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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.75348325135501798832991875.1	x^22 - 4x^21 + 10x^20 - 22x^19 + 47x^18 - 79x^17 + 124x^16 - 169x^15 + 213x^14 - 229x^13 + 259x^12 - 192x^11 + 188x^10 - 90x^9 + 134x^8 - 14x^7 + 62x^6 - 19x^5 + 22x^4 - 12x^3 + 3x^2 - x + 1	\( -\,5^{4}\cdot 7^{6}\cdot 83^{5}\cdot 127^{4} \)	22T52	Trivial (GRH)
22.0.492568978448025181133471744.1	x^22 + 2x^20 - 5x^18 - 22x^16 + 29x^14 + 153x^12 + 72x^10 - 195x^8 - 158x^6 + 66x^4 + 77x^2 + 11	\( -\,2^{18}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.4.931263224878297608080470016.1	x^22 - 4x^21 + 5x^20 + 4x^19 - 26x^18 + 31x^17 + 15x^16 - 79x^15 + 76x^14 + 60x^13 - 153x^12 + 84x^11 + 83x^10 - 192x^9 + 24x^8 + 58x^7 - 150x^6 + 30x^5 + 19x^4 - 23x^3 + 6x^2 + 29x + 1	\( -\,2^{12}\cdot 11^{7}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.4.1533107758369291702785569375.1	x^22 - 2x^21 + 7x^20 - 20x^19 + 38x^18 - 74x^17 + 107x^16 - 167x^15 + 185x^14 - 284x^13 + 308x^12 - 417x^11 + 466x^10 - 462x^9 + 446x^8 - 292x^7 + 170x^6 - 55x^5 - 7x^4 + 11x^3 - 8x^2 + x + 1	\( -\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997 \)	22T52	Trivial (GRH)
22.2.1767712543554828434373148672.1	x^22 - 5x^21 + 17x^20 - 40x^19 + 70x^18 - 93x^17 + 99x^16 - 86x^15 + 53x^14 + 37x^13 - 283x^12 + 778x^11 - 1493x^10 + 2198x^9 - 2575x^8 + 2425x^7 - 1840x^6 + 1108x^5 - 512x^4 + 173x^3 - 33x^2 + x + 1	\( 2^{16}\cdot 37^{5}\cdot 4441^{4} \)	22T52	Trivial (GRH)
22.6.4525438563861162255210415625.1	x^22 - 3x^21 - 5x^20 + 20x^19 + 6x^18 - 46x^17 - 22x^16 + 88x^15 + 102x^14 - 250x^13 - 116x^12 + 460x^11 - 50x^10 - 559x^9 + 321x^8 + 395x^7 - 287x^6 - 315x^5 + 200x^4 + 136x^3 + 14x^2 - 70x + 5	\( 5^{5}\cdot 7^{6}\cdot 83^{4}\cdot 127^{4}\cdot 997 \)	22T52	Trivial (GRH)
22.2.31524414620673611592542191616.1	x^22 - 2x^21 + x^20 - x^19 - 7x^17 + 5x^16 + 45x^15 + 31x^14 - 38x^13 - 205x^12 - 278x^11 - 123x^10 + 249x^9 + 532x^8 + 371x^7 + 205x^6 + 153x^5 + 236x^4 + 94x^3 + 34x^2 + 5x + 25	\( 2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.6.31524414620673611592542191616.1	x^22 - 6x^20 + 14x^18 - 15x^16 - 6x^14 + 47x^12 - 75x^10 + 21x^8 + 101x^6 - 110x^4 + 55x^2 - 11	\( 2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.6.6246529265931622277982705180820920018628868505654981941197288960425984.1	x^22 + 3x^20 - 36x^18 - 60x^16 + 213x^14 + 9x^12 - 114x^10 + 180x^8 - 108x^6 - 6x^4 + 36x^2 - 54	\( 2^{43}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.8.24986117063726489111930820723283680074515474022619927764789155841703936.1	x^22 - 3x^20 - 36x^18 + 60x^16 + 213x^14 - 9x^12 - 114x^10 - 180x^8 - 108x^6 + 6x^4 + 36x^2 + 54	\( -\,2^{45}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.4.66629645503270637631815521928756480198707930726986474039437748911210496.1	x^22 + 14x^20 + 49x^18 - 84x^16 - 873x^14 - 2112x^12 - 2265x^10 - 576x^8 + 1248x^6 + 1432x^4 + 632x^2 + 64	\( -\,2^{48}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.8.333148227516353188159077609643782400993539653634932370197188744556052480.1	x^22 - 8x^20 - 11x^18 + 234x^16 - 633x^14 + 30x^12 + 2835x^10 - 5934x^8 + 5448x^6 - 2104x^4 + 8x^2 + 80	\( -\,2^{48}\cdot 3^{28}\cdot 5\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.12.2571487881141851171102880299437945407668884201494634232459550622042030080.1	x^22 - 25x^20 + 244x^18 - 1152x^16 + 2229x^14 + 3057x^12 - 27810x^10 + 70572x^8 - 95244x^6 + 70846x^4 - 25252x^2 + 2470	\( -\,2^{43}\cdot 3^{28}\cdot 5\cdot 7^{4}\cdot 13\cdot 19\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.4.2873403462328546247872044383177623208569279512601291692950752921795952640.1	x^22 + 30x^20 + 369x^18 + 2328x^16 + 6999x^14 - 828x^12 - 83625x^10 - 301428x^8 - 506304x^6 - 378264x^4 - 11592x^2 + 99360	\( -\,2^{45}\cdot 3^{29}\cdot 5\cdot 7^{4}\cdot 23^{5}\cdot 137^{16} \)	22T52	$[2, 2]$ (GRH)
22.12.14991670238235893467158492433970208044709284413571956658873493505022361600.1	x^22 - 36x^20 + 549x^18 - 4638x^16 + 23559x^14 - 71010x^12 + 102675x^10 + 60498x^8 - 550584x^6 + 1014936x^4 - 865080x^2 + 291600	\( -\,2^{48}\cdot 3^{30}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.0.233978328890422752873824182193069474777787737239153876898740585020329558016.1	x^22 + 58x^20 + 1489x^18 + 22320x^16 + 216663x^14 + 1424964x^12 + 6438231x^10 + 19757580x^8 + 39484992x^6 + 46601624x^4 + 25144376x^2 + 898976	\( -\,2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161 \)	22T52	n/a
22.14.935913315561691011495296728772277899111150948956615507594962340081318232064.1	x^22 - 58x^20 + 1489x^18 - 22320x^16 + 216663x^14 - 1424964x^12 + 6438231x^10 - 19757580x^8 + 39484992x^6 - 46601624x^4 + 25144376x^2 - 898976	\( 2^{47}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161 \)	22T52	Trivial (GRH)
22.14.12690240639024486099207064421849753745845788293805139479005039009036081561600.1	x^22 - 74x^20 + 2449x^18 - 47772x^16 + 608919x^14 - 5307720x^12 + 32127975x^10 - 134044248x^8 + 373194336x^6 - 645946216x^4 + 597000440x^2 - 195030400	\( 2^{45}\cdot 3^{28}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 59\cdot 137^{16}\cdot 1033 \)	22T52	Trivial (GRH)