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
20.6.1108181030652775972732928.1	x^20 - 3x^18 - 2x^17 - 7x^16 + 18x^15 - 9x^14 + 10x^13 - 5x^12 - 40x^11 + 99x^10 - 150x^9 + 155x^8 - 78x^7 - 34x^6 + 162x^5 - 248x^4 + 192x^3 - 75x^2 + 14x - 1	\( -\,2^{20}\cdot 11^{16}\cdot 23 \)	20T749	Trivial (GRH)
20.4.11611809929883435192549376.1	x^20 - 4x^17 - 20x^14 + 44x^13 - 11x^12 + 16x^11 - 88x^10 + 264x^9 - 497x^8 + 572x^7 - 528x^6 + 384x^5 - 143x^4 - 88x^3 + 154x^2 - 44x - 11	\( 2^{20}\cdot 11^{16}\cdot 241 \)	20T749	Trivial (GRH)
20.8.11611809929883435192549376.1	x^20 - 5x^18 - 4x^17 + 4x^16 + 16x^15 + 16x^14 + 26x^13 - 214x^12 + 146x^11 + 368x^10 - 570x^9 - 103x^8 + 618x^7 - 214x^6 - 304x^5 + 216x^4 + 98x^3 - 69x^2 - 26x + 1	\( 2^{20}\cdot 11^{16}\cdot 241 \)	20T749	Trivial (GRH)
20.4.11611809929883435192549376.2	x^20 - 8x^19 + 27x^18 - 48x^17 + 59x^16 - 132x^15 + 358x^14 - 552x^13 + 336x^12 + 388x^11 - 1183x^10 + 1386x^9 - 921x^8 + 422x^7 - 316x^6 + 396x^5 - 335x^4 + 152x^3 - 28x^2 - 2x + 1	\( 2^{20}\cdot 11^{16}\cdot 241 \)	20T749	Trivial (GRH)
20.6.13167225195265942636954624.1	x^20 + x^18 + 3x^16 + 7x^14 - 3x^12 - 4x^10 - 13x^8 - 25x^6 + 7x^4 + 4x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.13167225195265942636954624.2	x^20 - 3x^16 - 11x^14 - 3x^12 + 88x^10 - 29x^8 - 143x^6 + 89x^4 + 11x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.13167225195265942636954624.3	x^20 - 5x^18 - 6x^16 + 54x^14 - 48x^12 - 44x^10 + 26x^8 + 43x^6 + 6x^4 - 27x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.8.22789983804294045004464128.1	x^20 - 2x^19 - 8x^18 + 14x^17 + 15x^16 - 50x^15 - 6x^14 + 90x^13 + x^12 - 44x^11 + 43x^10 + 38x^9 + 8x^8 + 8x^7 + 20x^6 + 20x^5 - 29x^4 - 24x^3 + 11x^2 + 4x - 1	\( 2^{20}\cdot 11^{17}\cdot 43 \)	20T749	Trivial (GRH)
20.2.35028156925416005746819072.1	x^20 - 2x^19 + 5x^18 + 6x^17 - 2x^16 + 42x^15 + 26x^14 + 44x^13 + 56x^12 + 224x^11 - 73x^10 + 224x^9 + 56x^8 + 44x^7 + 26x^6 + 42x^5 - 2x^4 + 6x^3 + 5x^2 - 2x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 727 \)	20T749	Trivial (GRH)
20.6.35028156925416005746819072.1	x^20 - 10x^19 + 38x^18 - 52x^17 - 65x^16 + 312x^15 - 293x^14 - 272x^13 + 660x^12 - 50x^11 - 688x^10 + 190x^9 + 823x^8 - 716x^7 - 145x^6 + 262x^5 + 346x^4 - 680x^3 + 489x^2 - 172x + 23	\( -\,2^{20}\cdot 11^{16}\cdot 727 \)	20T749	Trivial (GRH)
20.2.35028156925416005746819072.2	x^20 - 10x^19 + 45x^18 - 114x^17 + 140x^16 + 92x^15 - 754x^14 + 1604x^13 - 2033x^12 + 1774x^11 - 1276x^10 + 1074x^9 - 1111x^8 + 1014x^7 - 688x^6 + 318x^5 - 110x^4 + 44x^3 - 44x^2 + 22x - 11	\( -\,2^{20}\cdot 11^{16}\cdot 727 \)	20T749	Trivial (GRH)
20.6.35028156925416005746819072.2	x^20 - 8x^19 + 23x^18 - 4x^17 - 156x^16 + 446x^15 - 436x^14 - 380x^13 + 1303x^12 - 160x^11 - 4043x^10 + 8520x^9 - 9191x^8 + 5836x^7 - 2108x^6 + 522x^5 - 365x^4 + 290x^3 - 98x^2 + 8x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 727 \)	20T749	Trivial (GRH)
20.2.35028156925416005746819072.3	x^20 - 2x^19 - 7x^18 + 22x^17 + 4x^16 - 78x^15 + 54x^14 + 224x^13 - 562x^12 + 480x^11 - 68x^10 + 236x^9 - 1193x^8 + 1746x^7 - 1235x^6 + 496x^5 - 204x^4 + 132x^3 - 52x^2 + 6x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 727 \)	20T749	Trivial (GRH)
