Definite Eichler Orders with Class Number At Most Two

Information: In these tables, we list all (totally) definite Eichler orders with class number at most two.

Each Eichler order O is specified by the data

   n, d_F, D, N, f, frakD, frakN

where:

• n is the degree [F:Q];
• d_F is the discriminant of F;
• D is the norm of the discriminant frakD of B;
• N is the norm of the level frakN of O;
• f is a minimal polynomial for F with the convention:

  [a[0],a[1],...,a[n]] corresponds to a[n]*x^n + ... + a[1]*x + a[0];

• frakD is the discriminant of B, an ideal of the ring of integers of F, specified by (at most two) generators, with the convention:

  [b[0],...,b[n-1]] corresponds to b[0] + b[1]*alpha + ... + b[n-1]*alpha^n

  where alpha is a root of f (e.g. [[1,0,...,0]] is the unit ideal); and
• frakN is the level of O, an ideal with the same conventions as frakD.

Definite Eichler orders with class number 1

Definite Eichler orders with class number 2