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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.109115950462157402855641.1	x^20 + 3x^18 + 6x^16 + 11x^14 + 26x^12 + 48x^10 + 60x^8 + 55x^6 + 32x^4 + 20x^2 + 1	\( 11^{16}\cdot 23^{2}\cdot 67^{2} \)	20T341	Trivial
20.4.109115950462157402855641.1	x^20 - 2x^19 + 2x^18 + 2x^17 - 9x^16 + 2x^15 + 5x^14 - 7x^13 - 3x^12 + 5x^11 + 7x^10 + 5x^9 - 3x^8 - 7x^7 + 5x^6 + 2x^5 - 9x^4 + 2x^3 + 2x^2 - 2x + 1	\( 11^{16}\cdot 23^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.4.109115950462157402855641.2	x^20 - x^19 + 6x^18 - 8x^17 + 18x^16 - 13x^15 + 25x^14 + 10x^13 - 23x^12 + 65x^11 - 103x^10 + 107x^9 - 130x^8 + 94x^7 - 65x^6 + 53x^5 - 12x^4 + 5x^3 - 3x^2 - 4x + 1	\( 11^{16}\cdot 23^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.381390155774156971417921.1	x^20 - 3x^19 - x^18 + 10x^17 - 7x^16 - 7x^15 + 31x^14 - 30x^13 - 75x^12 + 104x^11 + 88x^10 - 139x^9 - 15x^8 + 81x^7 - 63x^6 - 18x^5 + 56x^4 + 2x^3 - 16x^2 - x + 1	\( 11^{16}\cdot 43^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.25488163705013847372857344.4	x^20 - 5x^18 + 4x^16 + 3x^14 + x^12 - 7x^10 + x^8 + 3x^6 + 4x^4 - 5x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T341	Trivial (GRH)
20.12.46148208848672993541568441.1	x^20 - x^19 - 6x^18 + 13x^17 - 4x^16 - 21x^15 - 17x^14 + 65x^13 + 252x^12 - 674x^11 + 87x^10 + 1178x^9 - 1094x^8 - 343x^7 + 983x^6 - 397x^5 - 148x^4 + 177x^3 - 54x^2 + 3x + 1	\( 11^{18}\cdot 43^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.57722337794481266110634089.4	x^20 - 5x^19 + 3x^18 + 14x^17 + 4x^16 - 66x^15 - 2x^14 + 158x^13 - 7x^12 - 227x^11 - 110x^10 + 430x^9 + 47x^8 - 332x^7 - 85x^6 + 165x^5 + 67x^4 - 39x^3 - 18x^2 + 2x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.57722337794481266110634089.5	x^20 - 2x^19 + 3x^18 + 3x^16 + 12x^15 + 16x^14 + 69x^13 + 79x^12 + 29x^11 + 37x^10 - 29x^9 + 79x^8 - 69x^7 + 16x^6 - 12x^5 + 3x^4 + 3x^2 + 2x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.8.57722337794481266110634089.5	x^20 - 5x^19 + 11x^18 - 12x^17 - 9x^16 + 13x^15 + 26x^14 + 61x^13 - 130x^12 - 65x^11 + 37x^10 + 147x^9 + 87x^8 - 177x^7 - 32x^6 + 2x^5 + 41x^4 + 28x^3 - 22x^2 - 4x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.57722337794481266110634089.6	x^20 + 13x^18 + 73x^16 + 235x^14 + 481x^12 + 660x^10 + 633x^8 + 445x^6 + 296x^4 + 43x^2 + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.4.57722337794481266110634089.6	x^20 - x^19 - 12x^18 + 17x^17 + 63x^16 - 92x^15 - 141x^14 + 314x^13 + 171x^12 - 496x^11 - 121x^10 + 496x^9 + 171x^8 - 314x^7 - 141x^6 + 92x^5 + 63x^4 - 17x^3 - 12x^2 + x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.57722337794481266110634089.6	x^20 - 4x^19 + 2x^18 + 14x^17 - 51x^16 + 74x^15 + 75x^14 - 309x^13 + 242x^12 + 186x^11 - 664x^10 - 182x^9 + 1507x^8 + 433x^7 - 2361x^6 + 355x^5 + 1054x^4 - 482x^3 + 129x^2 - 19x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.57722337794481266110634089.7	