20.4.138811719535245546845372416.1	x^20 - 2x^19 - x^18 + 6x^17 + 9x^16 - 6x^15 - 9x^14 + 24x^13 - 106x^12 - 342x^11 - 435x^10 + 118x^9 + 1012x^8 + 1884x^7 + 2111x^6 + 1568x^5 + 600x^4 + 4x^3 - 78x^2 - 20x - 1	\( 2^{20}\cdot 11^{16}\cdot 43\cdot 67 \)	20T749	Trivial (GRH)
20.10.144839477147925369006500864.1	x^20 - x^18 - 15x^16 + 14x^14 + 69x^12 - 133x^10 - 110x^8 + 517x^6 - 495x^4 + 165x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.2.144839477147925369006500864.1	x^20 + 9x^18 + 39x^16 + 112x^14 + 257x^12 + 397x^10 + 462x^8 + 286x^6 - 44x^4 - 132x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.144839477147925369006500864.1	x^20 + 2x^18 - 16x^16 - 68x^14 - 73x^12 + 87x^10 + 297x^8 + 286x^6 + 88x^4 - 22x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.10.144839477147925369006500864.2	x^20 + x^18 - 4x^16 - 36x^14 + 14x^12 + 254x^10 - 319x^8 - 33x^6 + 88x^4 + 44x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.6.144839477147925369006500864.2	x^20 - 5x^19 + 13x^18 - 27x^17 + 44x^16 - 73x^15 + 171x^14 - 356x^13 + 559x^12 - 591x^11 + 120x^10 + 632x^9 - 1061x^8 + 858x^7 - 44x^6 - 254x^5 + 18x^4 + 17x^3 + 18x^2 - 9x + 1	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.8.144839477147925369006500864.1	x^20 - 9x^19 + 31x^18 - 41x^17 - 28x^16 + 164x^15 - 190x^14 - 27x^13 + 313x^12 - 330x^11 - 32x^10 + 396x^9 - 250x^8 - 124x^7 + 224x^6 - 51x^5 - 77x^4 + 40x^3 + 7x^2 - 7x + 1	\( 2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.0.302846179491116680649956352.1	x^20 + 5x^18 + 13x^16 + 22x^14 + 9x^12 + 37x^10 + 78x^8 + 33x^6 - 3x^4 + 23x^2 + 23	\( 2^{10}\cdot 11^{16}\cdot 23^{5} \)	20T749	$[2]$ (GRH)
20.4.302846179491116680649956352.1	x^20 - 12x^18 + 63x^16 - 198x^14 + 419x^12 - 631x^10 + 691x^8 - 550x^6 + 310x^4 - 115x^2 + 23	\( 2^{10}\cdot 11^{16}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.0.677291336864611819508989952.1	x^20 - 8x^19 + 35x^18 - 122x^17 + 383x^16 - 1034x^15 + 2360x^14 - 4772x^13 + 8949x^12 - 15162x^11 + 21609x^10 - 24558x^9 + 21924x^8 - 15712x^7 + 9497x^6 - 5028x^5 + 2277x^4 - 836x^3 + 253x^2 - 66x + 11	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.4.677291336864611819508989952.1	x^20 - 4x^19 - 5x^18 + 44x^17 - 28x^16 - 228x^15 + 640x^14 - 736x^13 + 613x^12 - 1596x^11 + 4180x^10 - 5988x^9 + 4760x^8 - 1890x^7 + 70x^6 + 184x^5 + 42x^4 - 78x^3 + 19x^2 + 2x - 1	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.8.677291336864611819508989952.1	x^20 - 8x^19 + 16x^18 + 36x^17 - 207x^16 + 336x^15 - 205x^14 + 170x^13 - 910x^12 + 1976x^11 - 1654x^10 - 442x^9 + 2245x^8 - 2032x^7 + 454x^6 + 582x^5 - 487x^4 + 112x^3 + 15x^2 - 10x + 1	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.0.677291336864611819508989952.2	x^20 - 2x^19 + 3x^18 - 4x^17 + 11x^16 - 20x^15 + 56x^14 - 102x^13 + 225x^12 - 302x^11 + 473x^10 - 472x^9 + 560x^8 - 352x^7 + 321x^6 - 32x^5 + 44x^4 + 88x^3 + 22x + 11	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.4.677291336864611819508989952.2	x^20 - 4x^19 + 6x^18 + 6x^17 - 9x^16 + 66x^15 - 202x^14 + 344x^13 - 397x^12 + 306x^11 - 225x^10 + 130x^9 + 205x^8 - 706x^7 + 884x^6 - 648x^5 + 242x^4 + 22x^3 - 77x^2 + 44x - 11	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.0.677291336864611819508989952.3	x^20 - 8x^19 + 38x^18 - 124x^17 + 317x^16 - 676x^15 + 1303x^14 - 2280x^13 + 3666x^12 - 5318x^11 + 6770x^10 - 7170x^9 + 6383x^8 - 5142x^7 + 3902x^6 - 2806x^5 + 1837x^4 - 968x^3 + 363x^2 - 88x + 11	\( 2^{20}\cdot 11^{16}\cdot 14057 \)	20T749	Trivial (GRH)
