Elliptical poetry is poetry that is oblique and without prosaic information or a logical sequence of meaning.
From A Poet’s Glossary
The following definition of the term elliptical poetry is reprinted from A Poet's Glossary by Edward Hirsch.
In The Idiom of Poetry (1946), Frederick Pottle used the term elliptical for a kind of pure poetry that omits prosaic information. He recognized ellipticism in various historical works, but contended that “the modern poet goes much farther in employing private experiences or ideas than would formerly have been thought legitimate.” To the common reader, he says, “the prime characteristic of this kind of poetry is not the nature of its imagery but its obscurity, its urgent suggestion that you add something to the poem without telling what that something is.” He names that something “the prose frame.” Robert Penn Warren used the term “elliptical” in his essay “Pure and Impure Poetry” (1943) to summarize T. S. Eliot’s notion that some poets “become impatient of this meaning [explicit statement of ideas in logical order] which seems superfluous, and perceive possibilities of intensity through its elimination.”
Stephen Burt redeployed the term elliptical poetry to characterize a kind of oblique, gnomic poetry. He calls elliptical poets “post-avant-gardist, or post‘postmodern.’” Emily Dickinson and Marina Tsvetaeva could be considered two great precursors to the elliptical mode, since they charged their sometimes secretive and oblique poems with maximum intensity and meaning.