Let $K=\mathbb{Q}(\sqrt{-2})$. How can I compute the K-rational points on the modular curve $X_0(35)$.

Recall that $X_0(35)$ is a hyperelliptic curve of genus 3 and has the simplified affine model; \begin{align*} y^2&=x^8-4x^7-6x^6-4x^5-9x^4+4x^3-6x^2+4x+1\\ &=(x^2+x-1)(x^6-5x^5-9x^3-5x-1) \end{align*} My attemp at finding K-rational points on $X_0(35)$ is as follows; First I find a rational map f from $X_0(35)$ to a quotient curve $E$ of $X_0(35)$ with $E$ an elliptic curve (which is induced by the involution $w_5$ by Kubert) Second, I determine the preimages of $E(K)$ under f. If $E$ is of rank 0, $E(K)$ is finite. However, in my case $E(K)$ is of rank 1 as a result it is computationally infeasible to determine the preimages of the infinitely many points of $E(K)$. Is there a way to work-around this issue?

Any help in finding K-rational points on $X_0(35)$ would be appreciated.

Let $K=\mathbb{Q}(\sqrt{-2})$. How can I compute the $K$-rational points on the modular curve $X_0(35)$?

Recall that $X_0(35)$ is a hyperelliptic curve of genus 3 and has the simplified affine model: \begin{align*} y^2&=x^8-4x^7-6x^6-4x^5-9x^4+4x^3-6x^2+4x+1\\ &=(x^2+x-1)(x^6-5x^5-9x^3-5x-1) \end{align*} My attempt at finding $K$-rational points on $X_0(35)$ is as follows: First I find a rational map $f$ from $X_0(35)$ to a quotient curve $E$ of $X_0(35)$ with $E$ an elliptic curve (which is induced by the involution $w_5$ by Kubert). Second, I determine the preimages of $E(K)$ under $f$. If $E$ is of rank 0, $E(K)$ is finite. However, in my case $E(K)$ is of rank 1. As a result it is computationally infeasible to determine the preimages of the infinitely many points of $E(K)$. Is there a way to work-around this issue?

Any help in finding $K$-rational points on $X_0(35)$ would be appreciated.