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Greene, Lewallen and Vafaee characterized $(1,1)$ L-space knots in $S^3$ andlens space in the notation of coherent reduced $(1,1)$-diagrams. We analyzethese diagrams, and deduce an explicit description of these knots. With the newdescription, we prove that any L-space obtained by Dehn surgery on a$(1,1)$-knot in $S^3$ has non-left-orderable fundamental group.

An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries