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 82)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.24890784868177585325056.1	x^20 + 5x^18 + 8x^16 + 2x^14 - x^12 - 11x^10 - 37x^8 - 34x^6 - 5x^4 + 4x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 23^{2} \)	20T751	Trivial
20.4.2732857610451081915433984.1	x^20 - 2x^19 - x^18 + 15x^17 - 25x^16 - x^15 + 67x^14 - 92x^13 + 4x^12 + 157x^11 - 213x^10 + 114x^9 + 39x^8 - 65x^7 + 68x^6 - 61x^5 + 21x^4 - 3x^3 - 5x^2 + 4x + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T751	Trivial
20.8.2732857610451081915433984.1	x^20 + 8x^18 + 23x^16 + 23x^14 - 24x^12 - 73x^10 - 28x^8 + 53x^6 + 27x^4 - 12x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T751	Trivial (GRH)
20.4.2732857610451081915433984.2	x^20 + x^18 - 12x^16 - 5x^14 + 39x^12 + 11x^10 - 3x^8 - 37x^6 - 4x^4 + 9x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{2} \)	20T751	Trivial (GRH)
20.8.10527014003350667272569856.1	x^20 - 7x^18 + 16x^16 - 2x^14 - 52x^12 + 100x^10 - 95x^8 + 49x^6 - 2x^4 - 8x^2 + 1	\( 2^{10}\cdot 11^{18}\cdot 43^{2} \)	20T751	Trivial (GRH)
20.4.13167225195265942636954624.3	x^20 - 2x^19 - 5x^18 + 20x^17 - 29x^16 - 19x^15 + 106x^14 - 91x^13 - 45x^12 + 81x^11 + 95x^10 - 146x^9 - 290x^8 + 757x^7 - 515x^6 - 124x^5 + 355x^4 - 179x^3 + 29x^2 - x + 1	\( 2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.4.13167225195265942636954624.4	x^20 - x^19 - 4x^18 + 7x^17 + 8x^16 - 22x^15 - 23x^14 + 54x^13 + 12x^12 - 55x^11 + 10x^10 - 105x^9 + 104x^8 + 18x^7 + 184x^6 - 608x^5 + 789x^4 - 523x^3 + 174x^2 - 18x - 1	\( 2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.4.13167225195265942636954624.5	x^20 - 9x^19 + 34x^18 - 66x^17 + 49x^16 + 79x^15 - 249x^14 + 191x^13 + 191x^12 - 429x^11 + 216x^10 - 11x^9 - 32x^8 + 181x^7 - 217x^6 + 13x^5 + 124x^4 + 33x^3 - 62x^2 + 7x + 23	\( 2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.4.24868623129665465017517056.1	x^20 + 9x^18 + 18x^16 - 26x^14 - 47x^12 + 143x^10 + 127x^8 - 148x^6 - x^4 + 12x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial
20.8.24868623129665465017517056.1	x^20 - 7x^16 + 11x^14 + 2x^12 - 33x^10 + 28x^8 + 11x^6 - 13x^4 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.4.24868623129665465017517056.2	x^20 + 6x^18 - 7x^16 - 107x^14 - 219x^12 - 106x^10 + 67x^8 + 25x^6 - 29x^4 - 5x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.24868623129665465017517056.2	x^20 + 6x^18 - 7x^16 - 19x^14 + 12x^12 - 29x^10 + 56x^8 + 3x^6 - 29x^4 + 6x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.24868623129665465017517056.3	x^20 + 3x^18 - 10x^16 - 23x^14 + 20x^12 + 62x^10 + 27x^8 - 75x^6 - 39x^4 + x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.24868623129665465017517056.4	x^20 + 8x^18 + 13x^16 - 30x^14 - 75x^12 + 11x^10 + 101x^8 + 36x^6 - 20x^4 - 3x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.24868623129665465017517056.5	x^20 + 2x^18 - 15x^16 - 18x^14 + 63x^12 + 33x^10 - 71x^8 - 6x^6 - 12x^4 - x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.4.330675770864580911767512064.1	x^20 - 7x^19 + 23x^18 - 45x^17 + 58x^16 - 83x^15 + 140x^14 - 230x^13 + 258x^12 - 248x^11 + 297x^10 - 244x^9 + 520x^8 - 321x^7 + 354x^6 - 138x^5 + 111x^4 - 49x^3 + 31x^2 - 10x + 1	\( 2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T751	Trivial (GRH)
20.8.330675770864580911767512064.1	x^20 - 2x^19 - 9x^18 + 51x^16 + 63x^15 - 107x^14 - 165x^13 + 60x^12 - 10x^11 - 199x^10 - 53x^9 + 31x^8 + 55x^7 + 202x^6 + 245x^5 + 162x^4 + 88x^3 + 39x^2 + 10x + 1	\( 2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T751	Trivial (GRH)
20.12.390543519512736738731951104.1	x^20 - 4x^18 - 5x^16 + 23x^14 + 7x^12 - 44x^10 - x^8 + 31x^6 - 3x^4 - 5x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 43^{2}\cdot 67^{2} \)	20T751	Trivial (GRH)
20.12.1712060409270190644695047369.1	x^20 - 4x^19 + x^18 + 12x^17 - 25x^16 + 45x^15 - 45x^14 + 47x^13 - 14x^12 - 474x^11 + 671x^10 + 563x^9 - 1021x^8 - 201x^7 + 484x^6 + 41x^5 - 46x^4 - 38x^3 - 5x^2 + 10x - 1	\( 11^{16}\cdot 43^{2}\cdot 67^{4} \)	20T751	Trivial (GRH)
20.8.1712060409270190644695047369.1	x^20 - x^19 - 11x^18 + 11x^17 + 26x^16 - 31x^15 + 56x^14 - 29x^13 - 163x^12 + 114x^11 - 363x^10 + 231x^9 + 530x^8 - 190x^7 + 958x^6 - 836x^5 + 212x^4 + 57x^3 - 751x^2 + 509x - 89	\( 11^{16}\cdot 43^{2}\cdot 67^{4} \)	20T751	Trivial (GRH)
20.4.1869886852982764466338791424.1	x^20 + 11x^18 + 49x^16 + 110x^14 + 120x^12 + 33x^10 - 45x^8 - 33x^6 - 6x^4 + 1	\( 2^{20}\cdot 11^{16}\cdot 197^{2} \)	20T751	Trivial (GRH)
20.8.1869886852982764466338791424.1	x^20 - 8x^16 + 8x^12 - 11x^10 - 4x^8 + 22x^6 + x^4 - 11x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 197^{2} \)	20T751	Trivial (GRH)
20.0.2952180761584785045865268224.1	x^20 - x^19 + 6x^18 - 26x^17 + 10x^16 - 29x^15 + 153x^14 - 153x^13 + 366x^12 - 352x^11 - 81x^10 - 330x^9 + 1389x^8 + 395x^7 - 881x^6 - 543x^5 + 582x^4 + 840x^3 + 380x^2 + 100x + 23	\( 2^{10}\cdot 11^{16}\cdot 89^{4} \)	20T751	Trivial (GRH)
20.4.2952180761584785045865268224.1	x^20 + x^18 - 2x^17 - 25x^16 + 16x^15 + 6x^14 + 45x^13 + 251x^12 - 96x^11 + 51x^10 - 380x^9 - 1046x^8 + 1032x^7 + 19x^6 + 945x^5 + 620x^4 - 2463x^3 + 1552x^2 - 351x + 23	\( 2^{10}\cdot 11^{16}\cdot 89^{4} \)	20T751	Trivial (GRH)
20.0.2952180761584785045865268224.2	x^20 - 10x^19 + 45x^18 - 117x^17 + 187x^16 - 165x^15 + 23x^14 + 72x^13 + 174x^12 - 735x^11 + 1074x^10 - 874x^9 + 587x^8 - 1345x^7 + 3843x^6 - 6875x^5 + 8283x^4 - 7807x^3 + 5494x^2 - 2185x + 1277	\( 2^{10}\cdot 11^{16}\cdot 89^{4} \)	20T751	Trivial (GRH)
20.4.2952180761584785045865268224.2	x^20 - 10x^19 + 52x^18 - 161x^17 + 309x^16 - 353x^15 + 158x^14 + 286x^13 - 958x^12 + 1625x^11 - 1577x^10 + 256x^9 + 1564x^8 - 2213x^7 + 1037x^6 + 969x^5 - 2064x^4 + 1621x^3 - 551x^2 - 57x + 109	\( 2^{10}\cdot 11^{16}\cdot 89^{4} \)	20T751	Trivial (GRH)
20.12.3009103398689521267119563776.1	x^20 - 8x^19 + 21x^18 - 122x^16 + 250x^15 + 12x^14 - 682x^13 + 694x^12 + 410x^11 - 1134x^10 + 514x^9 + 518x^8 - 748x^7 + 155x^6 + 256x^5 - 188x^4 + 22x^3 + 43x^2 - 14x + 1	\( 2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.3009103398689521267119563776.1	x^20 - 7x^19 + 19x^18 - 141x^16 + 360x^15 - 215x^14 - 693x^13 + 1632x^12 - 1062x^11 - 892x^10 + 1646x^9 + 135x^8 - 1727x^7 + 603x^6 + 1081x^5 - 742x^4 - 275x^3 + 304x^2 + 17x - 43	\( 2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.12.3009103398689521267119563776.2	x^20 - x^19 - 5x^18 - 11x^17 - 3x^16 + 168x^15 - 51x^14 - 308x^13 - 442x^12 + 1047x^11 + 692x^10 - 1704x^9 - 61x^8 + 1089x^7 - 217x^6 - 311x^5 + 84x^4 + 55x^3 - 20x^2 - 2x + 1	\( 2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.3009103398689521267119563776.2	x^20 - 44x^16 - 22x^14 + 253x^12 + 121x^10 - 121x^8 - 726x^6 + 484x^2 + 121	\( 2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.8.3009103398689521267119563776.3	x^20 - x^19 - 5x^18 + 11x^17 - 25x^16 + 58x^15 - 51x^14 - 22x^13 + 31x^12 - 42x^11 + 560x^10 - 1473x^9 + 1589x^8 - 583x^7 - 855x^6 + 2054x^5 - 2259x^4 + 1617x^3 - 856x^2 + 295x - 43	\( 2^{10}\cdot 11^{18}\cdot 727^{2} \)	20T751	Trivial (GRH)
20.0.6965462128295683654948996096.5	x^20 - 3x^19 + x^18 + 26x^17 - 96x^16 + 191x^15 - 44x^14 - 676x^13 + 2492x^12 - 5379x^11 + 8623x^10 - 11136x^9 + 11981x^8 - 10163x^7 + 8050x^6 - 3668x^5 + 2997x^4 + 554x^3 + 1338x^2 + 686x + 593	\( 2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T751	$[2]$ (GRH)
20.8.6965462128295683654948996096.5	x^20 - 9x^19 + 26x^18 - 17x^17 - 21x^16 - 239x^14 + 1164x^13 - 1515x^12 + 1486x^11 - 6347x^10 + 14480x^9 - 16529x^8 + 20904x^7 - 35499x^6 + 33693x^5 - 5969x^4 - 12537x^3 + 8605x^2 - 1765x + 89	\( 2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T751	Trivial (GRH)
20.0.6965462128295683654948996096.6	x^20 - x^19 + 3x^18 - 11x^17 + 12x^16 + 2x^15 + 9x^14 + 23x^13 - 83x^12 + 77x^11 + 590x^10 - 913x^9 + 2621x^8 - 4347x^7 + 8288x^6 - 8424x^5 + 12027x^4 - 11924x^3 + 13150x^2 - 7824x + 3433	\( 2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T751	$[2]$ (GRH)
20.8.6965462128295683654948996096.6	x^20 - 2x^19 - 5x^18 + 31x^17 - 62x^16 - 85x^15 + 568x^14 - 894x^13 - 793x^12 + 5526x^11 - 7341x^10 - 3347x^9 + 25813x^8 - 33420x^7 + 926x^6 + 43095x^5 - 54931x^4 + 33723x^3 - 11202x^2 + 1913x - 131	\( 2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T751	Trivial (GRH)
20.12.9297543283501805026208859136.1	x^20 + 3x^18 - 31x^16 - 69x^14 + 277x^12 + 154x^10 - 1021x^8 + 1009x^6 - 361x^4 + 36x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.16.9297543283501805026208859136.1	x^20 - 8x^18 - 9x^16 + 140x^14 - 141x^12 - 297x^10 + 629x^8 - 432x^6 + 134x^4 - 19x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.4.9297543283501805026208859136.1	x^20 + 15x^18 + 83x^16 + 186x^14 + 7x^12 - 737x^10 - 1398x^8 - 