Tenth degree number fields with quintic fields having one real place

In this paper, we enumerate all number fields of degree 10 of discriminant smaller than 1011 in absolute value containing a quintic field having one real place. For each one of the 21509 (resp. 18167) found fields of signature (0, 5) (resp. (2, 4)) the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discriminant, the corresponding polynomial over Q, and the Galois group of the Galois closure are given. In a supplementary section, we give the first coincidence of discriminant of 19 (resp. 20) nonisomorphic fields of signature (0, 5) (resp. (2, 4)).