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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.26180786556913794244673536.5	x^20 - 6x^18 + 14x^16 - 6x^14 - 28x^12 + 18x^10 + 71x^8 - 106x^6 + 38x^4 + 4x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T313	Trivial (GRH)
20.4.26180786556913794244673536.6	x^20 + 4x^18 + 3x^16 - 4x^14 + 21x^12 + 34x^10 - 57x^8 - 60x^6 + 34x^4 + 10x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T313	Trivial (GRH)
20.0.26180786556913794244673536.7	x^20 - 4x^18 + 3x^16 + 4x^14 + 21x^12 - 34x^10 - 57x^8 + 60x^6 + 34x^4 - 10x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T313	Trivial (GRH)
20.0.26180786556913794244673536.8	x^20 + 6x^18 + 19x^16 + 48x^14 + 81x^12 + 114x^10 + 100x^8 + 70x^6 + 43x^4 + 20x^2 + 1	\( 2^{40}\cdot 47^{8} \)	20T313	Trivial (GRH)
20.16.271489728101173730019304802954487841.1	x^20 - x^19 - 48x^18 + 59x^17 + 852x^16 - 1472x^15 - 6765x^14 + 18479x^13 + 19331x^12 - 115489x^11 + 62348x^10 + 346538x^9 - 611373x^8 - 430728x^7 + 1650437x^6 + 83930x^5 - 1817602x^4 + 272865x^3 + 763668x^2 - 172476x - 58887	\( 67^{8}\cdot 401^{8} \)	20T313	Trivial (GRH)
20.8.271489728101173730019304802954487841.1	x^20 - 8x^19 + 14x^18 + 88x^17 - 726x^16 + 1881x^15 + 2036x^14 - 26437x^13 + 64297x^12 + 9772x^11 - 408312x^10 + 926094x^9 - 443907x^8 - 2079408x^7 + 5461757x^6 - 6648924x^5 + 4477551x^4 - 1228248x^3 - 502901x^2 + 527068x - 132651	\( 67^{8}\cdot 401^{8} \)	20T313	Trivial (GRH)
20.12.569045856917786506070759387613895321.1	x^20 - 8x^19 + 6x^18 + 124x^17 - 553x^16 + 827x^15 + 2210x^14 - 15873x^13 + 40372x^12 - 22278x^11 - 186071x^10 + 528525x^9 - 194363x^8 - 1254067x^7 + 1644786x^6 + 739936x^5 - 2287291x^4 + 296429x^3 + 1187010x^2 - 251494x - 231529	\( 67^{6}\cdot 97^{2}\cdot 401^{8} \)	20T313	Trivial (GRH)
20.0.63416710432928568752221553366630662144.1	x^20 + 70x^18 + 1764x^16 + 20868x^14 + 133613x^12 + 490412x^10 + 1030884x^8 + 1168480x^6 + 610638x^4 + 98758x^2 + 4489	\( 2^{20}\cdot 67^{6}\cdot 401^{8} \)	20T313	$[4, 8516]$ (GRH)
20.0.63416710432928568752221553366630662144.2	x^20 + 74x^18 + 2388x^16 + 44138x^14 + 515533x^12 + 3953635x^10 + 19980091x^8 + 64660896x^6 + 124191468x^4 + 117809316x^2 + 29452329	\( 2^{20}\cdot 67^{6}\cdot 401^{8} \)	20T313	$[4, 4360]$ (GRH)
20.20.193436331687014863594648221771906658401.1	x^20 - x^19 - 95x^18 + 164x^17 + 3369x^16 - 7746x^15 - 55436x^14 + 153799x^13 + 444659x^12 - 1476304x^11 - 1612214x^10 + 7068645x^9 + 1538915x^8 - 16039436x^7 + 3739572x^6 + 14603214x^5 - 7251611x^4 - 2917719x^3 + 2153723x^2 - 259240x - 403	\( 3^{6}\cdot 59^{6}\cdot 97^{2}\cdot 401^{8} \)	20T313	Trivial (GRH)
20.20.19137711650987108213394112044518079104001.1	x^20 - 5x^19 - 100x^18 + 646x^17 + 2594x^16 - 25906x^15 + 5192x^14 + 386795x^13 - 821850x^12 - 1701585x^11 + 7764587x^10 - 4210169x^9 - 17925526x^8 + 27771775x^7 + 1660750x^6 - 27788027x^5 + 12576568x^4 + 7901667x^3 - 5676139x^2 - 614574x + 693279	\( 3^{10}\cdot 61^{6}\cdot 97^{2}\cdot 401^{8} \)	20T313	Trivial (GRH)
20.16.43655819768396836960834231619884599320641.1	x^20 - 4x^19 - 144x^18 + 145x^17 + 8425x^16 + 13298x^15 - 207708x^14 - 784764x^13 + 1226595x^12 + 11165685x^11 + 12772327x^10 - 41538687x^9 - 125332665x^8 - 71352743x^7 + 160719269x^6 + 313068405x^5 + 172700638x^4 - 205510240x^3 - 392468850x^2 - 30598427x + 193923241	\( 67^{8}\cdot 401^{10} \)	20T313	Trivial (GRH)
20.4.2586678478322351446140555785611079357300736.1	x^20 + 48x^18 + 792x^16 + 3464x^14 - 50377x^12 - 779610x^10 - 4580346x^8 - 13389012x^6 - 17512326x^4 - 2573532x^2 + 9979281	\( 2^{40}\cdot 3^{6}\cdot 13^{6}\cdot 401^{8} \)	20T313	$[2, 2]$ (GRH)