A006832 Discriminants of totally real cubic fields.

49, 81, 148, 169, 229, 257, 316, 321, 361, 404, 469, 473, 564, 568, 621, 697, 733, 756, 761, 785, 788, 837, 892, 940, 961, 985, 993, 1016, 1076, 1101, 1129, 1229, 1257, 1300, 1304, 1345, 1369, 1373, 1384, 1396, 1425, 1436, 1489, 1492, 1509, 1524

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			The field Q[x]/(x^3 - x^2 - 2*x + 1) is the totally real cubic field with the smallest discriminant of 49. - _Robin Visser_, Apr 17 2025
		

References

• Pohst and Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, page 436.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Robin Visser, Table of n, a(n) for n = 1..10000 (terms n = 1..130 from R. J. Mathar).
• K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), no. 219, 1213-1237.
• T. W. Cusick and L. Schoenfeld, A table of fundamental pairs of units in totally real cubic fields, Math. Comp. 48 (1987), 147-158.
• V. Ennola and R. Turunen, On totally real cubic fields, Math. Comp. 44 (1985), no. 170, 495-518.
• P. Llorente and J. Quer, On totally real cubic fields with discriminant D < 10^7, Math. Comp. 50 (1988), no. 182, 581-594.

Crossrefs

Cf. A023679, A278790.