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The problem of computing
has been solved by Stein (and
is implemented in MAGMA). Stein has not published the algorithm,
though he wrote it up.

**Problem 8.2.1**
Implement in

*SAGE* Stein's algorithm to compute

.

**Problem 8.2.2**
Design an algorithm to compute

. This would use
Ribet's theory in [

Rib92] combined with some ideas
related to splitting of quaternion algebras (see
[

GL01]).

**Problem 8.2.3**
Implement in *SAGE* a basic framework for computing with modular
abelian varieties. Stein implemented such a package in MAGMA. Much
of the solution could be simply a ``design document'' and some basic
classes.

There is also a paper of Calegari-Stein (unpublished) that goes into
great detail in one case.

**Problem 8.2.4**
Help finish Calegari-Stein.

William Stein
2006-10-20