20.4.1405029001515895658298474496.1	x^20 - 8x^19 + 19x^18 + 10x^17 - 110x^16 + 122x^15 + 102x^14 - 124x^13 - 518x^12 + 792x^11 + 958x^10 - 3718x^9 + 3860x^8 + 8x^7 - 4639x^6 + 6172x^5 - 4444x^4 + 1968x^3 - 509x^2 + 58x + 1	\( 2^{20}\cdot 11^{18}\cdot 241 \)	20T749	Trivial (GRH)
20.10.3331307974402283487149519872.1	x^20 - 7x^19 + 17x^18 - 14x^17 + 9x^16 - 95x^15 + 244x^14 - 88x^13 - 198x^12 - 225x^11 + 329x^10 + 679x^9 - 396x^8 - 561x^7 + 51x^6 + 169x^5 + 67x^4 + 13x^3 + 2x^2 + 3x + 1	\( -\,2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.2.3331307974402283487149519872.1	x^20 - 5x^19 + 10x^18 + x^17 - 60x^16 + 171x^15 - 247x^14 - 4x^13 + 877x^12 - 2430x^11 + 3761x^10 - 3241x^9 - 707x^8 + 7783x^7 - 15249x^6 + 19250x^5 - 17674x^4 + 11921x^3 - 5555x^2 + 1562x - 197	\( -\,2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	$[2]$ (GRH)
20.10.3331307974402283487149519872.2	x^20 - 7x^19 + 24x^18 - 63x^17 + 123x^16 - 187x^15 + 282x^14 - 413x^13 + 570x^12 - 407x^11 + 252x^10 - 845x^9 + 454x^8 + 454x^7 + 299x^6 - 470x^5 - 232x^4 + 118x^3 + 48x^2 - x - 1	\( -\,2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.2.3331307974402283487149519872.2	x^20 - 5x^19 + 10x^18 - 8x^17 + 29x^16 - 117x^15 + 212x^14 - 216x^13 + 449x^12 - 883x^11 + 1079x^10 - 1452x^9 + 1861x^8 - 1653x^7 + 1348x^6 - 1076x^5 + 596x^4 - 231x^3 + 81x^2 - 23x - 1	\( -\,2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	$[2]$ (GRH)
20.12.3331307974402283487149519872.1	x^20 - 10x^18 + 29x^16 + 8x^14 - 195x^12 + 188x^10 + 902x^8 - 2728x^6 + 3069x^4 - 1518x^2 + 253	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.4.3331307974402283487149519872.1	x^20 - 8x^18 + 8x^16 + 106x^14 - 406x^12 + 386x^10 + 517x^8 - 946x^6 - 286x^4 + 638x^2 + 253	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.8.3331307974402283487149519872.1	x^20 - 17x^18 + 109x^16 - 331x^14 + 412x^12 + 309x^10 - 1771x^8 + 2332x^6 - 1067x^4 - 253x^2 + 253	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.12.3331307974402283487149519872.2	x^20 - 5x^19 + 8x^18 + 17x^17 - 128x^16 + 270x^15 - 148x^14 - 614x^13 + 1704x^12 - 1633x^11 - 232x^10 + 2736x^9 - 3292x^8 + 1713x^7 - 892x^6 + 798x^5 - 365x^4 + 7x^3 + 43x^2 - 12x + 1	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.4.3331307974402283487149519872.2	x^20 - 3x^19 + x^18 + 7x^17 - 10x^16 + 12x^15 - 23x^14 + 12x^13 - 15x^12 + 117x^11 - 208x^10 + 66x^9 + 95x^8 - 67x^7 - 4x^6 - 312x^5 + 605x^4 - 388x^3 + 241x^2 + 161x - 419	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	$[2]$ (GRH)
