A023681 Discriminants of quartic fields with 2 complex conjugates (negated).

275, 283, 331, 400, 448, 475, 491, 507, 563, 643, 688, 731, 751, 775, 848, 976, 1024, 1099, 1107, 1156, 1192, 1255, 1323, 1328, 1371, 1375, 1399, 1423, 1424, 1456, 1472, 1472, 1475, 1588, 1600, 1728, 1732, 1775, 1791, 1792, 1823, 1856, 1879, 1927, 1931, 1963, 1968, 1975, 1984, 1984, 2000

Offset

1,1

References

I. Gaal, Diophantine Equations and Power Integral Bases: New Computational Methods, Springer 2002. See page 164.

M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, 1989, pp. 439-440.

Links

Robin Visser, Table of n, a(n) for n = 1..10000 (taken from the Jones-Roberts database)

J. Buchmann, D. Ford and M. Pohst, Enumeration of quartic fields of small discriminant, Math. Comp. 61 (1993), no. 204, 873-879.

J. W. Jones and D. P. Roberts, A database of number fields, LMS J. Comput. Math. 17 (2014), no. 1, 595-618.

Example

The field Q[x]/(x^4 - x^3 + 2*x - 1) is the quartic field with 2 complex conjugates with the smallest absolute discriminant of 275. - Robin Visser, Mar 27 2025

Crossrefs

Cf. A023680, A023682.

Sequence in context: A001242 A214111 A344731 * A070272 A066127 A062377

Adjacent sequences: A023678 A023679 A023680 * A023682 A023683 A023684

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Added "negated" to definition and added more terms from the Gaal reference. - Michel Marcus and N. J. A. Sloane, Apr 30 2016

More terms added by Robin Visser, Mar 27 2025, taken from the database of John Jones and David Roberts.

Status

approved