You need to think slightly differently to what you've said there. Issues do not belong to a board. They are selected by a board. The difference is important because you need to understand that boards are not issues containers (projects contain issues), they are views of a selection of issues.
It is hard to ask "what board is an issue shown on" because the issue is not part of a board, and has no data to say "I am on boards x, y and z".
You can easily go the other way though, and ask "what issues are on a board", as the board knows what it is selecting for.
I'm not sure which of these might be best for you:
You'll see they're all on the same page of the docs and there are more calls that might help explained on the left.
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