Global number field search results

Further refine search

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 66)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.22905655334132142080000.1	x^20 - x^19 + x^18 - 6x^17 + 4x^16 + 4x^15 + 5x^14 - 14x^13 - 4x^12 + 19x^11 + 3x^10 - 62x^9 - 15x^8 + 52x^7 + 65x^6 + 34x^5 + 8x^4 + 3x^3 + 6x^2 + 3x + 1	\( 2^{15}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial
20.2.3734802819566549134737408.1	x^20 - 2x^19 + 4x^18 - 8x^17 + 6x^16 + 14x^15 - 58x^14 + 174x^13 - 423x^12 + 816x^11 - 1208x^10 + 1344x^9 - 1044x^8 + 308x^7 + 502x^6 - 788x^5 + 488x^4 - 138x^3 + 18x^2 - 4x + 1	\( -\,2^{30}\cdot 3^{7}\cdot 1123^{4} \)	20T804	Trivial (GRH)
20.2.3734802819566549134737408.2	x^20 - 6x^19 + 12x^18 - 4x^17 - 24x^16 + 46x^15 + 4x^14 - 108x^13 + 46x^12 + 186x^11 - 350x^10 + 152x^9 + 469x^8 - 650x^7 + 116x^6 + 400x^5 - 540x^4 + 54x^3 + 346x^2 - 70x - 83	\( -\,2^{30}\cdot 3^{7}\cdot 1123^{4} \)	20T804	Trivial (GRH)
20.0.6770156942057799680000000.1	x^20 - 2x^19 + 12x^18 - 26x^17 + 59x^16 - 126x^15 + 192x^14 - 324x^13 + 471x^12 - 568x^11 + 686x^10 - 654x^9 + 671x^8 - 616x^7 + 214x^6 - 194x^5 + 398x^4 - 254x^3 + 70x^2 - 10x + 1	\( 2^{30}\cdot 5^{7}\cdot 13^{4}\cdot 41^{4} \)	20T804	Trivial (GRH)
20.0.6770156942057799680000000.2	x^20 - 8x^19 + 36x^18 - 112x^17 + 289x^16 - 658x^15 + 1326x^14 - 2372x^13 + 3783x^12 - 5440x^11 + 7084x^10 - 8262x^9 + 8520x^8 - 7742x^7 + 6222x^6 - 4400x^5 + 2659x^4 - 1310x^3 + 498x^2 - 136x + 23	\( 2^{30}\cdot 5^{7}\cdot 13^{4}\cdot 41^{4} \)	20T804	Trivial (GRH)
20.0.9887242657808165864805153.1	x^20 - 2x^19 + 9x^17 - 17x^16 - 2x^15 + 37x^14 - 40x^13 - 5x^12 + 59x^11 - 47x^10 - 14x^9 + 25x^8 + 13x^7 + 78x^6 + 100x^5 + 104x^4 + 55x^3 + 23x^2 + 5x + 1	\( 3^{4}\cdot 17^{7}\cdot 4153^{4} \)	20T804	Trivial
20.0.23455391062151313489920000.1	x^20 - x^18 + 3x^16 + 2x^14 - 5x^12 + 15x^10 - 10x^8 + 8x^6 + 24x^4 - 16x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.4.23455391062151313489920000.1	x^20 - 10x^18 + 48x^16 - 151x^14 + 340x^12 - 561x^10 + 680x^8 - 604x^6 + 384x^4 - 160x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.0.23455391062151313489920000.2	x^20 + 2x^18 - 5x^16 - 11x^14 + 11x^12 + 43x^10 + 22x^8 - 44x^6 - 40x^4 + 32x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.4.23455391062151313489920000.2	x^20 - 3x^18 - 5x^16 + 32x^14 - 37x^12 - 71x^10 + 296x^8 - 444x^6 + 376x^4 - 176x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.0.23455391062151313489920000.3	x^20 + 8x^18 + 27x^16 + 53x^14 + 93x^12 + 195x^10 + 336x^8 + 352x^6 + 216x^4 + 