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In this article we introduce Hecke operators on the differential algebra ofgeometric quasi-modular forms. As an application for each natural number $d$ weconstruct a vector field in six dimensions which determines uniquely thepolynomial relations between the Eisenstein series of weight 2,4 and 6 andtheir transformation under multiplication of the argument by $d$, and inparticular, it determines uniquely the modular curve of degree $d$ isogeniesbetween elliptic curves.

Quasi-modular forms attached to elliptic curves: Hecke operators