Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (12 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
19.1.108...235.1	$x^{19} + 4 x - 1$	$19$	[1,9]	$-\,5\cdot 21\!\cdots\!47$	$2$	$61.8394363547$	$1.0399739563796986e+17$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$3430870317.91$
19.1.548...691.1	$x^{19} - 8 x - 9$	$19$	[1,9]	$-\,3^{24}\cdot 17\cdot 114155336693962142789083$	$3$	$76.0312939731$				?	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$18850130609.9$
19.1.239...280.1	$x^{19} + 6 x - 2$	$19$	[1,9]	$-\,2^{18}\cdot 5\cdot 31\cdot 257\cdot 6421\cdot 357578538648256624004557$	$6$	$92.7591546367$	$1.8441904977555664e+16$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$127473044450$
19.1.448...611.1	$x^{19} + 7 x - 1$	$19$	[1,9]	$-\,79\cdot 457\cdot 2027\cdot 182271319\cdot 561194741\cdot 59915457959389$	$6$	$108.21901362$	$2.117795036284736e+19$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$392294002413$
19.1.567...707.1	$x^{19} + 8 x - 1$	$19$	[1,9]	$-\,107\cdot 179\cdot 13183\cdot 140863\cdot 7165345423\cdot 22249984821389557$	$6$	$123.678872708$	$7.530215800281381e+19$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$1856682201710$
19.1.567...704.1	$x^{19} + 8 x - 2$	$19$	[1,9]	$-\,2^{18}\cdot 17\cdot 3463\cdot 7850009647\cdot 46806193038519194243$	$5$	$123.678872709$	$2.8361145837072944e+17$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$1117452131830$
19.1.351...704.1	$x^{19} - 7 x - 8$	$19$	[1,9]	$-\,2^{18}\cdot 1361\cdot 391137217\cdot 252180218096897279266793$	$4$	$136.151698449$	$7.327893298501467e+17$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$9970435330430$
19.1.356...760.1	$x^{19} + x - 8$	$19$	[1,9]	$-\,2^{18}\cdot 5\cdot 11\cdot 165384991\cdot 356502401\cdot 41925381140419433$	$6$	$136.242478613$	$7.3744413619255e+17$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$17797340693500$
19.1.531...715.1	$x^{19} + 9 x - 1$	$19$	[1,9]	$-\,5\cdot 7\cdot 23\cdot 197\cdot 229\cdot 457\cdot 7103\cdot 1661447\cdot 271375524417386192423$	$9$	$139.138731797$	$2.3054535981619066e+20$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$5318854980550$
19.1.887...072.1	$x^{19} + 9 x - 8$	$19$	[1,9]	$-\,2^{18}\cdot 7\cdot 17\cdot 47\cdot 6641419\cdot 22648163\cdot 402616284516711953$	$7$	$142.947763604$	$1.1639786242120543e+18$			✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$16296083868500$
19.1.296...203.1	$x^{19} - 4 x - 9$	$19$	[1,9]	$-\,3^{37}\cdot 659473194534239850398681$	$2$	$152.325572689$				✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$40674388401700$
19.1.296...715.1	$x^{19} + 4 x - 9$	$19$	[1,9]	$-\,3^{36}\cdot 5\cdot 395683945543581525410383$	$3$	$152.325573273$				✓	$S_{19}$ (as 19T8)	$[2]$	$2$	$9$	$12360677081400$