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 matches 1-50 of 52)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.25488163705013847372857344.1	x^20 + 5x^18 + 4x^16 - 3x^14 + x^12 + 7x^10 + x^8 - 3x^6 + 4x^4 + 5x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	$[2]$ (GRH)
20.4.25488163705013847372857344.1	x^20 - 5x^18 + 8x^16 - 13x^14 + 10x^12 - 4x^8 - 10x^6 + 6x^4 + 7x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.8.25488163705013847372857344.1	x^20 - 9x^18 + 40x^16 - 106x^14 + 184x^12 - 220x^10 + 193x^8 - 127x^6 + 54x^4 - 12x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.0.25488163705013847372857344.2	x^20 - x^18 - 6x^16 + 9x^14 + 16x^12 - 18x^10 - 24x^8 + 12x^6 + 34x^4 + 19x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.4.25488163705013847372857344.2	x^20 - 6x^16 - x^12 + 11x^10 - x^8 - 6x^4 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.8.25488163705013847372857344.2	x^20 - x^18 - x^16 - 17x^14 + 72x^12 - 121x^10 + 107x^8 - 62x^6 + 29x^4 - 9x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.0.25488163705013847372857344.3	x^20 + 2x^18 - 4x^16 + 4x^14 + 41x^12 + 77x^10 + 83x^8 + 60x^6 + 32x^4 + 10x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.4.25488163705013847372857344.3	x^20 + 5x^18 + 8x^16 + 2x^14 - 12x^12 - 22x^10 - 37x^8 - 67x^6 - 60x^4 - 18x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.8.25488163705013847372857344.3	x^20 - 5x^18 + 8x^16 - 2x^14 - x^12 - 33x^10 + 73x^8 - 54x^6 + 17x^4 - 4x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.0.25488163705013847372857344.4	x^20 + x^18 - 6x^16 + 2x^14 + 16x^12 - 4x^10 - 13x^8 - x^6 + 12x^4 + 14x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.4.25488163705013847372857344.4	x^20 + 3x^16 + 22x^14 + 41x^12 + 44x^10 + 7x^8 - 44x^6 - 32x^4 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.4.25488163705013847372857344.5	x^20 - 3x^18 + 2x^16 + 3x^14 - 9x^12 + 11x^10 - 9x^8 + 3x^6 + 2x^4 - 3x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.4.25488163705013847372857344.6	x^20 + 6x^18 + 19x^16 + 42x^14 + 65x^12 + 66x^10 + 29x^8 - 10x^6 - 16x^4 - 4x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	Trivial (GRH)
20.0.57722337794481266110634089.1	x^20 - 5x^19 + 15x^18 - 24x^17 + 15x^16 + 22x^15 - 57x^14 + 64x^13 - 10x^12 - 57x^11 + 95x^10 - 57x^9 - 10x^8 + 64x^7 - 57x^6 + 22x^5 + 15x^4 - 24x^3 + 15x^2 - 5x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$ (GRH)
20.4.57722337794481266110634089.1	x^20 - 6x^19 + 13x^18 + x^17 - 77x^16 + 220x^15 - 343x^14 + 307x^13 + 42x^12 - 877x^11 + 2141x^10 - 3339x^9 + 3919x^8 - 3765x^7 + 3191x^6 - 2431x^5 + 1485x^4 - 612x^3 + 149x^2 - 19x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.8.57722337794481266110634089.1	x^20 - 5x^19 + 9x^18 - 5x^17 - 20x^16 + 84x^15 - 130x^14 + 15x^13 + 222x^12 - 294x^11 + 143x^10 - 83x^9 + 5x^8 + 491x^7 - 698x^6 + 23x^5 + 539x^4 - 341x^3 - 77x^2 + 121x - 11	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.0.57722337794481266110634089.2	x^20 - 3x^19 + 10x^18 - 31x^17 + 95x^16 - 194x^15 + 426x^14 - 662x^13 + 1038x^12 - 1221x^11 + 1283x^10 - 1067x^9 + 753x^8 - 401x^7 + 172x^6 + 7x^5 - 14x^4 - 8x^3 + 8x^2 + 4x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.4.57722337794481266110634089.2	x^20 - 5x^19 + 11x^18 - 15x^17 - x^16 + 57x^15 - 124x^14 + 147x^13 - 28x^12 - 235x^11 + 430x^10 - 407x^9 - 82x^8 + 400x^7 - 631x^6 + 116x^5 + 116x^4 - 455x^3 + 160x^2 - 71x - 67	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.8.57722337794481266110634089.2	x^20 - 5x^19 + 2x^18 + 