Repelling periodic-point conjecture for invariant complex elliptic curves

Let $f$ be a rational map with an invariant complex elliptic curve. A periodic point is repelling when the derivative of the corresponding return map is expanding. Repelling-point conjecture. Every invariant complex elliptic curve contains a repelling periodic point. The source notes that all examples known to the authors have a repelling fixed point, but this stronger fixed-point assertion is not the conjecture stated.