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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.7.13044111284271602011807079518811.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 2x^14 + 2940x^13 + 28x^12 - 5733x^11 - 154x^10 + 7007x^9 + 420x^8 - 5144x^7 - 588x^6 + 2051x^5 + 392x^4 - 329x^3 - 98x^2 - 7x - 1	\( -\,7^{21}\cdot 19^{3}\cdot 23^{7} \)	21T87	Trivial (GRH)
21.7.20453552629840353822427943116187.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 2x^14 + 2940x^13 + 28x^12 - 5733x^11 - 154x^10 + 7007x^9 + 420x^8 - 5146x^7 - 588x^6 + 2065x^5 + 392x^4 - 357x^3 - 98x^2 + 7x + 3	\( -\,7^{21}\cdot 11^{3}\cdot 31^{7} \)	21T87	Trivial (GRH)
21.1.39987268032456435383175526376221.1	x^21 + 21x^19 + 189x^17 + 952x^15 + 2940x^13 + 5733x^11 + 7007x^9 + 5144x^7 + 2051x^5 + 329x^3 - 7x - 1	\( 7^{19}\cdot 23^{7}\cdot 101^{3} \)	21T87	Trivial (GRH)
21.1.283127009136682212088030700907133.1	x^21 + 21x^19 + 189x^17 + 952x^15 - 8x^14 + 2940x^13 - 112x^12 + 5733x^11 - 616x^10 + 7007x^9 - 1680x^8 + 5166x^7 - 2352x^6 + 2205x^5 - 1568x^4 + 637x^3 - 392x^2 + 147x - 19	\( 7^{21}\cdot 23^{7}\cdot 53^{3} \)	21T87	Trivial (GRH)
21.15.18446212894339753014854986922155963.1	x^21 - 21x^19 + 189x^17 - 952x^15 + 2940x^13 - 5733x^11 + 7007x^9 - 5149x^7 + 2086x^5 - 399x^3 + 28x - 1	\( -\,7^{21}\cdot 229^{7} \)	21T87	Trivial (GRH)
21.15.41360968886902952394795529728864551.1	x^21 - 21x^19 + 189x^17 - 952x^15 - x^14 + 2940x^13 + 14x^12 - 5733x^11 - 77x^10 + 7007x^9 + 210x^8 - 5149x^7 - 294x^6 + 2086x^5 + 196x^4 - 399x^3 - 49x^2 + 28x + 3	\( -\,7^{21}\cdot 257^{7} \)	21T87	Trivial (GRH)
21.9.797643132581855967205868099633068949.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 6x^14 + 2940x^13 + 84x^12 - 5733x^11 - 462x^10 + 7007x^9 + 1260x^8 - 5137x^7 - 1764x^6 + 2002x^5 + 1176x^4 - 231x^3 - 294x^2 - 56x + 1	\( 7^{17}\cdot 47^{3}\cdot 229^{7} \)	21T87	Trivial (GRH)
21.9.5296120176371912060661478404374557149.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 2x^14 + 2940x^13 + 28x^12 - 5733x^11 - 154x^10 + 7007x^9 + 420x^8 - 5150x^7 - 588x^6 + 2093x^5 + 392x^4 - 413x^3 - 98x^2 + 35x + 9	\( 3^{10}\cdot 7^{21}\cdot 107^{7} \)	21T87	Trivial (GRH)
21.3.1356016005699438692309242954734799683584.1	x^21 + 21x^19 + 189x^17 + 952x^15 - 10x^14 + 2940x^13 - 140x^12 + 5733x^11 - 770x^10 + 7007x^9 - 2100x^8 + 5175x^7 - 2940x^6 + 2268x^5 - 1960x^4 + 763x^3 - 490x^2 + 210x - 26	\( -\,2^{20}\cdot 7^{21}\cdot 29^{3}\cdot 37^{7} \)	21T87	Trivial (GRH)
21.3.9377081035056114579579765383879976402944.1	x^21 + 21x^19 + 189x^17 + 952x^15 - x^14 + 2940x^13 - 14x^12 + 5733x^11 - 77x^10 + 7007x^9 - 210x^8 + 5142x^7 - 294x^6 + 2037x^5 - 196x^4 + 301x^3 - 49x^2 - 21x + 1	\( -\,2^{14}\cdot 7^{21}\cdot 13^{3}\cdot 17^{3}\cdot 37^{7} \)	21T87	Trivial (GRH)
21.21.183191324793504092701098288277931973797104039377054776426496.1	x^21 - 3x^20 - 154x^19 + 702x^18 + 7773x^17 - 49095x^16 - 124542x^15 + 1333938x^14 - 546820x^13 - 14225596x^12 + 23697670x^11 + 60067750x^10 - 163471412x^9 - 64055772x^8 + 418640694x^7 - 137499162x^6 - 352348101x^5 + 231197815x^4 - 830652x^3 - 20082052x^2 + 2094423x + 189587	\( 2^{32}\cdot 3^{10}\cdot 7^{15}\cdot 47^{7}\cdot 6696671^{3} \)	21T87	Trivial (GRH)
21.21.1411787678306418347597299085327799505357680312763424671062556672.1	x^21 - 3x^20 - 154x^19 + 702x^18 + 7773x^17 - 49095x^16 - 125375x^15 + 1341897x^14 - 549949x^13 - 14368893x^12 + 23839329x^11 + 61218585x^10 - 162697023x^9 - 75688995x^8 + 413867107x^7 - 75283085x^6 - 379809836x^5 + 146533704x^4 + 64989214x^3 - 28197376x^2 - 1291883x + 851171	\( 2^{18}\cdot 7^{15}\cdot 67^{7}\cdot 239^{3}\cdot 239339207^{3} \)	21T87	Trivial (GRH)