Parity conjecture for modular degrees of non-Neumann–Setzer curves

Let $p$ be prime and let $E$ be an optimal elliptic curve quotient of $J_0(p)$. A Neumann–Setzer curve is the special curve family considered in the paper. The non-Neumann–Setzer modular-degree parity conjecture. If $p\not\equiv 3\pmod{8}$ and $E$ is not a Neumann–Setzer curve, then the modular degree of $E$ is even or $p=17$. The conjecture is based on computational data, and no proof or disproof is given in the paper.