The thaumaturge is confusing. The class progression table has "invocations" at several levels, and the entry for the ability does not state how many they know:
Thaumaturges control power in its purest form; whether through bargains with outsiders, the summoning of primal spirits, or simply an untamable spark in their soul, a thaumaturge can invoke a limited amount of truly wondrous power.
A thaumaturge may use invocations a number of times per day equal to his casting ability modifier, which refreshes when he rests to regain spell points. Whenever an invocation calls for a saving throw, the DC is equal to 10 + 1/2 the thaumaturge’s level + the thaumaturge’s casting ability modifier. A thaumaturge may only use invocations of his level or lower. Using an invocation is a free action that may be taken even when it isn't the Thaumaturge's turn.
I checked in the extra X feat section, and extra invocations only allows 2 more daily uses.
So I am prone to believe they know all invocations, but given the pattern from other PF/SP classes of pick N from the list below at the given levels the thaumaturge may seem to follow this, from the table progression.