96x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.4.23455391062151313489920000.3	x^20 - 12x^18 + 63x^16 - 203x^14 + 455x^12 - 747x^10 + 910x^8 - 812x^6 + 504x^4 - 192x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.4.23455391062151313489920000.4	x^20 + x^18 + 8x^16 + 3x^14 + 3x^12 - 11x^10 + 16x^8 + 4x^6 + 64x^4 - 96x^2 + 32	\( 2^{25}\cdot 5^{4}\cdot 5783^{4} \)	20T804	Trivial (GRH)
20.4.80539383770788832503762837.1	x^20 - 3x^19 + 5x^17 + 11x^16 - 2x^15 + 31x^14 - 11x^13 - 143x^12 - 82x^11 + 167x^10 + 124x^9 - 71x^8 - 41x^7 - 7x^6 - 14x^5 + 16x^4 + 5x^3 - x^2 + 3x - 1	\( 13^{7}\cdot 97^{4}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.6.127428669402529734781304832.2	x^20 - 4x^19 - 2x^18 + 36x^17 - 64x^16 - 18x^15 + 240x^14 - 408x^13 + 223x^12 + 376x^11 - 1000x^10 + 1154x^9 - 727x^8 + 132x^7 + 216x^6 - 216x^5 + 71x^4 + 18x^3 - 28x^2 + 10x - 1	\( -\,2^{30}\cdot 3^{9}\cdot 1567^{4} \)	20T804	Trivial (GRH)
20.6.342910396429794797621870592.2	x^20 - 8x^19 + 14x^18 + 46x^17 - 159x^16 - 92x^15 + 726x^14 - 20x^13 - 2003x^12 + 376x^11 + 3740x^10 - 354x^9 - 4893x^8 - 870x^7 + 4110x^6 + 2358x^5 - 1314x^4 - 1836x^3 - 720x^2 - 96x + 3	\( -\,2^{30}\cdot 3^{17}\cdot 223^{4} \)	20T804	Trivial (GRH)
20.4.770187838567219200000000000.1	x^20 - 6x^19 + 6x^18 + 48x^17 - 155x^16 + 16x^15 + 656x^14 - 958x^13 - 599x^12 + 2600x^11 - 1410x^10 - 1872x^9 + 2093x^8 + 228x^7 - 280x^6 - 1320x^5 + 1276x^4 - 258x^3 - 90x^2 + 20x + 5	\( 2^{30}\cdot 3^{6}\cdot 5^{11}\cdot 67^{4} \)	20T804	Trivial (GRH)
20.4.770187838567219200000000000.2	x^20 - 4x^19 + 4x^18 + 8x^17 - 15x^16 - 36x^15 + 64x^14 + 44x^13 - 242x^12 - 4x^11 + 408x^10 + 4x^9 - 242x^8 - 44x^7 + 64x^6 + 36x^5 - 15x^4 - 8x^3 + 4x^2 + 4x + 1	\( 2^{30}\cdot 3^{6}\cdot 5^{11}\cdot 67^{4} \)	20T804	Trivial (GRH)
20.0.1389444487197440029491200000.1	x^20 - 8x^18 + 22x^16 - 34x^15 - 68x^14 + 102x^13 + 81x^12 - 114x^11 + 454x^10 + 982x^9 + 1092x^8 + 3404x^7 + 6976x^6 + 9758x^5 + 13332x^4 + 17018x^3 + 17732x^2 + 12200x + 3721	\( 2^{30}\cdot 5^{5}\cdot 13^{4}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.12.2857413128106559934928689217.1	x^20 - 5x^19 - 9x^18 + 90x^17 - 58x^16 - 590x^15 + 1074x^14 + 1444x^13 - 5372x^12 + 1043x^11 + 11414x^10 - 11526x^9 - 6983x^8 + 17325x^7 - 6552x^6 - 4366x^5 + 3643x^4 - 406x^3 - 185x^2 + 18x + 1	\( 3^{4}\cdot 17^{9}\cdot 4153^{4} \)	20T804	Trivial (GRH)
20.8.6080288126995835830114472912.1	x^20 - 4x^19 + 3x^18 - 20x^17 + 79x^16 - 72x^15 + 120x^14 - 386x^13 + 384x^12 - 158x^11 - 237x^10 + 723x^9 - 494x^8 + 342x^7 - 61x^6 - 380x^5 + 165x^4 - 47x^3 - 6x^2 + 2x - 1	\( 2^{4}\cdot 53^{7}\cdot 4241^{4} \)	20T804	Trivial (GRH)
