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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.823067302269314181883621609.3	x^20 - 10x^19 + 41x^18 - 84x^17 + 71x^16 + 44x^15 - 141x^14 + 13x^13 + 280x^12 - 289x^11 - 199x^10 + 626x^9 - 393x^8 - 235x^7 + 468x^6 - 132x^5 - 134x^4 + 75x^3 + 6x^2 - 8x + 1	\( 11^{18}\cdot 23^{6} \)	20T314	Trivial (GRH)
20.4.823067302269314181883621609.5	x^20 - 12x^18 - 22x^17 + 23x^16 + 132x^15 + 197x^14 + 121x^13 - 21x^12 - 99x^11 - 111x^10 - 99x^9 - 21x^8 + 121x^7 + 197x^6 + 132x^5 + 23x^4 - 22x^3 - 12x^2 + 1	\( 11^{18}\cdot 23^{6} \)	20T314	Trivial (GRH)
20.8.823067302269314181883621609.5	x^20 - 3x^19 - 3x^18 + 12x^17 - 11x^16 + 21x^15 - 8x^14 - 30x^13 + 87x^12 - 132x^11 + 133x^10 - 132x^9 + 87x^8 - 30x^7 - 8x^6 + 21x^5 - 11x^4 + 12x^3 - 3x^2 - 3x + 1	\( 11^{18}\cdot 23^{6} \)	20T314	Trivial (GRH)
20.8.823067302269314181883621609.6	x^20 - 2x^18 - 22x^17 + 26x^16 + 55x^15 + 14x^14 - 242x^13 - 204x^12 + 1408x^11 - 1770x^10 + 792x^9 + 20x^8 - 253x^7 + 620x^6 - 715x^5 + 234x^4 + 110x^3 - 83x^2 + 11x + 1	\( 11^{18}\cdot 23^{6} \)	20T314	Trivial (GRH)
20.12.50522262278163705147147943936.3	x^20 - 2x^18 - 15x^16 + 18x^14 + 63x^12 + 22x^10 - 390x^8 + 424x^6 - 89x^4 - 32x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T314	Trivial (GRH)
20.8.50522262278163705147147943936.11	x^20 - 4x^18 - 16x^16 + 100x^14 - 158x^12 + 44x^10 + 87x^8 - 46x^6 - 14x^4 + 6x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T314	Trivial (GRH)
20.4.50522262278163705147147943936.12	x^20 + 10x^18 + 32x^16 + 16x^14 - 104x^12 - 176x^10 - 3x^8 + 180x^6 + 128x^4 + 24x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T314	Trivial (GRH)
20.8.50522262278163705147147943936.12	x^20 + 4x^18 - 16x^16 - 100x^14 - 158x^12 - 44x^10 + 87x^8 + 46x^6 - 14x^4 - 6x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T314	Trivial (GRH)
20.0.203681981950950327645213870961.5	x^20 - 5x^19 + 13x^18 - 17x^17 + 13x^16 - 3x^15 + 40x^14 - 85x^13 + 103x^12 - 84x^11 + 323x^10 - 242x^9 + 228x^8 - 523x^7 + 113x^6 - 292x^5 + 248x^4 + 26x^3 + 194x^2 + 37x + 43	\( 11^{16}\cdot 1451^{4} \)	20T314	Trivial (GRH)
20.0.203681981950950327645213870961.6	x^20 - 2x^19 + 8x^18 - 2x^17 + 15x^16 - 31x^15 - x^14 - 103x^13 + 56x^12 - 157x^11 + 513x^10 + 192x^9 + 1700x^8 + 1351x^7 + 1130x^6 - 130x^5 + 511x^4 - 1591x^3 - 1019x^2 - 331x + 859	\( 11^{16}\cdot 1451^{4} \)	20T314	Trivial (GRH)
20.20.246359373213147467442410887070161.1	x^20 - 10x^19 + 9x^18 + 201x^17 - 552x^16 - 1310x^15 + 5856x^14 + 2333x^13 - 27237x^12 + 6515x^11 + 65619x^10 - 29820x^9 - 85521x^8 + 36187x^7 + 58922x^6 - 11943x^5 - 19062x^4 - 271x^3 + 2043x^2 + 242x - 23	\( 11^{16}\cdot 43^{4}\cdot 199^{4} \)	20T314	Trivial (GRH)
