Number field search results

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

Results (6 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
17.1.133...504.1	$x^{17} - 3 x^{16} - 4 x^{14} + 12 x^{13} + 24 x^{12} + 12 x^{11} - 28 x^{10} - 90 x^{9} - 74 x^{8} + 116 x^{6} + 132 x^{5} + 72 x^{4} + 28 x^{3} + 12 x^{2} + 5 x + 1$	$17$	[1,8]	$2^{30}\cdot 137^{8}$	$2$	$34.4147774247$				?	$\PSL(2,16)$ (as 17T6)	$[15]$	$2$	$8$	$810656.541895$
17.1.861...144.1	$x^{17} - x^{16} - 4 x^{15} + 2 x^{14} + 54 x^{13} - 6 x^{12} - 36 x^{11} + 16 x^{10} + 714 x^{9} + 1238 x^{8} + 484 x^{7} - 764 x^{6} - 1084 x^{5} + 520 x^{4} + 668 x^{3} - 776 x^{2} + 382 x - 74$	$17$	[1,8]	$2^{30}\cdot 173^{8}$	$2$	$38.408519781$				?	$\PSL(2,16)$ (as 17T6)	$[15]$	$2$	$8$	$781146.759847$
17.1.264...424.1	$x^{17} - 2 x^{16} - 14 x^{15} + 16 x^{14} + 116 x^{13} - 92 x^{12} - 520 x^{11} - 12 x^{10} + 612 x^{9} - 1488 x^{8} - 1540 x^{7} - 180 x^{6} + 1580 x^{5} - 1192 x^{4} + 1608 x^{3} - 844 x^{2} + 122 x - 40$	$17$	[1,8]	$2^{30}\cdot 199^{8}$	$2$	$41.0244357557$				?	$\PSL(2,16)$ (as 17T6)	$[15]$	$2$	$8$	$5943625.48287$
17.1.397...976.1	$x^{17} + 221 x^{15} - 850 x^{14} + 19601 x^{13} - 97036 x^{12} + 2452233 x^{11} - 5536254 x^{10} + 159332007 x^{9} - 1851117488 x^{8} + 12939379031 x^{7} - 45700927246 x^{6} + 12487240571 x^{5} + 217180838276 x^{4} - 328446625597 x^{3} + 138506493022 x^{2} + 2281813189964 x + 1767616042808$	$17$	[1,8]	$2^{24}\cdot 17^{32}$	$2$	$550.963297739$	$585.7120239053163$				$D_{17}$ (as 17T2)	$[17]$	$2$	$8$	$5054960379310000000$
17.17.897...201.1	$x^{17} - 4 x^{16} - 476 x^{15} + 3026 x^{14} + 82996 x^{13} - 736812 x^{12} - 6121180 x^{11} + 80531352 x^{10} + 108448584 x^{9} - 4267795762 x^{8} + 9723361580 x^{7} + 95353221324 x^{6} - 524744382701 x^{5} - 7660737412 x^{4} + 6800548404356 x^{3} - 21491689501032 x^{2} + 27480501953536 x - 12878683864992$	$17$	[17,0]	$17^{12}\cdot 137^{16}$	$2$	$757.850081803$	$858.752101911667$				$C_{17}:C_{4}$ (as 17T3)	$[17]$	$2$	$16$	$31945964915800000000$
17.17.544...441.1	$x^{17} - 3502 x^{15} - 21012 x^{14} + 3586048 x^{13} + 27140500 x^{12} - 1455974010 x^{11} - 13391942168 x^{10} + 247158969538 x^{9} + 2699830692822 x^{8} - 15367054046543 x^{7} - 210262575924428 x^{6} + 207808365630713 x^{5} + 5600534069106679 x^{4} + 891648638079425 x^{3} - 50160692092741008 x^{2} - 11309428987726617 x + 145001801906376687$	$17$	[17,0]	$17^{24}\cdot 103^{16}$	$2$	$4280.94250015$	$4652.957318416284$				$D_{17}$ (as 17T2)	$[17]$	$2$	$16$	$10720674608800000000000000$