Let J be a Jacobian variety with toric reduction over a local field K. Let J → E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the functorially induced map φJ → φE on component groups of the Neron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which φJ → φE E is surjective and discuss when these criteria hold for the Jacobians of modular curves.
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