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Thanks hammerman.
The other koi are acting normally, which makes me think water is OK.
I inherited the fish when I bought the house. The filter is a large tank full of gravel, not like the modern stuff I see advertised. It keeps the water very clear apart from the inevitable blanketweed.
This particular koi has always been a bit of a loner, not going near the others, but it has never done anything like this before.
Trouble is, you can't just pop down to the vets, so I feel a bit helpless.