x^20 - 10x^19 + 52x^18 - 180x^17 + 461x^16 - 899x^15 + 1328x^14 - 1354x^13 + 507x^12 + 1410x^11 - 3813x^10 + 5599x^9 - 5270x^8 + 2768x^7 + 1115x^6 - 4240x^5 + 5356x^4 - 4383x^3 + 2573x^2 - 1021x + 197	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.4.57722337794481266110634089.7	x^20 - 2x^19 + 11x^18 - 2x^17 + 17x^16 + 53x^15 - 6x^14 + 113x^13 + 51x^12 + 19x^11 + 125x^10 - 104x^9 + 39x^8 - 145x^7 - 85x^6 - 35x^5 - 89x^4 - 30x^3 + x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.8.57722337794481266110634089.7	x^20 - 3x^19 - 2x^18 + 2x^17 + 11x^16 + 11x^15 - 41x^14 - 65x^13 - 65x^12 + 113x^11 + 172x^10 - 51x^9 - 184x^8 - 40x^7 + 258x^6 + 539x^5 + 77x^4 - 588x^3 - 305x^2 + 28x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.57722337794481266110634089.8	x^20 - 2x^19 + 8x^18 - 8x^17 + 19x^16 + 22x^15 + x^14 + 90x^13 - 10x^12 + 102x^11 + 95x^10 - 124x^9 + 320x^8 - 431x^7 + 694x^6 - 363x^5 + 591x^4 - 322x^3 + 195x^2 - 20x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.4.57722337794481266110634089.8	x^20 - x^19 - 7x^18 + x^17 + 38x^16 - 38x^15 - 91x^14 + 124x^13 + 237x^12 - 361x^11 - 232x^10 + 418x^9 + 132x^8 + 143x^7 - 561x^6 - 264x^5 + 605x^4 + 242x^3 - 363x^2 - 121x + 121	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.4.57722337794481266110634089.9	x^20 - 5x^19 + 11x^18 - 12x^17 + 13x^16 - 42x^15 + 92x^14 - 93x^13 + 24x^12 - 32x^11 + 169x^10 - 194x^9 + 10x^8 + 142x^7 + 89x^6 - 174x^5 - 135x^4 + 61x^3 + 44x^2 + 7x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.216288028113057014852091904.1	x^20 + 4x^16 + 33x^14 + 46x^12 + 44x^10 + 72x^8 + 77x^6 + 42x^4 + 11x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.0.381647910600027760000761856.3	x^20 + 4x^18 + 7x^16 + 11x^14 + 14x^12 + 15x^10 + 14x^8 + 11x^6 + 7x^4 + 4x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 89^{2} \)	20T341	$[4]$ (GRH)
20.12.572447775008070927479996416.2	x^20 - 9x^18 + 42x^16 - 149x^14 + 377x^12 - 590x^10 + 543x^8 - 293x^6 + 91x^4 - 15x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T341	Trivial (GRH)
20.12.572447775008070927479996416.3	x^20 - 3x^18 + 12x^16 - 32x^14 - 2x^12 + 70x^10 - 17x^8 - 68x^6 + 49x^4 - 12x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T341	Trivial (GRH)
20.0.10779662339431083287111532544.1	x^20 + 8x^18 + 20x^16 + 28x^14 + 59x^12 + 131x^10 + 179x^8 + 156x^6 + 82x^4 + 18x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	$[2]$ (GRH)
20.4.10779662339431083287111532544.1	x^20 - 4x^18 - 6x^16 + 57x^14 - 74x^12 - x^10 + 37x^8 - 104x^6 + 75x^4 + 19x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.0.10779662339431083287111532544.2	x^20 + 13x^18 + 70x^16 + 206x^14 + 368x^12 + 406x^10 + 251x^8 + 73x^6 + 14x^4 + 6x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	$[2]$ (GRH)
