754889x^10 - 13086344x^9 + 2499505x^8 + 19735158x^7 - 7618260x^6 - 15249644x^5 + 7359840x^4 + 5211574x^3 - 2533933x^2 - 639053x + 247031	\( 5^{11}\cdot 74843^{8} \)	22T13	Trivial (GRH)