Cannot enchant fishing rods on enchantment table with levels < 4

This report describes that the enchanting table does not show three enchantments for fishing rods if too few bookshelves are placed around it.

See MC-36937 for the bug that a first enchantment is shown despite it not being available.

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You cannot enchant fishing rods with enchantment levels < 4, as clicking the available does nothing. Tested in survival and creative