20.20.246359373213147467442410887070161.2	x^20 - 2x^19 - 46x^18 + 115x^17 + 707x^16 - 2064x^15 - 4437x^14 + 15259x^13 + 11851x^12 - 52015x^11 - 13592x^10 + 85401x^9 + 12862x^8 - 73500x^7 - 14084x^6 + 31918x^5 + 8971x^4 - 5475x^3 - 2091x^2 - x + 23	\( 11^{16}\cdot 43^{4}\cdot 199^{4} \)	20T314	Trivial (GRH)
20.12.3169879955721756225795296761087000576.1	x^20 + 12x^18 - 312x^16 - 1224x^14 + 16536x^12 + 24608x^10 - 321145x^8 + 65582x^6 + 2098140x^4 - 3123010x^2 + 958441	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.16.3169879955721756225795296761087000576.1	x^20 - 32x^18 + 319x^16 - 156x^14 - 18874x^12 + 146458x^10 - 497799x^8 + 811232x^6 - 508541x^4 - 7476x^2 + 7921	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.8.3169879955721756225795296761087000576.1	x^20 + 34x^18 + 209x^16 - 1542x^14 - 3881x^12 + 11906x^10 + 17705x^8 - 30400x^6 - 23386x^4 + 21894x^2 + 7921	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.12.3169879955721756225795296761087000576.2	x^20 - 8x^18 - 135x^16 + 1162x^14 + 4522x^12 - 48256x^10 + 3509x^8 + 467192x^6 - 472747x^4 - 839982x^2 + 958441	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.16.3169879955721756225795296761087000576.2	x^20 - 24x^18 - 55x^16 + 4680x^14 - 34937x^12 + 86178x^10 - 17733x^8 - 218070x^6 + 289498x^4 - 117658x^2 + 7921	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.8.3169879955721756225795296761087000576.2	x^20 + 6x^18 - 166x^16 - 1198x^14 + 5439x^12 + 48080x^10 - 14432x^8 - 449746x^6 - 283624x^4 + 1098438x^2 + 958441	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	$[2]$ (GRH)
20.12.3169879955721756225795296761087000576.3	x^20 - 16x^18 - 11x^16 + 1108x^14 - 2358x^12 - 21740x^10 + 50410x^8 + 143868x^6 - 231803x^4 - 112852x^2 + 7921	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.12.3169879955721756225795296761087000576.4	x^20 - 20x^18 - 88x^16 + 1524x^14 - 529x^12 - 17648x^10 + 7666x^8 + 71660x^6 - 15378x^4 - 89890x^2 + 7921	\( 2^{40}\cdot 11^{16}\cdot 89^{4} \)	20T314	Trivial (GRH)
20.8.383555474642332503321230908091527069696.1	x^20 - 869x^16 - 11440x^14 + 6281x^12 + 710622x^10 + 1933338x^8 - 12218580x^6 - 43809865x^4 + 41697568x^2 + 115971361	\( 2^{40}\cdot 11^{18}\cdot 89^{4} \)	20T314	$[2]$ (GRH)
20.8.383555474642332503321230908091527069696.2	x^20 - 22x^18 - 781x^16 - 2266x^14 + 41041x^12 + 164538x^10 - 344124x^8 - 2218656x^6 - 2348247x^4 + 689216x^2 + 958441	\( 2^{40}\cdot 11^{18}\cdot 89^{4} \)	20T314	$[4]$ (GRH)