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An Enneper type surface is a complete immersed minimal surface in R3 with only one end and finite total curvature. In this paper we construct a family of Enneper type surfaces of genus 1, total curvature -8(2n + \)n,n = 0,1,2, • ■ • . We use the Weierstrass p elliptic function as a tool and also prove some results about p on a square torus.doi:10.1090/s0002-9939-1990-1012931-6 fatcat:rru6jo54pzgsjl7lwrz26zrwea