The method found by W. Castryck and T. Decru to break SIDH requires computing $(2^n,2^n)$-isogenies from a product of elliptic curves to another abelian surface (which is also a product), which are realized as degree 2 correspondences between curves. Transposing the attack to the other side of the SIDH exchange involves degree $(3,3)$-isogenies that can be evaluated using either theta functions, or divisors on genus 2 curves. Methods for the curve approach exist for the Jacobian case, but the case of a product of elliptic curves (Bröker, Howe, Lauter, Stevenhagen 2014) can be difficult to implement for cryptographically relevant field sizes due to various limitations in CAS such as SageMath/Singular. I will explain how traditional algebraic geometry can be called to the rescue to give a simple construction of the curve correspondence associated to the quotient of $E_1 \times E_2$ by an isotropic $(3,3)$-kernel. This leads to a rather fast computation method relying only on elementary field operations and 2 square roots. The journey will bring back some memories of 19th century projective geometry. Theta function experts might recognize familiar objects in the geometric construction.