Shimura Curves of Genus At Most Two

Information: In these tables, we list all Shimura curves of genus at most two.

[PDF] Shimura Curves of Genus at most Two (with description)

Here is also a computer-readable file. Each Shimura curve X is specified by the data

   n, d_F, D, N, sigma, 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 X;
• sigma is the signature of X, where X has genus g, exactly t elliptic cycles of orders m_1, ..., m_t [and s parabolic cycles];
• 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-1)

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

[TXT] Shimura Curves of Genus at most Two