20.12.13611155857263312693135919453.1	x^20 - 12x^18 - 5x^17 + 45x^16 + 22x^15 - 75x^14 + 223x^13 + 466x^12 - 1337x^11 - 2860x^10 + 1281x^9 + 5752x^8 + 2419x^7 - 2291x^6 - 1705x^5 + 81x^4 + 251x^3 + 37x^2 - 5x - 1	\( 13^{9}\cdot 97^{4}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.0.14569381426075428763637645312.1	x^20 + 8x^18 + 28x^16 + 104x^14 + 360x^12 + 848x^10 + 1496x^8 + 1872x^6 + 1280x^4 + 384x^2 + 32	\( 2^{45}\cdot 13^{4}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.8.17546689939912502804480000000.1	x^20 - 10x^19 + 36x^18 - 30x^17 - 145x^16 + 304x^15 + 694x^14 - 3734x^13 + 6114x^12 - 2704x^11 - 5266x^10 + 8416x^9 - 3323x^8 - 1660x^7 + 1702x^6 - 1050x^5 + 1165x^4 - 258x^3 - 474x^2 + 210x + 13	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T804	Trivial (GRH)
20.8.17546689939912502804480000000.2	x^20 - 6x^19 + 8x^18 + 12x^17 - 60x^16 + 176x^15 - 418x^14 + 626x^13 - 563x^12 + 414x^11 - 164x^10 - 688x^9 + 1168x^8 - 212x^7 - 462x^6 + 62x^5 + 40x^4 + 110x^3 - 26x^2 - 20x + 1	\( 2^{30}\cdot 5^{7}\cdot 3803^{4} \)	20T804	Trivial (GRH)
20.8.93029066167317032621951684577.1	x^20 - 6x^19 + 15x^18 - 110x^16 + 344x^15 - 463x^14 - 169x^13 + 1704x^12 - 2748x^11 + 1233x^10 + 2492x^9 - 4964x^8 + 4152x^7 + 564x^6 - 4702x^5 + 3117x^4 - 749x^3 - 1176x^2 + 1313x + 169	\( 3^{4}\cdot 17^{7}\cdot 97^{2}\cdot 4153^{4} \)	20T804	Trivial (GRH)
20.4.234816118336367364984012800000.1	x^20 - 6x^19 + 4x^18 + 24x^17 - 2x^16 - 54x^15 - 50x^14 - 32x^13 - 722x^12 + 1424x^11 + 3738x^10 - 1104x^9 - 5565x^8 - 4246x^7 - 14422x^6 - 28294x^5 + 55230x^4 + 81154x^3 + 1850x^2 - 41408x - 15557	\( 2^{30}\cdot 5^{5}\cdot 13^{6}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.4.485822685091899819825439453125.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 479x^16 - 976x^15 + 1492x^14 - 1422x^13 - 392x^12 + 5160x^11 - 12784x^10 + 20728x^9 - 25522x^8 + 25308x^7 - 21158x^6 + 15263x^5 - 9312x^4 + 4500x^3 - 1560x^2 + 336x - 32	\( 3^{4}\cdot 5^{13}\cdot 23^{8}\cdot 89^{4} \)	20T804	Trivial (GRH)
20.0.1562252014965587119190673828125.1	x^20 - 2x^19 + x^18 - 18x^17 + 28x^16 + 37x^15 + 79x^14 - 240x^13 - 319x^12 - 82x^11 + 1821x^10 - 343x^9 + 2254x^8 - 16026x^7 + 36493x^6 - 64500x^5 + 94122x^4 - 96418x^3 + 73914x^2 - 38878x + 24331	\( 5^{13}\cdot 61^{6}\cdot 397^{4} \)	20T804	$[2]$ (GRH)
20.4.1562252014965587119190673828125.1	x^20 + 11x^18 - 27x^17 - 30x^16 - 232x^15 - 210x^14 - 124x^13 + 880x^12 + 369x^11 + 558x^10 - 1353x^9 - 1452x^8 - 314x^7 - 149x^6 + 1862x^5 + 167x^4 + 756x^3 - 159x^2 + 90x + 53	\( 5^{13}\cdot 61^{6}\cdot 397^{4} \)	20T804	$[2]$ (GRH)