20.8.3331307974402283487149519872.2	x^20 - 7x^18 - 9x^16 + 61x^14 + 108x^12 - 131x^10 - 517x^8 - 242x^6 + 605x^4 + 759x^2 + 253	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.4.3331307974402283487149519872.3	x^20 - 5x^18 - 23x^16 + 144x^14 - 83x^12 - 551x^10 + 1100x^8 - 187x^6 - 1683x^4 + 1771x^2 + 253	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.8.3331307974402283487149519872.3	x^20 - 6x^19 + 7x^18 + 36x^17 - 119x^16 + 23x^15 + 388x^14 - 473x^13 - 378x^12 + 902x^11 + 232x^10 - 1034x^9 - 478x^8 + 1703x^7 - 284x^6 - 1113x^5 + 461x^4 + 386x^3 - 183x^2 - 40x + 1	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.8.3331307974402283487149519872.4	x^20 - 2x^19 - 17x^18 + 45x^17 + 66x^16 - 288x^15 + 69x^14 + 731x^13 - 917x^12 - 462x^11 + 1869x^10 - 1136x^9 - 1003x^8 + 1910x^7 - 824x^6 - 494x^5 + 791x^4 - 379x^3 + 44x^2 + 42x - 23	\( 2^{10}\cdot 11^{17}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.10.310114487798903480985555304448.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 233x^16 + 844x^15 - 1344x^14 + 146x^13 + 4020x^12 - 9274x^11 + 9966x^10 - 1656x^9 - 11045x^8 + 17316x^7 - 12163x^6 + 2060x^5 + 3613x^4 - 3318x^3 + 1030x^2 + 26x - 109	\( -\,2^{20}\cdot 11^{16}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.10.310114487798903480985555304448.2	x^20 - 2x^19 + 3x^18 - 4x^17 - 42x^16 + 34x^15 - 12x^14 - 38x^13 + 145x^12 + 732x^11 + 1386x^10 - 1638x^9 - 2924x^8 + 486x^7 + 537x^6 + 380x^5 + 777x^4 + 392x^3 + 47x^2 - 6x - 1	\( -\,2^{20}\cdot 11^{16}\cdot 23^{5} \)	20T749	Trivial (GRH)
20.10.164050564045619941441358756052992.1	x^20 - 8x^19 + 12x^18 + 44x^17 - 188x^16 + 372x^15 - 87x^14 - 1468x^13 + 3597x^12 - 4178x^11 + 1309x^10 + 5112x^9 - 7205x^8 + 1440x^7 + 3952x^6 - 3346x^5 + 62x^4 + 880x^3 - 299x^2 + 20x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)
20.14.164050564045619941441358756052992.1	x^20 - 4x^19 - 21x^18 + 68x^17 + 147x^16 - 308x^15 - 177x^14 + 556x^13 - 511x^12 - 174x^11 + 869x^10 - 174x^9 - 511x^8 + 556x^7 - 177x^6 - 308x^5 + 147x^4 + 68x^3 - 21x^2 - 4x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)
20.6.164050564045619941441358756052992.1	x^20 - 8x^19 + 48x^18 - 212x^17 + 747x^16 - 2218x^15 + 5300x^14 - 10874x^13 + 17055x^12 - 21060x^11 + 13387x^10 + 9816x^9 - 42832x^8 + 75706x^7 - 50153x^6 + 52442x^5 + 54384x^4 - 27680x^3 - 4063x^2 + 2748x + 263	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)
20.10.164050564045619941441358756052992.2	x^20 - 2x^19 - 5x^18 + 6x^17 - 38x^16 + 86x^15 - 86x^14 + 272x^13 + 565x^12 - 1322x^11 - 44x^10 + 848x^9 - 1324x^8 + 540x^7 + 855x^6 - 1056x^5 - 95x^4 + 398x^3 - 45x^2 - 28x + 1	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)
20.14.164050564045619941441358756052992.2	x^20 - 2x^19 - 28x^18 + 14x^17 + 286x^16 + 376x^15 - 1282x^14 - 3300x^13 + 2043x^12 + 9250x^11 + 1041x^10 - 8094x^9 - 4200x^8 - 6158x^7 - 2366x^6 + 13408x^5 + 8954x^4 - 5566x^3 - 4763x^2 + 220x + 473	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)
20.6.164050564045619941441358756052992.2	x^20 - 8x^19 + 27x^18 - 32x^17 - 80x^16 + 512x^15 - 1951x^14 + 7066x^13 - 19377x^12 + 28030x^11 + 21352x^10 - 207504x^9 + 491401x^8 - 566768x^7 + 74459x^6 + 782588x^5 - 1132323x^4 + 463204x^3 + 426643x^2 - 519028x + 150457	\( -\,2^{20}\cdot 11^{16}\cdot 23^{7} \)	20T749	Trivial (GRH)