Tricky, these slender Planktothrix -species.
But if they really are only 3 µm wide, have no particular features in end cells, no calyptra like Pl. prolifica, nor those characteristically elongated aerotopes like Pl. suspensa – then we are just stuck with the good old Plantktothrix agardhii. Sensu lato that is.
In lugol preserved samples the red color – which would reveal the true nature of Pl. profilica – can not either be observed.
So, to be on the safe side it’s better to call it Planktothrix cf. agardhii.
Literature:
KOMÁREK J. & ANAGNOSTIDIS K. (2005): Cyanoprokaryota 2. Teil/ 2nd Part: Oscillatoriales. – In: BÜDEL B., KRIENITZ L., GÄRTNER G. & SCHAGERL M. (eds): Süsswasserflora von Mitteleuropa 19/2, Elsevier/Spektrum, Heidelberg, 759 pp.