Arithmetic data for knotted graphs

The following tables contain arithmetic data on the hyperbolic structures with parabolic meridians for knotted trivalent graphs in the census of Heard, Hodgson, Martelli and Petonio.

theta_arith (data on theta curves)

handcuff_arith(data on handcuff graphs)

4vertex_arith (data on 4-vertex graphs)

Each row contains the following information:
name of graph; old file name and number; hyperbolic volume; details of invariant trace field: minimal polynomial, signature, discriminant, root number; whether all traces are algebraic integers; whether the group is arithmetic (after doubling to obtain a finite covolume group). The trace field is listed separately in the few cases where it is different to the invariant trace field.

For full details of the knotted graphs, including pictures and other invariants, see the preprint

Hyperbolic graphs of small complexity, by Heard, Hodgson, Martelli and Petronio (available here).