Corps sextiques primitifs
Annales de l'Institut Fourier, Volume 40 (1990) no. 4, p. 757-767
We describe four tables of primitive sextic fields (one for each signature). The tables provide for each field, the discriminant, the Galois group of the Galois closure and a polynomial which defines the sextic field.
Nous décrivons quatre tables de corps sextiques primitifs (une par signature). Les tables fournissent pour chaque corps, le discriminant, le groupe de Galois de la clôture galoisienne et un polynôme définissant le corps.
@article{AIF_1990__40_4_757_0,
     author = {Olivier, Michel},
     title = {Corps sextiques primitifs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {40},
     number = {4},
     year = {1990},
     pages = {757-767},
     doi = {10.5802/aif.1233},
     mrnumber = {92a:11123},
     zbl = {0734.11054},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_1990__40_4_757_0}
}
Corps sextiques primitifs. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 757-767. doi : 10.5802/aif.1233. https://aif.centre-mersenne.org/item/AIF_1990__40_4_757_0/

[1] A.-M. Bergé, J. Martinet et M. Olivier, The computation of sextic fields with a quadratic subfield, Math. Comp., 54 (1990), 869-884. | MR 90k:11169 | Zbl 0709.11056

[2] B. J. Birch et W. Kuyk, éd., Modular Functions of One Variable IV, dit "Anvers IV", Lectures Notes 476 (1975), Springer-Verlag, Heidelberg. | Zbl 0315.14014

[3] A. Brumer, Exercices diédraux et courbes à multiplications réelles, Actes du Séminaire de théorie des nombres de Paris (1989/1990), Birkhäuser, Boston, à paraître.

[4] G. Butler and J. Mckay, The transitive groups of degree up to eleven, Comm. Alg., 11 (1983), 863-911. | MR 84f:20005 | Zbl 0518.20003

[5] F. Diaz Y Diaz, Discriminant minimal et petits discriminants des corps de nombres de degré 7 avec 5 places réelles, J. London Math. Soc., 38 (1988), 33-46. | MR 90b:11113 | Zbl 0653.12003

[6] J. Martinet, Méthodes géométriques dans la recherche des petits discriminants, Progress in Mathematics, 59 (1985), 147-179, Birkhäuser. | MR 88h:11083 | Zbl 0567.12009

[7] M. Olivier, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. (à paraître). | Zbl 0746.11041

[8] M. Pohst, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory, 14 (1982), 99-117. | MR 83g:12009 | Zbl 0478.12005

[9] R. P. Stauduhar, The determination of Galois groups, Math. Comp., 27 (1973), 981-996. | MR 48 #6054 | Zbl 0282.12004