20.12.2462225461006747461054762057728.1	x^20 - 12x^18 + 38x^16 - 296x^14 + 2896x^12 - 12152x^10 + 25992x^8 - 34736x^6 + 34320x^4 - 21632x^2 + 5408	\( 2^{45}\cdot 13^{6}\cdot 347^{4} \)	20T804	Trivial (GRH)
20.10.3045133133202651972569845989376.1	x^20 - 5x^18 - 34x^16 + 101x^14 + 386x^12 - 375x^10 - 1218x^8 + 443x^6 + 1124x^4 - 75x^2 - 1	\( -\,2^{36}\cdot 83^{4}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.10.3045133133202651972569845989376.2	x^20 - 5x^18 - 24x^16 + 95x^14 + 113x^12 - 338x^10 - 240x^8 + 320x^6 + 187x^4 - 37x^2 - 1	\( -\,2^{36}\cdot 83^{4}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.0.3950343780922120183946533203125.1	x^20 - 7x^19 + 19x^18 - 6x^17 - 110x^16 + 344x^15 - 337x^14 - 671x^13 + 2982x^12 - 4929x^11 + 3037x^10 + 4663x^9 - 13613x^8 + 13486x^7 + 4502x^6 - 34910x^5 + 60516x^4 - 66447x^3 + 54732x^2 - 32966x + 12443	\( 5^{13}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T804	$[2]$ (GRH)
20.4.3950343780922120183946533203125.1	x^20 - 2x^19 - 14x^18 + 27x^17 + 87x^16 - 155x^15 - 251x^14 + 350x^13 + 612x^12 - 315x^11 - 3546x^10 - 3522x^9 + 5218x^8 + 4396x^7 - 8664x^6 - 5440x^5 + 5818x^4 + 2562x^3 - 2400x^2 - 830x + 157	\( 5^{13}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T804	$[2]$ (GRH)
20.0.4372404165827098378428955078125.1	x^20 - x^19 + 2x^18 - 3x^17 + 18x^16 - 34x^15 + 42x^14 - 51x^13 + 94x^12 - 179x^11 + 228x^10 - 212x^9 + 115x^8 - 55x^7 + 180x^6 - 590x^5 + 1035x^4 - 1060x^3 + 650x^2 - 200x + 25	\( 3^{6}\cdot 5^{13}\cdot 23^{8}\cdot 89^{4} \)	20T804	$[2]$ (GRH)
20.12.5953585045674588487496499200000.1	x^20 - 24x^18 + 262x^16 - 1730x^14 + 7799x^12 - 25496x^10 + 59835x^8 - 91800x^6 + 78375x^4 - 28750x^2 + 3125	\( 2^{30}\cdot 5^{5}\cdot 36497^{4} \)	20T804	Trivial (GRH)
20.4.10367525357153855329853928112128.1	x^20 - 63x^16 + 122x^14 + 1155x^12 - 3654x^10 - 4357x^8 + 26704x^6 - 21794x^4 - 4046x^2 + 4913	\( 2^{20}\cdot 3^{4}\cdot 17^{7}\cdot 4153^{4} \)	20T804	Trivial (GRH)
20.0.24904860168174943560148881047552.1	x^20 + 8x^18 - 66x^16 - 497x^14 + 1260x^12 + 12574x^10 + 13313x^8 - 32876x^6 - 2915x^4 + 168540x^2 + 148877	\( 2^{16}\cdot 53^{7}\cdot 4241^{4} \)	20T804	Trivial (GRH)
