The designation P-40J was given to a projected version of the P-40E which was to have a turbosupercharged engine.
This study was abandoned in May 1942 without anything ever being built.
Sources:
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War Planes of the Second World War, Fighters, Volume Four, William Green,
Doubleday, 1964.
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The American Fighter, Enzo Anguluci and Peter Bowers, Orion Books, 1987.
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United States Military Aircraft since 1909, Gordon Swanborough and Peter
M. Bowers, Smithsonian Institution Press, 1989.
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Curtiss Aircraft, 1907-1947, Peter M. Bowers, Naval Institute Press, 1979.
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The Curtiss P-40 Tomahawk, Ray Wagner, Aircraft in Profile, Volume 2,
Doubleday, 1965.