32x^17 - 66x^16 + 130x^14 - 98x^13 - 167x^12 + 272x^11 + 282x^10 - 1050x^9 + 861x^8 + 212x^7 - 703x^6 + 209x^5 + 165x^4 - 81x^3 - 16x^2 + 8x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.0.57722337794481266110634089.3	x^20 - 5x^19 + 17x^18 - 29x^17 + 27x^16 - 2x^15 - 36x^14 + 32x^13 + 3x^12 - 45x^11 + 88x^10 - 95x^9 + 136x^8 - 123x^7 + 101x^6 - 31x^5 + 64x^4 - 9x^3 + 21x^2 - 7x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.4.57722337794481266110634089.3	x^20 - 4x^19 + 5x^18 + 6x^17 - 29x^16 + 26x^15 + 49x^14 - 145x^13 + 100x^12 + 133x^11 - 319x^10 + 21x^9 + 606x^8 - 944x^7 + 698x^6 - 334x^5 + 224x^4 - 193x^3 + 93x^2 - 18x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.8.57722337794481266110634089.3	x^20 - 4x^19 + 2x^18 + 20x^17 - 44x^16 + 33x^15 + 26x^14 - 193x^13 + 375x^12 - 196x^11 - 407x^10 + 845x^9 - 628x^8 - 49x^7 + 568x^6 - 451x^5 + 55x^4 + 112x^3 - 68x^2 + 15x - 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.0.57722337794481266110634089.4	x^20 - x^19 + 6x^18 - x^17 + 10x^16 - 48x^15 + 49x^14 - 24x^13 + 58x^12 - 161x^11 + 114x^10 - 49x^9 + 136x^8 - 224x^7 + 356x^6 - 315x^5 + 194x^4 - 83x^3 + 21x^2 + 3x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.4.57722337794481266110634089.4	x^20 - 3x^19 + 7x^18 - 6x^17 - 10x^16 + 31x^15 - 81x^14 + 85x^13 + 23x^12 - 262x^11 + 407x^10 - 585x^9 + 254x^8 + 223x^7 - 147x^6 - 262x^5 + 408x^4 - 280x^3 + 106x^2 - 19x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.4.57722337794481266110634089.5	x^20 - 3x^19 + x^18 + 14x^17 - 19x^16 - 33x^15 + 111x^14 - 105x^13 - 62x^12 + 356x^11 - 543x^10 + 375x^9 - 8x^8 - 52x^7 - 205x^6 + 253x^5 - 46x^4 - 72x^3 + 49x^2 - 12x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.8.89088118507694903199268864.1	x^20 - 7x^18 + 22x^16 - 51x^14 + 94x^12 - 128x^10 + 134x^8 - 101x^6 + 44x^4 - 10x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 43^{2} \)	20T263	Trivial (GRH)
20.0.381647910600027760000761856.1	x^20 + 6x^18 + 13x^16 + 33x^14 + 97x^12 + 128x^10 + 23x^8 + 11x^6 + 19x^4 - x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T263	Trivial (GRH)
20.4.381647910600027760000761856.1	x^20 - 4x^18 + 7x^16 - 11x^14 + 14x^12 - 15x^10 + 14x^8 - 11x^6 + 7x^4 - 4x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T263	Trivial (GRH)
20.0.381647910600027760000761856.2	x^20 + 5x^18 + 11x^16 + 3x^14 - 15x^12 - 18x^10 + 19x^8 + 23x^6 - 33x^4 + 14x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T263	Trivial (GRH)
20.4.381647910600027760000761856.2	x^20 - 3x^18 + 6x^16 - 11x^14 + 15x^12 - 15x^10 + 27x^8 - 11x^6 + 10x^4 - 9x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T263	Trivial (GRH)
20.4.381647910600027760000761856.3	x^20 - 7x^18 + 22x^16 - 40x^14 + 50x^12 - 62x^10 + 90x^8 - 101x^6 + 66x^4 - 21x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T263	Trivial (GRH)
20.4.489821501624624581418972449.1	x^20 - 7x^19 + 26x^18 - 63x^17 + 85x^16 - 40x^15 - 115x^14 + 250x^13 + 197x^12 - 331x^11 - 682x^10 + 106x^9 + 529x^8 + 152x^7 - 119x^6 - 23x^5 + 77x^4 + 11x^3 - 11	\( 11^{16}\cdot 23^{2}\cdot 67^{4} \)	20T263	Trivial (GRH)
20.8.489821501624624581418972449.1	x^20 - 6x^19 + 12x^18 - 2x^17 - 35x^16 + 84x^15 - 97x^14 - 3x^13 + 212x^12 - 368x^11 + 282x^10 + 121x^9 - 562x^8 + 566x^7 - 159x^6 - 298x^5 + 484x^4 - 253x^3 - 132x^2 + 165x - 11	\( 11^{16}\cdot 23^{2}\cdot 67^{4} \)	20T263	Trivial (GRH)
20.12.572447775008070927479996416.1	x^20 - 13x^18 + 73x^16 - 235x^14 + 481x^12 - 649x^10 + 578x^8 - 335x^6 + 120x^4 - 21x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T263	Trivial (GRH)
