... proved

Much interesting new work has been done on related conjectures and problems.

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... Fix

This section is based on correspondence with Robert Pollack and Koopa Koo.

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... here

Add proof or good reference.

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... have

I copied this from Bertolini-Darmon, and I don't trust it exactly yet, especially because the line from Bertolini-Darmon for $\chi=1$ was wrong.

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... defined

When $E$ is defined over $\mathbb{Q}$ it is now known that $L(E,s)$ is defined overwhere.

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... point

This is not yet implemented in SAGE; if it were, there would be an example right here.

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