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The supersingular K3 surface X in characteristic 2 with Artin invariant 1admits several genus 1 fibrations (elliptic and quasi-elliptic). We use abijection between fibrations and definite even lattices of rank 20 anddiscriminant 4 to classify the fibrations, and exhibit isomorphisms between theresulting models of X. We also study a configuration of (-2)-curves on Xrelated to the incidence graph of points and lines of IP^2(IF_4).

Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1