Landweber provided two proofs of the existence of (level 2) elliptic c
ohomology (Lecture Notes in Math., vol. 1326, Springer-Verlag, New Yor
k, 1988, pp. 69-93). As Baker pointed out (J. Pure Appl. Algebra 63 (1
990), 1-11), one of these proofs gives a level 1 elliptic cohomology t
heory as well. In this note we provide an alternative proof of the exi
stence of level 1 elliptic cohomology. The idea here is to use Landweb
er's direct proof of the existence of level 2 elliptic cohomology and
an integrality argument to deduce the existence of level 1 elliptic co
homology from that.