20.0.26568108197548595633541786632192.1	x^20 + 24x^18 + 389x^16 + 4706x^14 + 38547x^12 + 208133x^10 + 738104x^8 + 1687099x^6 + 2359773x^4 + 1804918x^2 + 571787	\( 2^{20}\cdot 83^{7}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.0.26568108197548595633541786632192.2	x^20 + 19x^18 - 65x^16 - 1483x^14 + 8341x^12 + 16688x^10 - 169338x^8 + 98984x^6 + 866520x^4 - 1370911x^2 + 571787	\( 2^{20}\cdot 83^{7}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.0.26568108197548595633541786632192.3	x^20 + 40x^18 + 661x^16 + 5736x^14 + 26889x^12 + 56823x^10 - 19764x^8 - 293223x^6 - 310669x^4 + 275560x^2 + 571787	\( 2^{20}\cdot 83^{7}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.0.26568108197548595633541786632192.4	x^20 + 6x^18 - 236x^16 + 37x^14 + 17007x^12 - 93234x^10 + 148889x^8 + 130705x^6 - 541243x^4 + 110224x^2 + 571787	\( 2^{20}\cdot 83^{7}\cdot 983^{4} \)	20T804	Trivial (GRH)
20.4.55374574082926437693343023378125.1	x^20 - 8x^19 + 31x^18 - 82x^17 + 149x^16 - 325x^15 + 803x^14 - 1401x^13 + 977x^12 + 1395x^11 - 100x^10 - 5031x^9 + 4780x^8 + 3244x^7 + 4131x^6 + 1926x^5 + 1649x^4 + 716x^3 + 156x^2 + 19x + 1	\( 5^{5}\cdot 61^{10}\cdot 397^{4} \)	20T804	Trivial (GRH)
20.4.67818189235974116781402778056633.1	x^20 - 3x^19 + 9x^18 - 22x^17 - 85x^16 + 323x^15 - 905x^14 + 1420x^13 + 4054x^12 - 9823x^11 + 20495x^10 - 36252x^9 - 84009x^8 + 175959x^7 - 191010x^6 + 103206x^5 + 1774933x^4 - 1390951x^3 - 3945749x^2 + 1720233x + 3305893	\( 3^{10}\cdot 17^{7}\cdot 97^{2}\cdot 4153^{4} \)	20T804	$[2]$ (GRH)
20.4.109310104145677459460723876953125.1	x^20 - 5x^19 + 6x^18 + 42x^17 - 194x^16 + 286x^15 + 542x^14 - 2646x^13 + 4396x^12 - 410x^11 - 11360x^10 + 24527x^9 - 25338x^8 + 6420x^7 + 23867x^6 - 51534x^5 + 61726x^4 - 56047x^3 + 38917x^2 - 19558x + 6277	\( 3^{6}\cdot 5^{15}\cdot 23^{8}\cdot 89^{4} \)	20T804	$[2]$ (GRH)
20.4.140021329628125464191524995153125.1	x^20 - 2x^19 - 4x^18 + 27x^17 - 21x^16 - 212x^15 + 262x^14 + 1552x^13 - 398x^12 - 7151x^11 - 2083x^10 + 12227x^9 + 26908x^8 + 15592x^7 - 55616x^6 - 66315x^5 - 32222x^4 + 26316x^3 + 30850x^2 + 14893x + 2029	\( 5^{5}\cdot 61^{8}\cdot 97^{2}\cdot 397^{4} \)	20T804	Trivial (GRH)
20.8.232661492322232563893534720000000.1	x^20 - 3x^18 - 36x^16 - 149x^14 + 142x^12 + 1808x^10 + 1645x^8 - 2368x^6 - 4680x^4 + 1600x^2 + 2000	\( 2^{28}\cdot 5^{7}\cdot 57713^{4} \)	20T804	Trivial (GRH)
20.8.354164737431994968652745361328125.1	x^20 - 6x^19 + 4x^18 + 72x^17 - 332x^16 + 592x^15 + 664x^14 - 6779x^13 + 17531x^12 - 14690x^11 - 38498x^10 + 145502x^9 - 211414x^8 + 80164x^7 + 286423x^6 - 669021x^5 + 759600x^4 - 511875x^3 + 191745x^2 - 29025x - 675	\( 3^{10}\cdot 5^{13}\cdot 23^{8}\cdot 89^{4} \)	20T804	Trivial (GRH)
20.4.1731773388610969272320000000000000.1	x^20 + 16x^16 - 458x^14 + 268x^12 - 5858x^10 + 44349x^8 - 63932x^6 + 184490x^4 - 585180x^2 + 262205	\( 2^{30}\cdot 5^{13}\cdot 6029^{4} \)	20T804	$[3]$ (GRH)