The refined Eisenstein conjecture
I have computed the torsion subgroup and component group of
hundreds of optimal quotients at prime level. In every example,
the same pattern emerges: the torsion subgroup is generated by
the image of 0-oo and has the same order as the component group;
furthermore, the product of the orders of the component groups
equals the numerator of (p-1)/12. This indicates that a refinement
of the conjecture of Ogg and other theorems proved by Mazur
may be true.
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