20.12.705190398026416240151735929.1	x^20 - x^19 - 3x^18 + 8x^17 - 32x^16 - 25x^15 + 185x^14 + x^13 - 381x^12 + 111x^11 + 282x^10 + 3x^9 + 171x^8 - 385x^7 - 362x^6 + 397x^5 + 177x^4 - 133x^3 - 25x^2 + 13x - 1	\( 11^{16}\cdot 43^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.4.705190398026416240151735929.1	x^20 - 7x^19 + 25x^18 - 51x^17 + 46x^16 + 57x^15 - 282x^14 + 548x^13 - 683x^12 + 489x^11 + 275x^10 - 1773x^9 + 3045x^8 - 2346x^7 + 218x^6 + 449x^5 + 272x^4 - 145x^3 - 191x^2 - 37x + 1	\( 11^{16}\cdot 43^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.12.13483238599952325260241534976.2	x^20 - 2x^18 - 12x^16 + 11x^14 + 93x^12 - 282x^10 + 400x^8 - 308x^6 + 116x^4 - 19x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	Trivial (GRH)
20.0.13483238599952325260241534976.3	x^20 + 2x^18 + 6x^14 - x^12 + 7x^10 - x^8 + 6x^6 + 2x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	$[4]$ (GRH)
20.12.13483238599952325260241534976.3	x^20 - 12x^18 + 66x^16 - 207x^14 + 365x^12 - 334x^10 + 160x^8 - 92x^6 + 66x^4 - 15x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	Trivial (GRH)
20.8.13483238599952325260241534976.3	x^20 - 13x^18 + 84x^16 - 356x^14 + 1108x^12 - 2662x^10 + 4824x^8 - 6165x^6 + 5158x^4 - 2507x^2 + 529	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	Trivial (GRH)
20.0.13483238599952325260241534976.4	x^20 + 2x^18 + 11x^16 + 17x^14 + 43x^12 + 128x^10 + 131x^8 + 193x^6 + 77x^4 + 13x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	$[4]$ (GRH)
20.8.13483238599952325260241534976.4	x^20 - 11x^18 + 45x^16 - 110x^14 + 315x^12 - 781x^10 + 866x^8 - 803x^6 + 2214x^4 - 2024x^2 + 529	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T263	Trivial (GRH)
20.12.259115574359426403570636425521.1	x^20 - 3x^19 - 15x^18 + 49x^17 + 45x^16 - 156x^15 - 158x^14 + 52x^13 + 1101x^12 - 724x^11 - 847x^10 - 35x^9 + 276x^8 + 1928x^7 - 983x^6 - 1461x^5 + 562x^4 + 435x^3 - 26x^2 - 19x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{4} \)	20T263	Trivial (GRH)
20.12.259115574359426403570636425521.2	x^20 - 2x^19 - 3x^17 - 85x^16 + 194x^15 - 115x^14 + 649x^13 + 473x^12 - 2676x^11 - 136x^10 - 633x^9 + 736x^8 + 4356x^7 + 1398x^6 + 155x^5 - 3806x^4 - 3113x^3 + 1705x^2 + 902x - 253	\( 11^{16}\cdot 23^{4}\cdot 67^{4} \)	20T263	Trivial (GRH)
20.16.1631471870594231356489225732096.1	x^20 - 19x^18 + 141x^16 - 567x^14 + 1368x^12 - 2012x^10 + 1763x^8 - 882x^6 + 236x^4 - 29x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 23^{4} \)	20T263	Trivial (GRH)
20.4.3023033099862819886966034661376.1	x^20 - 9x^18 + 54x^16 - 319x^14 + 1050x^12 - 3480x^10 + 5559x^8 - 7711x^6 + 15175x^4 - 17889x^2 + 7921	\( 2^{20}\cdot 11^{16}\cdot 89^{4} \)	20T263	Trivial (GRH)
20.4.3023033099862819886966034661376.2	x^20 - 9x^18 + 54x^16 - 242x^14 + 863x^12 - 3315x^10 + 9651x^8 - 15356x^6 + 13217x^4 - 14952x^2 + 7921	\( 2^{20}\cdot 11^{16}\cdot 89^{4} \)	20T263	Trivial (GRH)
20.16.7132633219374780062667772002304.1	x^20 - 26x^18 + 270x^16 - 1429x^14 + 4088x^12 - 6270x^10 + 5059x^8 - 2125x^6 + 437x^4 - 38x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{6} \)	20T263	Trivial (GRH)
20.0.24930508171311849406186598170624.1	x^20 + 4x^18 + 33x^16 + 26x^14 + 369x^12 - 7x^10 + 1080x^8 - 684x^6 + 1001x^4 - 1385x^2 + 529	\( 2^{20}\cdot 11^{16}\cdot 23^{4}\cdot 43^{2} \)	20T263	$[2, 6]$ (GRH)
20.20.231385857613781853791004981723136.1	x^20 - 33x^18 + 460x^16 - 3542x^14 + 16528x^12 - 48257x^10 + 87947x^8 - 96690x^6 + 58766x^4 - 15686x^2 + 529	\( 2^{20}\cdot 11^{16}\cdot 23^{4}\cdot 131^{2} \)	20T263	Trivial (GRH)