Number field search results

Results (9 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
20.0.320...000.1	x^20 - 10x^18 + 55x^16 - 200x^14 + 485x^12 - 798x^10 + 865x^8 - 420x^6 + 35x^4 + 50x^2 + 5	$20$	[0,10]	$2^{30}\cdot 5^{25}$	$2$	$21.1474252688$				$D_{20}$ (as 20T10)	trivial	$4$	$9$	$665063.298986$
20.2.400...000.1	x^20 - 5x^18 + 15x^14 - 120x^12 + 371x^10 - 505x^8 + 420x^6 - 140x^4 - 80x^2 - 16	$20$	[2,9]	$-\,2^{28}\cdot 5^{26}$	$2$	$21.3846919998$				$D_{20}$ (as 20T10)	trivial	$2$	$10$	$320036.323885$
20.2.351...875.1	x^20 - 5x^18 + 15x^16 - 18x^15 + 70x^14 + 360x^13 + 205x^12 - 225x^11 - 312x^10 - 630x^9 - 260x^8 + 450x^7 + 550x^6 + 342x^5 + 90x^4 - 180x^3 - 170x^2 - 45x + 1	$20$	[2,9]	$-\,5^{26}\cdot 11^{9}$	$2$	$23.8389824525$				$D_{20}$ (as 20T10)	trivial	$2$	$10$	$1089848.04881$
20.0.772...125.1	x^20 - 5x^17 + 25x^16 - 79x^15 + 120x^14 - 130x^13 + 160x^12 + 45x^11 - 39x^10 - 315x^9 + 810x^8 - 1330x^7 + 1810x^6 - 1714x^5 + 1445x^4 - 1055x^3 + 550x^2 - 255x + 81	$20$	[0,10]	$5^{25}\cdot 11^{10}$	$2$	$24.7975541901$				$D_{20}$ (as 20T10)	trivial	$2$	$9$	$2264798.97636$
20.2.558...771.1	x^20 - 8x^19 + 38x^18 - 133x^17 + 323x^16 - 570x^15 + 608x^14 + 608x^13 - 2280x^12 + 5662x^11 - 2527x^10 + 4731x^9 + 8265x^8 - 6935x^7 + 27265x^6 - 20539x^5 + 29469x^4 - 20178x^3 + 16226x^2 - 6696x + 729	$20$	[2,9]	$-\,7^{10}\cdot 19^{19}$	$2$	$43.3875313929$				$D_{20}$ (as 20T10)	trivial	$2$	$10$	$1336347065.64$
20.20.132...213.1	x^20 - 6x^19 - 26x^18 + 210x^17 + 139x^16 - 2755x^15 + 1437x^14 + 17203x^13 - 18778x^12 - 55009x^11 + 79884x^10 + 92609x^9 - 165018x^8 - 78936x^7 + 175998x^6 + 29276x^5 - 90960x^4 - 3681x^3 + 17377x^2 + 1089x - 103	$20$	[20,0]	$13^{10}\cdot 277^{9}$	$2$	$45.298891252$			?	$D_{20}$ (as 20T10)	trivial	$2$	$19$	$12870125339.9$
20.0.818...125.1	x^20 - 3x^19 + 5x^18 + 29x^17 + 2x^16 - 447x^15 + 1875x^14 - 2988x^13 - 797x^12 + 13317x^11 - 13069x^10 - 45010x^9 + 158294x^8 - 203394x^7 + 94740x^6 + 88164x^5 - 87665x^4 + 23262x^3 + 85694x^2 - 52120x + 15161	$20$	[0,10]	$5^{15}\cdot 401^{9}$	$2$	$49.618367447$	✓			$D_{20}$ (as 20T10)	$[404]$	$2$	$9$	$2526424.45141$
20.20.282...077.1	x^20 - 4x^19 - 42x^18 + 167x^17 + 590x^16 - 2576x^15 - 2936x^14 + 18115x^13 - 262x^12 - 56895x^11 + 34045x^10 + 71526x^9 - 65218x^8 - 32272x^7 + 41379x^6 + 787x^5 - 8208x^4 + 1108x^3 + 440x^2 - 113x + 7	$20$	[20,0]	$13^{9}\cdot 277^{10}$	$2$	$52.7854700266$			?	$D_{20}$ (as 20T10)	trivial	$2$	$19$	$84757731927.8$
20.0.328...125.1	x^20 - 4x^19 + 42x^18 - 108x^17 + 585x^16 - 1163x^15 + 4645x^14 - 10617x^13 + 31833x^12 - 75285x^11 + 168816x^10 - 330321x^9 + 666734x^8 - 1317875x^7 + 2500617x^6 - 4132047x^5 + 5546802x^4 - 5570593x^3 + 3798320x^2 - 1539672x + 282861	$20$	[0,10]	$5^{15}\cdot 401^{10}$	$2$	$66.9575708556$	✓			$D_{20}$ (as 20T10)	$[2, 808]$	$2$	$9$	$31495162.1453$