20.4.10779662339431083287111532544.2	x^20 - x^18 - 10x^16 - x^14 + x^12 - 23x^10 + x^8 - x^6 - 10x^4 - x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.4.10779662339431083287111532544.3	x^20 + 10x^18 + 23x^16 - x^14 - 32x^12 - 45x^10 - 32x^8 - x^6 + 23x^4 + 10x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.4.10779662339431083287111532544.4	x^20 + 2x^18 - 18x^16 + 52x^14 - 72x^12 + 32x^10 + 9x^8 - 48x^6 - 8x^4 + 6x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.8.10779662339431083287111532544.5	x^20 - 3x^18 - 24x^16 + 6x^14 + 169x^12 + 65x^10 - 305x^8 + 2x^6 - 17x^4 - 4x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.12.10779662339431083287111532544.6	x^20 - x^18 + x^16 - 34x^14 + 45x^12 - 45x^10 + 298x^8 - 375x^6 + 155x^4 - 23x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.8.10779662339431083287111532544.6	x^20 - 5x^18 + 14x^16 - 4x^14 - 24x^12 - 12x^10 - 6x^8 + 63x^6 + 4x^4 - 9x^2 + 1	\( 2^{20}\cdot 11^{18}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.0.16943076141218174697198321664.1	x^20 + 11x^18 + 38x^16 + 77x^14 + 109x^12 + 121x^10 + 109x^8 + 77x^6 + 38x^4 + 11x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 593^{2} \)	20T341	$[10]$ (GRH)
20.16.25465470084777436177937465344.1	x^20 - 20x^18 + 161x^16 - 667x^14 + 1515x^12 - 1892x^10 + 1315x^8 - 567x^6 + 175x^4 - 23x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 727^{2} \)	20T341	Trivial (GRH)
20.4.46179397182603358960092184576.2	x^20 + 22x^16 - 44x^14 + 231x^12 - 627x^10 + 1573x^8 - 2904x^6 + 2904x^4 - 1210x^2 + 121	\( 2^{20}\cdot 11^{18}\cdot 89^{2} \)	20T341	Trivial (GRH)
20.4.47127614690570603792413229056.1	x^20 - 3x^18 + 2x^16 - 8x^14 + 2x^12 - 11x^10 + 2x^8 - 8x^6 + 2x^4 - 3x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 43^{2} \)	20T341	Trivial (GRH)
20.16.85328038161196365058360047409.1	x^20 - 5x^19 - 4x^18 + 44x^17 - 5x^16 - 118x^15 - 24x^14 - 33x^13 + 421x^12 + 821x^11 - 1266x^10 - 1964x^9 + 1566x^8 + 2387x^7 - 842x^6 - 1631x^5 + 167x^4 + 572x^3 - 14x^2 - 73x + 1	\( 11^{18}\cdot 43^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.20.437402377341742634765604880384.1	x^20 - 21x^18 + 170x^16 - 713x^14 + 1721x^12 - 2479x^10 + 2121x^8 - 1035x^6 + 265x^4 - 30x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 131^{2} \)	20T341	Trivial (GRH)
20.20.4474727508215936058626208169984.1	x^20 - 20x^18 + 164x^16 - 715x^14 + 1798x^12 - 2644x^10 + 2204x^8 - 979x^6 + 226x^4 - 25x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 419^{2} \)	20T341	Trivial (GRH)
20.0.89224910880483379681166705557504.1	x^20 - 6x^19 - x^18 + 74x^17 - 83x^16 - 408x^15 + 860x^14 + 572x^13 - 1375x^12 - 6690x^11 + 21065x^10 - 24252x^9 + 30228x^8 - 73634x^7 + 184343x^6 - 315514x^5 + 483947x^4 - 450102x^3 + 380763x^2 - 164600x + 108019	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 1871^{2} \)	20T341	$[2, 36]$ (GRH)
20.0.89224910880483379681166705557504.2	x^20 + 20x^18 + 174x^16 + 886x^14 + 3105x^12 + 6464x^10 + 18132x^8 + 91406x^6 + 289754x^4 + 444360x^2 + 279841	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 1871^{2} \)	20T341	$[72]$ (GRH)