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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.
Implement in SAGE
Stein's algorithm to compute
Design an algorithm to compute
. This would use
Ribet's theory in [Rib92
] combined with some ideas
related to splitting of quaternion algebras (see
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
There is also a paper of Calegari-Stein (unpublished) that goes into
great detail in one case.
Help finish Calegari-Stein.