Hi Michael and Sheldon,

Loic Merel and I spent some time today thinking about torsion on J_1(29).

By reducing mod p and taking into account Kubert-Lang, we get that
J_1(p)'s torsion is Q-rational for p<29, but for p=29 maybe there is
some 2-torsion that isn't rational.  After thinking about the problem
today, one little observation is that (1) it is possible to explicitly
compute the kernel of the Eisenstein ideal, and (2) the torsion is
contained in there, (3) it looks very likely that in the case p=29 the
kernel of the Eisenstein ideal is the cuspidal subgroup, and (4) we
can compute the action of Galois on the cuspidal subgroup.  I just
need to do some more subtle calculations to fully verify (3), which
gives me ideas to improve Sage's modular abelian varieties code.
Anyway, combining (1)-(4) is highly likely to resolve this question
for p=29.