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The minimum discriminant of totally real octic fields

1990; Elsevier BV; Volume: 36; Issue: 2 Linguagem: Inglês

10.1016/0022-314x(90)90069-4

1096-1658

Michael Pohst, Jacques Martinet, Fredéric Diaz,

Coding theory and cryptography

The minimum discriminant of totally real octic algebraic number fields is determined. It is 282,300,416 and belongs to the ray class field over Q(√2) of conductor (7 + 2 √2): F = Q(√α) for α = (7 + 2 √2 + (1 + √2) √7 + 2 √2)/2. There is—up to isomorphy—only one field of that discriminant. The next two smallest discriminant values are 309,593,125 and 324,000,000. For each field we present a full system of fundamental units and its class number.