The totally real {$A\sb 5$} extension of degree {$6$} with minimum discriminant
Ford, David ; Pohst, Michael
Experiment. Math., Tome 1 (1992) no. 4, p. 231-235 / Harvested from Project Euclid
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We determine the totally real algebraic number field $F$ of degree 6 with Galois group $A_5$ and minimum discriminant, showing that it is unique up to isomorphism and that it is generated by a root of the polynomial $$ f(t) = t^6 - 10 t^4 + 7 t^3 + 15 t^2 - 14 t + 3 $$ over the rationals. We also list the fundamental units and class number of $F$, as well as data for several other fields that arose in our computations and that might be of interest.
Publié le : 1992-05-14
Classification:  11R80,  11R29,  11Y40 
@article{1048622026,
     author = {Ford, David and Pohst, Michael},
     title = {The totally real {$A\sb 5$} extension of degree {$6$} with minimum discriminant},
     journal = {Experiment. Math.},
     volume = {1},
     number = {4},
     year = {1992},
     pages = { 231-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1048622026}
}

Ford, David; Pohst, Michael. The totally real {$A\sb 5$} extension of degree {$6$} with minimum discriminant. Experiment. Math., Tome 1 (1992) no. 4, pp.  231-235. http://gdmltest.u-ga.fr/item/1048622026/