1131x^6 - 410x^4 - 50x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.8.9297543283501805026208859136.1	x^20 + 11x^18 + 26x^16 - 88x^14 - 438x^12 - 484x^10 + 61x^8 + 297x^6 + 64x^4 - 22x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.12.9297543283501805026208859136.2	x^20 - 12x^18 + 21x^16 + 71x^14 - 137x^12 - 176x^10 + 217x^8 + 213x^6 - 37x^4 - 31x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.4.9297543283501805026208859136.2	x^20 - 3x^19 - 4x^18 + 29x^17 - 38x^16 - 14x^15 + 115x^14 - 123x^13 - 137x^12 + 136x^11 + 81x^10 - 395x^9 + 92x^8 + 343x^7 - 229x^6 - 945x^5 - 738x^4 - 264x^3 - 11x^2 - 6x - 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.8.9297543283501805026208859136.2	x^20 + 8x^18 + 2x^16 - 85x^14 - 108x^12 + 231x^10 + 409x^8 - 30x^6 - 207x^4 - 25x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.8.9297543283501805026208859136.3	x^20 - x^18 - 56x^16 + 49x^14 + 479x^12 + 341x^10 - 245x^8 - 337x^6 - 114x^4 - 9x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.8.9297543283501805026208859136.4	x^20 + 6x^18 - 47x^16 - 112x^14 + 153x^12 + 264x^10 - 158x^8 - 164x^6 + 61x^4 + 18x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.12.13483238599952325260241534976.4	x^20 - 6x^19 + 6x^18 + 44x^17 - 100x^16 - 44x^15 + 379x^14 - 370x^13 - 497x^12 + 1176x^11 - 301x^10 - 1288x^9 + 1443x^8 + 458x^7 - 1257x^6 + 304x^5 + 465x^4 - 394x^3 - 249x^2 - 12x + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.12.13483238599952325260241534976.5	x^20 - 10x^19 + 37x^18 - 44x^17 - 121x^16 + 590x^15 - 974x^14 + 176x^13 + 2093x^12 - 3664x^11 + 2295x^10 + 1070x^9 - 3655x^8 + 3378x^7 - 1051x^6 - 766x^5 + 1186x^4 - 718x^3 + 199x^2 - 24x + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.4.13483238599952325260241534976.6	x^20 - 2x^19 + x^18 + 20x^17 - 16x^16 - 32x^15 + 149x^14 + 52x^13 - 495x^12 + 436x^11 + 502x^10 - 2202x^9 + 924x^8 + 1926x^7 - 3829x^6 + 1462x^5 + 1119x^4 - 1710x^3 + 884x^2 - 246x + 67	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.4.13483238599952325260241534976.7	x^20 - 6x^19 + 6x^18 + 48x^17 - 176x^16 + 136x^15 + 580x^14 - 1854x^13 + 1688x^12 + 2626x^11 - 9977x^10 + 12802x^9 - 2698x^8 - 18940x^7 + 37486x^6 - 35210x^5 + 8013x^4 + 25224x^3 - 38321x^2 + 25944x - 7613	\( 2^{20}\cdot 11^{16}\cdot 23^{4} \)	20T751	Trivial (GRH)
20.0.158727102872609288730321224704.1	x^20 - 6x^19 + 25x^18 - 69x^17 + 110x^16 - 71x^15 - 8x^14 - 223x^13 + 1444x^12 - 3917x^11 + 6992x^10 - 9616x^9 + 12222x^8 - 15447x^7 + 18849x^6 - 19430x^5 + 17395x^4 - 15276x^3 + 12073x^2 - 6960x + 1979	\( 2^{10}\cdot 11^{16}\cdot 241^{4} \)	20T751	Trivial (GRH)
20.4.158727102872609288730321224704.1	x^20 - x^19 + 4x^18 + 27x^17 - 41x^16 + 80x^15 + 237x^14 - 579x^13 + 284x^12 + 1251x^11 - 2585x^10 - 1157x^9 + 6148x^8 + 475x^7 - 1067x^6 + 2276x^5 + 1937x^4 - 5626x^3 + 4456x^2 - 3720x + 1231	\( 2^{10}\cdot 11^{16}\cdot 241^{4} \)	20T751	Trivial (GRH)