Computing ideals of a given norm in Quaternion algebra

asked 2 years ago

DrewC gravatar image

updated 2 years ago

slelievre gravatar image

Let B be the quaternion algebra over Q ramified at prime p and and OB be a maximal order. How do you compute all integral right ideals IO of a given norm?

Say l is prime. You know BrandtModule(p).hecke_matrix(l) returns l-Brandt matrix of B and we can draw the l-Brandt graph from it, then O is a vertex and there are l+1 integral right O-ideals of norm l representing each of edge from O in general. I'd like to compute these l-neighbors of O.

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