Stevens's conjecture on the Manin constant for $X_1(N)$

Let $E$ be an elliptic curve over $\mathbb{Q}$, and let $\mathrm{c}_1(E)$ be the Manin constant obtained from a modular parametrisation by the modular curve $\mathrm{X}_1(N)$ associated to $\Gamma_1(N)$. Stevens's conjecture. One has

$$\mathrm{c}_1(E)=1.$$

The conjecture is the $\mathrm{X}_1(N)$ analogue of the conjecture that the $\Gamma_0(N)$-optimal Manin constant is one. Its resolution status is not specified in the source.